LRFDSI-4-E5...NORMAS FINAL

Pete Rahn, President Director, Missouri Department of Transportation

John Horsley, Executive Director

444 North Capitol Street NW, Suite 249, Washington, DC 20001 (202) 624-5800 Fax: (202) 624-5806 • www.transportation.org

LRFDSI-4-E5 11/15/2007

ERRATA

Dear Customer: A number of technical corrections and one significant editorial correction have come to light since both the print and the CD-ROM versions of AASHTO LRFD Bridge Design Specifications, 4th Edition were produced. Please note that these errata corrections supersede the previous SI Units errata (LRFDSI-4-E, LRFDSI-4-E2, LRFDSI-4-E3, and LRFDSI-4-E4). LRFDSI-4-E4 had just been uploaded but not distributed in print when new corrections came to light, necessitating production of LRFDSI-4-E5. The following replacement pages are attached:

Front Matter

pp. i/ii Photo credits Add credits “Cover photos courtesy of the Louisiana Department of Transportation and Development (top) and the Maryland Department of Transportation (bottom).”

Section 4: Structural Analysis and Evaluation

pp. 4-47/4-48 Article C4.6.2.5 Correct Table C4.6.2.5-1 design value of K for columns c and d to 1.0 and 1.2, respectively.

Section 5: Concrete Structures

pp. 5-25/5-26 Article 5.5.4.2.1 Correct Figure C5.5.4.2.1-1 so that labels display completely

Section 6: Steel Structures

pp. 6-27/6-28 and 6-29/6-30

Article 6.5.4.2 Display all phi factors.

pp. 6-147/6-148 Article 6.10.11.1.3 Correct Eq. 3 to read “

( )2

2.52.0 0.5

/o

Jd D

= − ≥ ”

pp. 6-289/6-290 Table D6.1-1 Correct condition equations for Condition VI and revise label under right-most figure section to read “Cases III–VII”

We apologize to Louisiana and Maryland for the photo credit omission and thank them again for providing us with great photos of their states’ bridges. The CD-ROM version of the book contains a number of technical corrections which were not received in time to appear in the printed version of the publication. These late corrections were included in the CD-ROM but not in the printed book. Therefore, the following replacement pages are also attached:

LRFDSI-4-E5 11/14/2007

Section 8: Wood Structures

pp. 8-3/8-4 Article 8.3 For Ag, delete “; net cross-sectional area of the component (in.2)(8.9)”

Article 8.3 For d, change “(8.4.4.3)” to “(8.4.4.4)” and change “(8.4.4.4)” to “(8.4.4.5)”

Article 8.3 For Pn, change “(8.8.8.9) to “(8.8)” and add “(8.9)”

Article 8.3 For Pr, change “(8.8.8.9) to “(8.8)” and add “(8.9)”

pp. 8-13–8-34 Article 8.4.1.2.3 Insert Tables 8.4.1.2.3-1 and 8.4.1.2.3-2

Article 8.4.1.3 In the title for Table 8.4.1.3-1, change “Base Resistance and Modulus of Elasticity” to “Reference Design Values”

Article 8.4.4.4 Relocate Tables 8.4.4.4-1 and Table 8.4.4.4-2 to the end of Article 8.4.4.4

Article 8.4.4.4 Delete Table 8.4.4.4-1, Deck Factors, Cp, for Mechanically Laminated Solid Sawn Lumber Decks

Article 8.5.2.4.3 Change article header “8.5.2.4.3 Stability” to “8.5.2.3 Stability”

Section 11: Abutments, Piers, and Walls

pp. 11-3/11-4 Article 11.3.1 For PH, change “(11.10.11.1)” to “(11.10.10.1)”

Article 11.3.1 For Pv, change “(11.10.11.1)” to “(11.10.10.1)”

Article 11.3.1 For P′v, change “(11.10.11.1)” to “(11.10.10.1)”

Article 11.3.1 For ΔsH, change “(11.10.11.2)” to “(11.10.10.2)”

pp. 11-9/11-10 Article 11.5.6 In paragraphs 1 and 2, change “Tables 10.5.5-1 through 10.5.5-3” to “Tables 10.5.5.2.2-1, 10.5.5.2.3-1, 10.5.5.2.4-1,”

pp. 11-13/11-14 Article 11.6.2.1 Change “Articles 10.6.2.2.3, 10.7.2.3, 10.2.2.3,” to “Articles 10.6.2.4, 106.2.5, 10.7.2.3 through 10.7.2.5, 10.8.2.2 through 10.8.2.4,”

pp. 11-15/11-16 Article 11.6.3.1 Change “Article 10.6.2.2.4” to “Article 10.6.2.5”

pp. 11-19/11-20 Article 11.6.4 Change “Article 10.6.3.1.5” to “Article 10.6.1.3”

pp. 11-31/11-32 Article 11.9.4.3 Change “Articles 11.6.3.6, 11.6.3.7,” to “Articles 11.6.3.5, 11.6.3.6,”

pp. 11-79/11-80 Article C11.10.11 In paragraph 2, change “Article C10.6.2.2” to “Article C10.5.2.2”

Section 12: Buried Structures and Tunnel Liners

pp. 12-1/12-2 Article 12.3 For Bd, change “Article 12.10.2.1.2” to “Article 12.11.2.2”

Article 12.3 For Cd, change “Article 12.10.2.1.2” to “Article 12.11.2.2”

pp. 12-5/12-6 Article 12.3 For γs, change “Article 12.9.2.2” to “Article C12.9.2”

Article 12.3 For μ′, change “μ′ ” to “μ” [no prime] and “(12.10.2.1.2)” to “(12.10.2.1)”

pp. 12-79/12-80 Article 12.13.3.3 Change “Article 12.3.2.2” to “Article 12.13.2.2”

pp. 12-83/12-84 Article 12.14.5.8 Change “Article 5.10.8.2” to “Article 5.10.8”

Section 14: Joints and Bearings

pp. 14-27/14-28 Article 14.5.6.9.7a In paragraph 1, change “Article 6.10.7.4.2” to “Article 6.10.10.2”

pp. 14-41/14-42 Article 14.7.1.2 Change “Table 6.4.1-2” to “Table 6.4.2-1” We apologize for any inconvenience these discrepancies may cause the user. Please note that these errata corrections supersede the previous SI Units errata (LRFDSI-4-E, LRFDSI-4-E2, LRFDSI-4-E3, and LRFDSI-4-E4). LRFDSI-4-E4 had just been uploaded but not distributed in print when new corrections came to light, necessitating production of LRFDSI-4-E5.

AASHTO Publications Staff November 2007

Amer i can As soc i a t i on o f S t a t e H ighway and Transpo r ta t i on O f f i c i a l s

AASHTO LRFD Bridge Design Specifications

SI Units4th Edition

2007

AASHTO LRFD Bridge Design Specifications

SI Units4th Edition

2007

ISBN: 1-56051-355-1 Publication Code: LRFDSI-4

American Association of State Highway and Transportation Officials

444 North Capitol Street, NW Suite 249 Washington, DC 20001

202-624-5800 phone/202-624-5806 fax www.transportation.org

© 2007 by the American Association of State Highway and Transportation Officials. All rights reserved. Duplication is a violation of applicable law. Cover photos courtesy of the Louisiana Department of Transportation and Development (top) and the Maryland Department of Transportation (bottom).

SECTION 4 (SI): STRUCTURAL ANALYSIS AND EVALUATION 4-47

250 0.42 1 1E LW= + (4.6.2.3-1) The equivalent width of longitudinal strips per lane

for both shear and moment with more than one laneloaded may be determined as:

2100 0.12 1 1L

WE L WN

= + ≤ (4.6.2.3-2)

where: E = equivalent width (mm) L1 = modified span length taken equal to the lesser

of the actual span or 18 000 (mm) W1 = modified edge-to-edge width of bridge taken to

be equal to the lesser of the actual width or18 000 for multilane loading, or 9000 for single-lane loading (mm)

W = physical edge-to-edge width of bridge (mm) NL = number of design lanes as specified in

Article 3.6.1.1.1 For skewed bridges, the longitudinal force effects

may be reduced by the factor r: 1.05 0.25tan 1.00r = − θ ≤ (4.6.2.3-3)

where: θ = skew angle (°)

In Eq. 1, the strip width has been divided by 1.20 to account for the multiple presence effect.

Table 4.6.2.3-1 Typical Schematic Cross-Section.

Supporting Components Type of Deck Typical Cross-Section Cast-in-Place Concrete Slab or Voided Slab

Monolithic

Stressed Wood Deck Integral Wood

Glued/Spiked Wood Panels with Spreader Beam

Integral Wood

© 2007 by the American Association of State Highway and Transportation Officials.All rights reserved. Duplication is a violation of applicable law.

4-48 AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS (SI)

4.6.2.4 Truss and Arch Bridges

The lever rule may be used for the distribution ofgravity loads in trusses and arches when analyzed asplanar structures. If a space analysis is used, either thelever rule or direct loading through the deck or decksystem may be used.

Where loads, other than the self-weight of themembers and wind loads thereon, are transmitted to thetruss at the panel points, the truss may be analyzed as apin-connected assembly.

4.6.2.5 Effective Length Factor, K

Physical column lengths shall be multiplied by an

effective length factor, K, to compensate for rotationaland translational boundary conditions other than pinnedends.

In the absence of a more refined analysis, wherelateral stability is provided by diagonal bracing or othersuitable means, the effective length factor in the bracedplane, K, for the compression members in triangulatedtrusses, trusses, and frames may be taken as:

• For bolted or welded end connections at both

ends: K = 0.750

• For pinned connections at both ends: K = 0.875

• For single angles, regardless of end connection:K = 1.0

Vierendeel trusses shall be treated as unbracedframes.

C4.6.2.5

Equations for the compressive resistance of columns and moment magnification factors for beam-columns include a factor, K, which is used to modify the length according to the restraint at the ends of the column against rotation and translation.

K is the ratio of the effective length of an idealized pin-end column to the actual length of a column with various other end conditions. KL represents the length between inflection points of a buckled column influenced by the restraint against rotation and translation of column ends. Theoretical values of K, as provided by the Structural Stability Research Council, are given in Table C1 for some idealized column end conditions. Table C4.6.2.5-1 Effective Length Factors, K.

Buckled shape of column is shown by dashed line

(a)

(b)

(c)

(d)

(e)

(f)

Theoretical K value 0.5 0.7 1.0 1.0 2.0 2.0

Design value of K when ideal conditions are approximated

0.65 0.80 1.0 1.2 2.1 2.0

Rotation fixed Translation fixed Rotation free Translation fixed Rotation fixed Translation free

End condition code

Rotation free Translation free

Because actual column end conditions seldom comply fully with idealized restraint conditions against rotation and translation, the design values suggested by the Structural Stability Research Council are higher than the idealized values.

Lateral stability of columns in continuous frames, unbraced by attachment to shear walls, diagonal bracing, or adjacent structures, depends on the flexural stiffness of the rigidly connected beams. Therefore, the effectivelength factor, K, is a function of the total flexural restraint provided by the beams at the ends of the column. If the stiffness of the beams is small in relation to that of the column, the value of K could exceed 2.0.


SECTION 5 (SI): CONCRETE STRUCTURES 5-25

5.5.4 Strength Limit State 5.5.4.1 General The strength limit state issues to be considered shall

be those of strength and stability.

C5.5.4.1

Factored resistance shall be the product of nominalresistance as determined in accordance with theapplicable provisions of Articles 5.6, 5.7, 5.8, 5.9, 5.10,5.13, and 5.14, unless another limit state is specifically identified, and the resistance factor is as specified inArticle 5.5.4.2.

Additional resistance factors are specified in Article 12.5.5 for buried pipes and box structures made of concrete.

5.5.4.2 Resistance Factors 5.5.4.2.1 Conventional Construction Resistance factor φ shall be taken as: • For tension-controlled reinforced concrete

sections as defined in Article 5.7.2.1 .......... 0.90• For tension-controlled prestressed concrete

sections as defined in Article 5.7.2.1 .......... 1.00• For shear and torsion: normal weight concrete ....................... 0.90 lightweight concrete ............................ 0.70• For compression-controlled sections with

spirals or ties, as defined in Article 5.7.2.1,except as specified in Article 5.10.11.4.1bfor Seismic Zones 3 and 4 at the extremeevent limit state ................................... 0.75

• For bearing on concrete .............................. 0.70• For compression in strut-and-tie models 0.70

C5.5.4.2.1 In applying the resistance factors for tension-

controlled and compression-controlled sections, the axial tensions and compressions to be considered are those caused by external forces. Effects of prestressing forces are not included.

In editions of and interims to the LRFD Specifications prior to 2005, the provisions specified the magnitude of the resistance factor for cases of axial load or flexure, or both, it terms of the type of loading. For these cases, the φ-factor is now determined by the strain conditions at a cross-section, at nominal strength. The background and basis for these provisions are given in Mast (1992) and ACI 318-02.

A lower φ-factor is used for compression-controlled sections than is used for tension-controlled sections because compression-controlled sections have less ductility, are more sensitive to variations in concrete strength, and generally occur in members that support larger loaded areas than members with tension-controlled sections.

For sections subjected to axial load with flexure, factored resistances are determined by multiplying both Pn and Mn by the appropriate single value of φ. Compression-controlled and tension-controlled sections are defined in Article 5.7.2.1 as those that have net tensile strain in the extreme tension steel at nominal strength less than or equal to the compression-controlled strain limit, and equal to or greater than 0.005, respectively. For sections with net tensile strain εt in the extreme tension steel at nominal strength between the above limits, the value of φ may be determined by linear interpolation, as shown in Figure C1. The concept of net tensile strain εt is discussed in Article C5.7.2.1. Classifying sections as tension-controlled, transition or compression-controlled, and linearly varying the resistance factor in the transition zone between reasonable values for the two extremes, provides a rational approach for determining φ and limiting the capacity of over-reinforced sections.



0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

0.001 0.002 0.003 0.004 0.005 0.006 0.007

ε t

φ

Compression

Controlled Controlled

TensionTransition

Prestressed

Non-prestressed

⎟⎟⎠

⎞⎜⎜⎝

⎛−+= 115.065.0

cd tφ

⎟⎟⎠

⎞⎜⎜⎝

⎛ −+= 125.0583.0c

d tφ

Figure C5.5.4.2.1-1 Variation of φ with net tensile strain εt and dt/c for Grade 420 reinforcement and for prestressing steel.

• For compression in anchorage zones: normal weight concrete........................ 0.80 lightweight concrete............................. 0.65• For tension in steel in anchorage zones....... 1.00• For resistance during pile driving 1.00 For sections in which the net tensile strain in the

extreme tension steel at nominal resistance is betweenthe limits for compression-controlled and tension-controlled sections, φ may be linearly increased from0.75 to that for tension-controlled sections as the nettensile strain in the extreme tension steel increases fromthe compression-controlled strain limit to 0.005.

This variation in,φ, may be computed forprestressed members such that:

0.75 0.583 0.25 1 1.0⎛ ⎞≤ = + − ≤⎜ ⎟⎝ ⎠

tdc

φ (5.5.4.2.1-1)

and for nonprestressed members such that:

0.75 0.65 0.15 1 0.9⎛ ⎞≤ = + − ≤⎜ ⎟⎝ ⎠

tdc

φ (5.5.4.2.1-2)

where: c = distance from the extreme compression fiber to

the neutral axis (mm) dt = distance from the extreme compression fiber to

the centroid of the extreme tension steelelement (mm)

The φ-factor of 0.8 for normal density concrete reflects the importance of the anchorage zone, the brittle failure mode for compression struts in the anchorage zone, and the relatively wide scatter of results of experimental anchorage zone studies. The φ-factor of 0.65 for low-density concrete reflects its often lower tensile strength and is based on the multipliers used in ACI 318-89, Section 11.2.1.2.

The design of intermediate anchorages, anchorages, diaphragms, and multiple slab anchorages are addressed in Breen et al. (1994).


SECTION 6 (SI): STEEL STRUCTURES 6-27

6.4.8.2 Galvanized Wire

Galvanized wire shall conform to ASTM A 641M—Standard Specification for Zinc-Coated (Galvanized)Carbon Steel Wire.

6.4.8.3 Epoxy-Coated Wire

Epoxy-coated wire shall conform to ASTM A 99—

Standard Specification for Steel Wire Epoxy-Coated.

6.4.8.4 Bridge Strand Bridge strand shall conform to ASTM A 586—

Standard Specification for Zinc-Coated Parallel andHelical Steel Wire Structural Strand, or ASTM A 603—Standard Specification for Zinc-Coated Steel StructuralWire Rope.

6.5 LIMIT STATES

6.5.1 General

The structural behavior of components made of steel

or steel in combination with other materials shall beinvestigated for each stage that may be critical duringconstruction, handling, transportation, and erection as wellas during the service life of the structure of which they arepart.

Structural components shall be proportioned to satisfythe requirements at strength, extreme event, service, andfatigue limit states.

6.5.2 Service Limit State

The provisions of Article 2.5.2.6 shall apply as

applicable. Flexural members shall be investigated at the service

limit state as specified in Articles 6.10 and 6.11.

C6.5.2 The intent of the service limit state provisions

specified for flexural members in Articles 6.10 and 6.11 is primarily to prevent objectionable permanent deformations due to localized yielding that would impair rideability under expected severe traffic loadings.

6.5.3 Fatigue and Fracture Limit State

Components and details shall be investigated for

fatigue as specified in Article 6.6. The fatigue load combination specified in

Table 3.4.1-1 and the fatigue live load specified inArticle 3.6.1.4 shall apply.

Flexural members shall be investigated at the fatigueand fracture limit state as specified in Articles 6.10and 6.11.

Bolts subject to tensile fatigue shall satisfy theprovisions of Article 6.13.2.10.3.

Fracture toughness requirements shall be inconformance with Article 6.6.2.



6.5.4 Strength Limit State 6.5.4.1 General Strength and stability shall be considered using the

applicable strength load combinations specified inTable 3.4.1-1.

6.5.4.2 Resistance Factors Resistance factors, φ, for the strength limit state shall

be taken as follows:

C6.5.4.2 Base metal φ as appropriate for resistance under

consideration.

• For flexure φf = 1.00• For shear φv = 1.00• For axial compression, steel only φc = 0.90• For axial compression, composite φc = 0.90• For tension, fracture in net section φu = 0.80• For tension, yielding in gross section φy = 0.95• For bearing on pins in reamed, drilled or bored holes and on milled surfaces φb = 1.00• For bolts bearing on material φbb = 0.80• For shear connectors φsc = 0.85• For A 325M and A 490M bolts in

tension φt = 0.80• For A 307 bolts in tension φt = 0.80• For A 307 bolts in shear φs = 0.65• For A 325M and A 490M bolts in shear φs = 0.80• For block shear φbs = 0.80• For web crippling φw = 0.80• For weld metal in complete penetration welds:

o shear on effective area φe1 = 0.85o tension or compression normal to

effective area same as base metalo tension or compression parallel

to axis of the weld same as base metal• For weld metal in partial penetration welds:

o shear parallel to axis of weld φe2 = 0.80o tension or compression parallel

to axis of weld same as base metalo compression normal to the

effective area same as base metalo tension normal to the effective

area φe1 = 0.80• For weld metal in fillet welds:

o tension or compression parallel to axis of the weld same as base metal

o shear in throat of weld metal • For resistance during pile driving φ = 1.00

• For axial resistance of piles in compression andsubject to damage due to severe drivingconditions where use of a pile tip is necessary: o H-piles φc = 0.50o pipe piles φc = 0.60

The basis for the resistance factors for driven steel piles is described in Article 6.15.2. Further limitations on usable resistance during driving are specified in Article 10.7.8.


SECTION 6 (SI): STEEL STRUCTURES 6-29

• For axial resistance of piles in compression undergood driving conditions where use of a pile tip isnot necessary: o H-piles φc = 0.60o pipe piles φc = 0.70

• For combined axial and flexural resistance ofundamaged piles: o axial resistance for H-piles φc = 0.70o axial resistance for pipe piles φc = 0.80o flexural resistance φf = 1.00

Indicated values of φc and φf for combined axial and flexural resistance are for use in interaction equations in Article 6.9.2.2.

6.5.5 Extreme Event Limit State

All applicable extreme event load combinations in

Table 3.4.1-1 shall be investigated. All resistance factors for the extreme event limit state,

except for bolts, shall be taken as 1.0. Bolted joints not protected by capacity design or

structural fuses may be assumed to behave as bearing-type connections at the extreme event limit state, and the values of resistance factors for bolts given in Article 6.5.4.2 shallapply.

6.6 FATIGUE AND FRACTURE CONSIDERATIONS

6.6.1 Fatigue

6.6.1.1 General Fatigue shall be categorized as load- or distortion-

induced fatigue.

C6.6.1.1 In the AASHTO Standard Specifications for Highway

Bridges (2002), the provisions explicitly relating to fatigue deal only with load-induced fatigue.

6.6.1.2 Load-Induced Fatigue 6.6.1.2.1 Application The force effect considered for the fatigue design of a

steel bridge detail shall be the live load stress range. For flexural members with shear connectors providedthroughout their entire length, and with concrete deck reinforcement satisfying the provisions of Article 6.10.1.7, live load stresses and stress ranges for fatigue design may be computed using the short-term composite section assuming the concrete deck to be effective for bothpositive and negative flexure.

C6.6.1.2.1



Residual stresses shall not be considered ininvestigating fatigue.

Concrete can provide significant resistance to tensile stress at service load levels. Recognizing this behavior will have a significantly beneficial effect on the computation of fatigue stress ranges in top flanges in regions of stress reversal and in regions of negative flexure. By utilizing shear connectors in these regions to ensure composite action in combination with the required one percent longitudinal reinforcement wherever the longitudinal tensile stress in the concrete deck exceeds the factored modulus of rupture of the concrete, crack length and width can be controlled so that full-depth cracks should not occur. When a crack does occur, the stress in the longitudinal reinforcement increases until the crack is arrested. Ultimately, the cracked concrete and the reinforcement reach equilibrium. Thus, the concrete deck may contain a small number of staggered cracks at any given section. Properly placed longitudinal reinforcement prevents coalescence of these cracks.

It has been shown that the level of total applied stress is insignificant for a welded steel detail. Residual stresses due to welding are implicitly included through the specification of stress range as the sole dominant stress parameter for fatigue design. This same concept of considering only stress range has been applied to rolled, bolted, and riveted details where far different residual stress fields exist. The application to nonwelded details is conservative.

These provisions shall be applied only to detailssubjected to a net applied tensile stress. In regions wherethe unfactored permanent loads produce compression,fatigue shall be considered only if the compressive stress isless than twice the maximum tensile live load stressresulting from the fatigue load combination specified inTable 3.4.1-1.

The live load stress due to the passage of the fatigue load is approximately one-half that of the heaviest truck expected to cross the bridge in 75 years.

Cross-frames and diaphragms connecting adjacent girders are stressed when one girder deflects with respect to the adjacent girder connected by the diaphragm or cross-frame. The sense of stress is reversed when the vehicle is placed over the adjacent girder. These two transverse positions of the vehicle usually create the largest stress range in these bracing members. To simulate such a stress cycle, two vehicles traverse the bridge in adjacent lanes, one vehicle leading the other. For cases where the force effects in these members are available from an analysis, it may be desirable in some instances to check fatigue-sensitive details on a bracing member subjected to a net applied tensile stress determined as specified herein. For such cases, it is recommended that one cycle of stress be taken as 75 percent of the stress range in the member determined by the passage of the factored fatigue load in two different transverse positions. The factor of 0.75 is distinct from the load factor of 0.75 specified for the fatigue load combination in Table 3.4.1-1, i.e., both apply. It accounts in an approximate fashion for the probability of two vehicles being located in the critical relative position. However, in no case should the calculated range of stress be less than the stress range due to a single passage of the factored fatigue load. If the maximum stress in a bracing member is caused by a single axle, the number of cycles of stress range should be taken equal to two times the number of truck passages. There is no allowance in this recommended procedure for the fact that two trucks are required to cause the critical stress range.


SECTION 6 (SI): STEEL STRUCTURES

6-147

6.10.11.1.3 Moment of Inertia For transverse stiffeners adjacent to web panels in

which neither panel supports shear forces larger than theshear buckling resistance, the moment of inertia of thetransverse stiffener shall satisfy the smaller of thefollowing limits:

3

t wI bt J≥ (6.10.11.1.3-1)

1 54 1 3

40

..ywt

tFD

IE

⎛ ⎞ρ≥ ⎜ ⎟

⎝ ⎠ (6.10.11.1.3-2)

where: It = moment of inertia of the transverse stiffener taken

about the edge in contact with the web for singlestiffeners and about the mid-thickness of the webfor stiffener pairs (mm4)

b = the smaller of do and D (mm) do = the smaller of the adjacent web panel widths

(mm) J = stiffener bending rigidity parameter

( )2

2.52.0 0.5

/o

Jd D

= − ≥ (6.10.11.1.3-3)

ρt = the larger of Fyw/Fcrs and 1.0 Fcrs = local buckling stress for the stiffener (MPa)

20 31

ys

t

p

. E Fbt

= ≤⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠

(6.10.11.1.3-4)

Fys = specified minimum yield strength of the stiffener

(MPa) For transverse stiffeners adjacent to web panels in

which the shear force is larger than the shear bucklingresistance and thus the web postbuckling or tension-field resistance is required in one or both panels, the moment ofinertia of the transverse stiffeners shall satisfy Eq. 2.

Transverse stiffeners used in web panels withlongitudinal stiffeners shall also satisfy:

3.0t

to

b DI Ib d

⎛ ⎞⎛ ⎞≥ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

(6.10.11.1.3-5)

C6.10.11.1.3 For the web to adequately develop the shear-buckling

resistance or the combined shear-buckling and postbuckling tension-field resistance, the transverse stiffener must have sufficient rigidity to maintain a vertical line of near zero lateral deflection along the line of the stiffener. For ratios of (do /D) less than 1.0, much larger values of It are required to develop the shear-buckling resistance, as discussed in Bleich (1952) and represented by Eq. 1. For single stiffeners, a significant portion of the web is implicitly assumed to contribute to the bending rigidity such that the neutral axis of the stiffener is located close to the edge in contact with the web. Therefore, for simplicity, the neutral axis is assumed to be located at this edge and the contribution of the web to the moment of inertia about this axis is neglected. The term b in Eq. 1 replaces do in prior Specifications. This term and Eq. 3 give a constant value for the It required to develop the shear-buckling resistance for web panels with do > D (Kim et al., 2004).

Eq. 1 requires excessively large stiffener sizes as D/tw

is reduced below 1 12 yw. Ek / F , the web slenderness required for C = 1, since Eq. 1 is based on developing the web elastic shear-buckling resistance. Inelastic buckling solutions using procedures from Bleich (1952) show that larger stiffeners are not required as D/tw is reduced below this limit. These results are corroborated by refined FEA solutions (Kim et al., 2004). k is the shear-buckling coefficient defined in Article 6.10.9.

To develop the web shear postbuckling resistance associated with tension-field action, the transverse stiffeners generally must have a larger It than defined by Eq. 1. The It defined by Eq. 2, which for ρt = 1 is approximately equal to the value required by Eq. 1 for a web with D/tw =1 12 yw. Ek / F , provides an accurate to slightly conservative stiffener size relative to refined FEA solutions for straight and curved I-girders at all values of D/tw permitted by these Specifications (Kim et al., 2004). Eq. 2 is an approximate upper bound to the results for all values of do/D from an equation recommended by Kim et al. (2004), recognizing that the stiffener demands are insensitive to this parameter.

Multiple research studies have shown that transverse stiffeners in I-girders designed for tension-field action are loaded predominantly in bending due to the restraint they provide to lateral deflection of the web. Generally, there is evidence of some axial compression in the transverse stiffeners due to the tension field, but even in the most slender web plates permitted by these Specifications, the effect of the axial compression transmitted from the postbuckled web plate is typically minor compared to the lateral loading effect. Therefore, the transverse stiffener area requirement from prior Specifications is no longer specified.


AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS (SI)

6-148

bt = projecting width of the transverse stiffener (mm) bℓ = projecting width of the longitudinal stiffener

(mm) Iℓ = moment of inertia of the longitudinal stiffener

determined as specified in Article 6.10.11.3.3(mm4)

requires slightly larger stiffeners than in previous Specifications for small D/tw slightly exceeding1 12 yw. Ek / F , where the It requirement comparable to Eq. 1 governs relative to the area requirement for single-sided stiffeners given in previous Specifications. For larger D/tw values, Eq. 2 typically gives comparable or smaller single-sided stiffeners compared to the area requirement in previous Specifications at Vu = φvVn. For girders with stiffener pairs, the previous Specifications substantially underestimated the required stiffener size for increasing D/tw > 1 12 yw. Ek / F . Eq. 2 recognizes the fact that single- and double-sided transverse stiffeners with the same It exhibit essentially identical performance (Horne and Grayson, 1983; Rahal and Harding, 1990; Stanway et al., 1996; Lee et al., 2003; Kim et al., 2004).

The term ρt in Eq. 2 accounts conservatively for the effect of early yielding in transverse stiffeners with Fys < Fyw and for the effect of potential local buckling of stiffeners having a relatively large width-to-thickness ratio bt/tp. The definition of the stiffener local buckling stress Fcrs is retained from AASHTO (2004).

Lateral loads along the length of a longitudinal stiffener are transferred to the adjacent transverse stiffeners as concentrated reactions (Cooper, 1967). Eq. 5 gives a relationship between the moments of inertia of the longitudinal and transverse stiffeners to ensure that the latter does not fail under the concentrated reactions. This equation applies whether the stiffeners are on the same or opposite side of the web.

6.10.11.2 Bearing Stiffeners 6.10.11.2.1 General

Bearing stiffeners shall be placed on the webs of built-

up sections at all bearing locations. At bearing locations onrolled shapes and at other locations on built-up sections orrolled shapes subjected to concentrated loads, where theloads are not transmitted through a deck or deck system,either bearing stiffeners shall be provided or the web shallsatisfy the provisions of Article D6.5.

Bearing stiffeners shall consist of one or more platesor angles welded or bolted to both sides of the web. Theconnections to the web shall be designed to transmit thefull bearing force due to the factored loads.

The stiffeners shall extend the full depth of the weband as closely as practical to the outer edges of the flanges.

Each stiffener shall be either milled to bear against theflange through which it receives its load or attached to thatflange by a full penetration groove weld.

C6.10.11.2.1

Webs of built-up sections and rolled shapes without bearing stiffeners at the indicated locations must be investigated for the limit states of web local yielding and web crippling according to the procedures specified in Article D6.5. The section should either be modified to comply with these requirements or else bearing stiffeners designed according to these Specifications should be placed on the web at the location under consideration.

In particular, inadequate provisions to resist temporary concentrated loads during construction that are not transmitted through a deck or deck system can result in failures. The Engineer should be especially cognizant of this issue when girders are incrementally launched over supports.


SECTION 6 (SI): STEEL STRUCTURES

6-289

APPENDIX D6 FUNDAMENTAL CALCULATIONS FOR FLEXURAL MEMBERS

D6.1 PLASTIC MOMENT The plastic moment, Mp, shall be calculated as the

moment of the plastic forces about the plastic neutral axis. Plastic forces in steel portions of a cross-section shall be calculated using the yield strengths of the flanges, the web,and reinforcing steel, as appropriate. Plastic forces inconcrete portions of the cross-section that are incompression may be based on a rectangular stress blockwith the magnitude of the compressive stress equal to0.85f ′c. Concrete in tension shall be neglected.

The position of the plastic neutral axis shall bedetermined by the equilibrium condition that there is nonet axial force.

The plastic moment of a composite section in positiveflexure can be determined by:

• Calculating the element forces and using them to

determine whether the plastic neutral axis is inthe web, top flange or concrete deck;

• Calculating the location of the plastic neutral axiswithin the element determined in the first step;and

• Calculating Mp. Equations for the various potential locations of the plastic neutral axis (PNA) are given in Table 1.

The forces in the longitudinal reinforcement may beconservatively neglected. To do this, set Prb and Prt equal to zero in the equations in Table 1.

The plastic moment of a composite section in negativeflexure can be calculated by an analogous procedure. Equations for the two cases most likely to occur in practiceare given in Table 2.

The plastic moment of a noncomposite section may becalculated by eliminating the terms pertaining to theconcrete deck and longitudinal reinforcement from theequations in Tables 1 and 2 for composite sections.

In the equations for Mp given in Tables 1 and 2, d is the distance from an element force to the plastic neutralaxis. Element forces act at (a) mid-thickness for theflanges and the concrete deck, (b) mid-depth of the web,and (c) center of reinforcement. All element forces,dimensions, and distances should be taken as positive. The condition should be checked in the order listed in Tables 1 and 2.


AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS (SI)

6-290

Table D6.1-1 Calculation of Y and Mp for Sections in Positive Flexure.

CASE PNA CONDITION Y AND Mp I In Web t w c s rb rt + + + + P P P P P P≥

12

t c s rt rb

w

P P P P PDY P

⎡ ⎤− − − −⎛ ⎞= +⎢ ⎥⎜ ⎟⎝ ⎠ ⎣ ⎦

( )22[ ]

2w

p s s rt rt rb rb c c t tPM Y P d P d P d P d PdD YD⎡ ⎤= + + + + + +−⎢ ⎥⎣ ⎦

II In Top Flange

t w c s rb rt + + + + P P P P P P≥ 1

2c w t s rt rb

c

t P P P P PY P

⎡ ⎤+ − − −⎛ ⎞= +⎢ ⎥⎜ ⎟⎝ ⎠ ⎣ ⎦

( )22[ ]

2c

P s s rt rt rb rb w w t tcc

PM Y P d P d P d P d Pdt Yt⎡ ⎤= + + + + + +−⎢ ⎥⎣ ⎦

III Concrete Deck, Below Prb

rbt w c s rb rt

s

c + + + + P P P P P Pt

⎛ ⎞≥ ⎜ ⎟⎝ ⎠

( ) c w t rt rbs

s

P P P P PY t P

⎡ ⎤+ + − −= ⎢ ⎥

⎣ ⎦

2

[ ]2

sp rt rt rb rb c c w w t t

s

Y PM P d P d P d P d Pd t

⎛ ⎞⎜ ⎟= + + + + +⎜ ⎟⎝ ⎠

IV Concrete Deck, at Prb

rbt w c rb s rt

s

c + + +P P P P P Pt

⎛ ⎞+ ≥ ⎜ ⎟

⎝ ⎠ rbY c=

2

[ ]2

sp rt rt c c w w t t

s

Y PM P d P d P d Pdt

⎛ ⎞⎜ ⎟= + + + +⎜ ⎟⎝ ⎠

V Concrete Deck, Above Prb Below Prt

rtt w c rb s rt

s

c+ + + +P P P P P Pt

⎛ ⎞≥ ⎜ ⎟⎝ ⎠

( ) rb c w t rts

s

P P P P PY t P

+ + + −⎡ ⎤= ⎢ ⎥

⎣ ⎦

2

[ ]2


s

Y PM P d P d P d P d Pdt

⎛ ⎞⎜ ⎟= + + + + +⎜ ⎟⎝ ⎠

VI Concrete Deck, at Prt + rt

t w c rb rt ss

cP P P P P P

t⎛ ⎞

+ + + ≥⎜ ⎟⎝ ⎠

rtY c= 2

[ ]2

sp rb rb c c w w t t

s

Y PM P d P d P d Pdt

⎛ ⎞⎜ ⎟= + + + +⎜ ⎟⎝ ⎠

VII Concrete Deck, Above Prt

< rtt w c rb rt s

s

cP P P P P P

t⎛ ⎞

+ + + + ⎜ ⎟⎝ ⎠

( ) rb c w t rts

s

P P P P PY tP

+ + + +⎡ ⎤= ⎢ ⎥

⎣ ⎦

2

[ ]2


s

Y PM P d P d P d P d Pdt

⎛ ⎞⎜ ⎟= + + + + +⎜ ⎟⎝ ⎠

Crt

CASES III–VII


SECTION 8: WOOD STRUCTURES 8-3 Sawn Lumber—The product of a sawmill not further manufactured other than by sawing, resawing, passing lengthwise through a standard planing mill, drying, and cross-cutting to length. Sawn Timbers—Lumber that is nominally 5.0 in. or more in least dimension. Softwood—Generally, one of the conifers or the wood produced by such trees. The term has no reference to the actual hardness of the wood. SPIB—Grading rules by Southern Pine Inspection Bureau. Stress Grades—Lumber grades having assigned working stress and modulus of elasticity in accordance with accepted principles of resistance grading. Structural Glued Laminated Timber (glulam)—An engineered, stress-rated product of a timber laminating plant comprised of assemblies of specially selected and prepared wood laminations securely bonded together with adhesives. The grain of all laminations is approximately parallel longitudinally. Glued laminated timber is permitted to be comprised of pieces end joined to form any length, of pieces placed or bonded edge to edge to make any width, or of pieces bent to curbed form during bonding. Structural Lumber—Lumber that has been graded and assigned design values based on standardized procedures to ensure acceptable reliability. Vertically Laminated Timber—Laminated wood in which the laminations are arranged with their wider dimension approximately parallel to the direction of load. Visually Graded Lumber—Structural lumber graded solely by visual examination. Waterborne Preservative—A preservative that is introduced into wood in the form of a water-based solution. WCLIB—Grading rules by West Coast Lumber Inspection Bureau. Wet-Use—Use conditions where the moisture content of the wood in service exceeds 16 percent for glulam and 19 percent for sawn lumber. WWPA—Grading rules by Western Wood Products Association. 8.3 NOTATION A = parameter for beam stability (8.6.2) Ab = bearing area (in.2) (8.8.3) Ag = gross cross-sectional area of the component (in.2) (8.8.2) An = net cross-sectional area of the component (in.2) (8.9) a = coefficient (8.4.4.5) B = parameter for compression (8.8.2) b = width of the glued laminated timber component; thickness of lumber component (see Figure 1) (in.) (8.4.4.5) Cb = bearing factor (8.8.3) Cc = curvature factor (8.4.1.2) Cd = deck factor (8.4.4.8) CF = size factor (8.4.4.4) Cfu = flat use factor (8.4.4.6) Ci = incising factor (8.4.4.7) CKF = format conversion factor (8.4.4.2) CL = beam stability factor (8.6.2) CM = wet service factor (8.4.4.3) CP = column stability factor (8.8.2) CV = volume factor (8.4.4.5) Cλ = time effect factor (8.4.4.9)


8-4 AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS d = depth of the beams or stringers or width of the dimension lumber component (8.4.4.4) or glulam depth

(8.4.4.5) as shown in Figure 1 (in.) E = adjusted modulus of elasticity (ksi) (8.4.4.1) Eo = reference modulus of elasticity (ksi) (8.4.1.1.4) F = adjusted design value (ksi) (8.4.4.1) Fb = adjusted design value in flexure (ksi) (8.4.4.1) Fbo = reference design value of wood in flexure (ksi) (8.4.1.1.4) Fc = adjusted design value of wood in compression parallel to grain (ksi) (8.4.4.1) Fco = reference design value of wood in compression parallel to grain (ksi) (8.4.1.1.4) Fcp = adjusted design value of wood in compression perpendicular to grain (ksi) (8.4.4.1) Fcpo = reference design value of wood in compression perpendicular to grain (ksi) (8.4.1.1.4) Fo = reference design value (ksi) (8.4.4.1) Ft = adjusted design value of wood in tension (ksi) (8.4.4.1) Fto = reference design value of wood in tension (ksi) (8.4.1.1.4) Fv = adjusted design value of wood in shear (ksi) (8.4.4.1) Fvo = reference design value of wood in shear (ksi) (8.4.1.1.4) G = specific gravity (8.4.1.1.4) K = effective buckling length factor (8.8.2) L = length (ft.) (8.4.4.5) Le = effective length (in.) (8.6.2) Lu = laterally unsupported length of the component (in.) (8.6.2) Mn = nominal flexural resistance (kip-in.) (8.6) Mr = factored flexural resistance, φ Mn (kip-in.) (8.6) Mu = factored moment (kip-in.) (8.10) Pn = nominal compression or tension resistance (kips) (8.8) (8.9) Pr = factored axial resistance (kips) (8.8) (8.9) Pu = factored axial load (kips) (8.10) S = section modulus (in.3) (8.6.2) Vn = nominal shear resistance (kips) (8.7) Vr = factored shear resistance, φ Vn (kips) (8.7) φ = resistance factor (8.5.2.2)

Figure 8.3-1 Dimensions as Defined for Various Types of Wood Products.


SECTION 8: WOOD STRUCTURES 8-13

8.4.1.2.3 Reference Design Values Grade combinations for structural glued laminated

timber shall be as provided in AITC 117-2004, Standard Specifications for Structural Glued Laminated Timber ofSoftwood Species, or AITC 119-96, Standard Specifications for Structural Glued Laminated Timber ofHardwood Species.

Reference Design Values for structural gluedlaminated timber shall be as specified in Tables 1 and 2:

• Table 1 contains design values for timbers with

layups optimized to resist bending loads appliedperpendicular to the wide face of the laminations (bending about the x-x axis). Design values arealso included, however, for axial loads andbending loads applied parallel to the wide facesof the laminations. The design values in Table 1are applicable to timbers with four or more laminations.

• Table 2 contains design values for timbers withuniform-grade layups. These layups are intendedprimarily for timbers loaded axially or in bendingdue to loads applied parallel to the wide faces ofthe laminations (bending about the y-y axis). Design values are also included, however, forbending due to loads applied perpendicular to thewide faces of the laminations. The design valuesin Table 2 are applicable to timbers with two or more laminations.

In Table 1, the tabulated design values, Fbx, for bending about the x-x axis (Fbx), require the use of special tensionlaminations. If these special tension laminations are omitted,value shall be multiplied by 0.75 for members greater thanor equal to 15 in. in depth or by 0.85 for members less than15 in. in depth.

In Table 1, the design value for shear, Fvx, shall be decreased by multiplying by a factor of 0.72 fornonprismatic members, notched members, and for allmembers subject to impact or cyclic loading. The reduced design value shall be used for design of members at connections that transfer shear by mechanical fasteners. The reduced design value shall also be used for determination ofdesign values for radial tension and torsion. Design values,Fvy, shall be used for timbers with laminations made from asingle piece of lumber across the width or multiple piecesthat have been edge bonded. For timber manufactured frommultiple-piece laminations (across width) that are not edge-bonded, in addition to other reduction, design value shall bemultiplied by 0.4 for members with five, seven, or ninelaminations or by 0.5 for all other members. If combination24F-V4 contain lumber with wane, then, in addition, thedesign value for shear parallel to grain, Fvx, shall be multiplied by 0.67 if wane is allowed on both sides. If wane is limited to one side, Fvx, shall be multiplied by 0.83.

C8.4.1.2.3

The combinations in Table 1 are applicable to members consisting of four or more laminations and are intended primarily for members stressed in bending due to loads applied perpendicular to the wide faces of the laminations. However, design values are tabulated for loading both perpendicular and parallel to the wide faces of the laminations. The combinations and design values applicable to members loaded primarily axially or parallel to the wide faces of the laminations, are specified in Table 2. Design values for members of two or threelaminations, are specified in Table 2.


8-14 AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS

In Table 2, for members with two or three laminations,the shear design value for transverse loads parallel to thewide faces of the laminations, Fvy, shall be reduced bymultiplying by a factor of 0.84 or 0.95, respectively. For members with five, seven, or nine laminations, in addition,Fvy, shall be multiplied by 0.4 for members manufacturedfrom multiple-piece laminations (across width) that are notedge bonded. The shear design value, Fvy, shall bemultiplied by 0.5 for all other members manufactured frommultiple-piece laminations with unbonded edge joints.

In Table 2, the design value for shear, Fvx, shall bedecreased by multiplying by a factor of 0.72 fornonprismatic members, notched members, and for allmembers subject to impact or cyclic loading. The reduceddesign value shall be used for design of members atconnections that transfer shear by mechanical fasteners. The reduced design value shall also be used fordetermination of design values for radial tension andtorsion.

In Table 2, the tabulated design values shall apply totimbers without special tension laminations. If specialtension laminations are used, for members to 15 in. deepthe design value for bending, Fbx, may be increased bymultiplying by 1.18. For members greater than 15 in. deepand without special tension laminations, the bendingdesign value, Fbx, shall be reduced by multiplying by afactor of 0.88.

Reference design values for combinations not given inTable 1 or Table 2 shall be obtained from AITC 117-2004.


SEC

TIO

N 8

: WO

OD

ST

RU

CT

UR

ES

8-15

T

able

8.4

.1.2

.3-1

Ref

eren

ce D

esig

n V

alue

s, ks

i, fo

r St

ruct

ural

Glu

ed L

amin

ated

Sof

twoo

d T

imbe

r C

ombi

natio

ns (M

embe

rs st

ress

ed p

rim

arily

in b

endi

ng)

Shea

r Par

alle

lM

odul

usEx

trem

eC

ompr

essi

onSh

ear P

aral

lel

Mod

ulus

Tens

ion

Com

pres

sion

Mod

ulus

to G

rain

ofFi

ber i

nPe

rpen

dicu

lar

to G

rain

ofPa

ralle

l to

Para

llel t

oof

(Hor

izon

tal)

Elas

ticity

Ben

ding

to G

rain

(Hor

izon

tal)

Elas

ticit y

Gra

inG

rain

Elas

ticity

Tens

ion

Com

pres

sion

Tens

ion

Com

pres

sion

Zone

Zone

Face

Face

Stre

ssed

Stre

ssed

inin

Tens

ion

Tens

ion

Com

bina

tion

Spec

ies

F bxo

+F b

xo-

F vxo

E x

o F b

yo

F cpo

F v

yoE y

o F t

o F c

o E o

axi

alSy

mbo

lO

uter

/ Cor

e(1

03 )(1

03 )(1

03 )2

1.1

0.21

1.5

0.8

0.31

50.

185

1.2

0.72

50.

925

1.3

20F-

V3

DF/

DF

2.00

01.

450

0.65

00.

560

0.26

51.

61.

450.

560.

231.

50.

975

1.55

01.

60.

50.

520

F-V

7D

F/D

F2.

000

2.00

00.

650

0.65

00.

265

1.6

1.45

0.56

0.23

1.6

1.00

01.

600

1.6

0.5

0.5

20F-

V9

HF/

HF

2.00

02.

000

0.50

00.

500

0.21

51.

51.

350.

380.

191.

40.

975

1.40

01.

50.

430.

4320

F-V

12A

C/A

C2.

000

1.40

00.

560

0.56

00.

265

1.5

1.25

0.47

0.23

1.4

0.90

01.

500

1.4

0.46

0.46

20F-

V13

AC

/AC

2.00

02.

000

0.56

00.

560

0.26

51.

51.

250.

470.

231.

40.

925

1.55

01.

50.

460.

46

20F-

V2

SP/S

P2.

000

1.55

00.

740

0.65

00.

300

1.5

1.45

0.65

0.26

1.4

0.97

51.

350

1.5

0.55

0.55

20F-

V3

SP/S

P2.

000

1.45

00.

650

0.65

00.

300

1.5

1.75

0.65

0.26

1.4

1.05

01.

400

1.5

0.55

0.55

20F-

V5

SP/S

P2.

000

2.00

00.

740

0.74

00.

300

1.6

1.45

0.65

0.26

1.4

1.05

01.

500

1.5

0.55

0.55

2.4

1.45

0.21

1.7

1.05

0.31

50.

185

1.2

0.77

51

1.4

24F-

V5

DF/

HF

2.40

01.

600

0.65

00.

650

0.21

51.

71.

200.

380.

191.

51.

150

1.45

01.

60.

50.

4324

F-V

10D

F/H

F2.

400

2.40

00.

650

0.65

00.

215

1.8

1.45

0.38

0.19

1.5

1.10

01.

550

1.6

0.5

0.43

24F-

V1

SP/S

P2.

400

1.75

00.

740

0.65

00.

300

1.7

1.45

0.65

0.26

1.5

1.10

01.

550

1.6

0.55

0.55

24F-

V4

SP/S

P2.

400

1.45

00.

740

0.65

00.

210

1.7

1.05

0.47

0.19

1.3

0.87

51.

000

1.5

0.55

0.43

24F-

V5

SP/S

P2.

400

2.40

00.

740

0.74

00.

300

1.7

1.75

0.65

0.26

1.5

1.15

01.

650

1.6

0.55

0.55

2.4

1.45

0.26

51.

81.

450.

560.

231.

61.

11.

61.

724

F-V

4D

F/D

F2.

400

1.85

00.

650

0.65

00.

265

1.8

1.45

0.56

0.23

1.6

1.10

01.

650

1.7

0.5

0.5

24F-

V8

DF/

DF

2.40

02.

400

0.65

00.

650

0.26

51.

81.

450.

560.

231.

61.

100

1.65

01.

70.

50.

5

24F-

V3

SP/S

P2.

400

1.95

00.

740

0.74

00.

300

1.8

1.75

0.65

0.26

1.6

1.15

01.

650

1.7

0.55

0.55

2.6

1.95

0.26

51.

91.

60.

560.

231.

61.

151.

61.

726

F-V

1D

F/D

F2.

600

1.95

00.

650

0.65

00.

265

2.0

1.75

00.

560

0.23

01.

81.

300

1.85

01.

90.

50.

526

F-V

2D

F/D

F2.

600

2.60

00.

650

0.65

00.

265

2.0

1.75

00.

560

0.23

01.

81.

300

1.85

01.

90.

50.

5

26F-

V2

SP/S

P2.

600

2.10

00.

740

0.74

00.

300

1.9

2.20

00.

740

0.26

01.

81.

250

1.65

01.

90.

550.

5526

F-V

4SP

/SP

2.60

02.

600

0.74

00.

740

0.30

01.

92.

100

0.65

00.

260

1.8

1.20

01.

600

1.9

0.55

0.55

to G

rain

Ben

ding

Ben

ding

Abo

ut X

-X A

xis

20F-

1.5E

0.42

5

Perp

endi

cula

r

F cpo

0.65

0.65

0.42 0.5

0.5

0.42

Top

or

Bot

tom

Fac

e Go

Fast

ener

s

Spec

ific

Gra

vity

fo

r Fa

sten

er D

esig

n

Side

Fac

e

26F-

1.9E

24F-

1.7E

24F-

1.8E

Axi

ally

Loa

ded

Extre

me

Fibe

r in

Com

pres

sion

(Loa

ded

Para

llel t

o W

ide

Face

sof

Lam

inat

ions

)(L

oade

d Pe

rpen

dicu

lar t

o W

ide

Face

sof

Lam

inat

ions

)

Ben

ding

Abo

ut Y

-Y A

xis

0.5


8-16

AA

SHT

O L

RFD

BR

IDG

E D

ESI

GN

SPE

CIF

ICA

TIO

NS

Tab

le 8

.4.1

.2.3

-2 R

efer

ence

Des

ign

Val

ues,

ksi,

for

Stru

ctur

al G

lued

Lam

inat

ed S

oftw

ood

Tim

ber

(Mem

bers

stre

ssed

pri

mar

ily in

axi

al te

nsio

n an

d co

mpr

essi

on)

Tens

ion

Para

llel

Shea

r Par

alle

lB

endi

ngSh

ear P

aral

lel

to G

rain

to G

rain

to G

rain

Mod

ulus

Com

pres

sion

2 or

Mor

e4

or M

ore

2 or

34

or M

ore

32

2 La

mi-

Iden

tific

atio

nSp

ecie

s G

rade

ofPe

rpen

dicu

lar

Lam

i-La

mi-

Lam

i-La

mi-

Lam

i-La

mi-

natio

ns to

Num

ber

Elas

ticity

to G

rain

na

tions

natio

nsna

tions

natio

nsna

tions

natio

ns15

in. D

eep

E oF c

poF t

oF c

poF c

poF b

yoF b

yoF b

yoF v

yoF b

xoF v

xo

(103 )

1D

FL3

1.5

0.56

00.

900

1.55

01.

200

1.45

01.

250

1.00

00.

230

1.25

00.

265

2D

FL2

1.6

0.56

01.

250

1.95

01.

600

1.80

01.

600

1.30

00.

230

1.70

00.

265

3D

FL2

D1.

90.

650

1.45

02.

300

1.85

02.

100

1.85

01.

550

0.23

02.

000

0.26

55

DF

L12.

00.

650

1.60

02.

400

2.10

02.

400

2.10

01.

800

0.23

02.

200

0.26

514

HF

L31.

30.

375

0.80

01.

100

0.97

51.

200

1.05

00.

850

0.19

01.

100

0.21

515

HF

L21.

40.

375

1.05

01.

350

1.30

01.

500

1.35

01.

100

0.19

01.

450

0.21

516

HF

L11.

60.

375

1.20

01.

500

1.45

01.

750

1.55

01.

300

0.19

01.

600

0.21

517

HF

L1D

1.7

0.50

01.

400

1.75

01.

700

2.00

01.

850

1.55

00.

190

1.90

00.

215

69A

CL3

1.2

0.47

00.

725

1.15

01.

100

1.10

00.

975

0.77

50.

230

1.00

00.

265

70A

CL2

1.3

0.47

00.

975

1.45

01.

450

1.40

01.

250

1.00

00.

230

1.35

00.

265

71A

CL1

D1.

60.

560

1.25

01.

900

1.90

01.

850

1.65

01.

400

0.23

01.

700

0.26

5

47SP

N2M

141.

40.

650

1.20

01.

900

1.15

01.

750

1.55

01.

300

0.26

01.

400

0.30

048

SPN

2D14

1.7

0.74

01.

400

2.20

01.

350

2.00

01.

800

1.50

00.

260

1.60

00.

300

49SP

N1M

161.

70.

650

1.35

02.

100

1.45

01.

950

1.75

01.

500

0.26

01.

800

0.30

050

SPN

1D14

1.9

0.74

01.

550

2.30

01.

700

2.30

02.

100

1.75

00.

260

2.10

00.

300

Vis

ually

Gra

ded

Sout

hern

Pin

e

Vis

ually

Gra

ded

Wes

tern

Spe

cies

Com

pres

sion

to G

rain

Para

llel

Face

s of L

amin

atio

nsFa

ces o

f Lam

inat

ions

Ben

ding

All

Load

ing

Axi

ally

Loa

ded

Load

ed P

erpe

ndic

ular

to W

ide

Load

ed P

aral

lel t

o W

ide

Ben

ding

abo

ut Y

-Y A

xis

Ben

ding

Abo

ut X

-X A

xis



8.4.1.3 Piles Wood piles shall comply with the requirements of

AASHTO M 168. Reference design values for round wood piles shall be

as specified in Table 1.

C8.4.1.3 The reference design values for wood piles are based

on wet-use conditions.

Table 8.4.1.3-1 Reference Design Values for Piles, ksi.

Species Fco Fbo Fcpo Fvo Eo

Pacific Coast Douglas-Fir1 1.25 2.45 0.23 0.115 1500 Red Oak2 1.10 2.45 0.35 0.135 1250 Red Pine3 0.90 1.90 1.55 0.085 1280 Southern Pine4 1.20 2.40 0.25 0.11 1500

1 Pacific Coast Douglas-Fir reference strengths apply to this species as defined in ASTM Standard D 1760-01. For connection

design, use Douglas Fir-Larch reference design values. 2 Red Oak reference strengths apply to Northern and Southern Red Oak. 3 Red Pine reference strengths apply to Red Pine grown in the U.S. For connection design, use Northern Pine reference design

values. 4 Southern Pine reference strengths apply to Loblolly, Longleaf, Shortleaf, and Slash Pine. 8.4.2 Metal Fasteners and Hardware

8.4.2.1 General Structural metal, including shapes, plates, bars, and

welded assemblies, shall comply with the applicablematerial requirements of Section 6.

8.4.2.2 Minimum Requirements

8.4.2.2.1 Fasteners Bolts and lag screws shall comply with the

dimensional and material quality requirements ofANSI/ASME B18.2.1, Square and Hex Bolts andScrews—Inch Series. Strengths for low-carbon steel bolts,Grade 1 through Grade 8, shall be as specified in Society of Automotive Engineers Specification SAE-429,Mechanical and Material Requirements for ExternallyThreaded Fasteners. Bolt and lag screw grades not givenin SAE-429 shall have a minimum tensile yield strength of 33.0 ksi.

8.4.2.2.2 Prestressing Bars Prestressing bars shall comply with the requirements

of AASHTO M 275 (ASTM A 722) and the applicableprovisions of Section 5.

8.4.2.2.3 Split Ring Connectors Split ring connectors shall be manufactured from

hot-rolled carbon steel complying with the requirements ofSociety of Automotive Engineers Specification SAE-1010. Each circular ring shall be cut through in one place in itscircumference to form a tongue and slot.



8.4.2.2.4 Shear Plate Connectors Shear plate connectors shall be manufactured from

pressed steel, light gage steel, or malleable iron. Pressed steel connectors shall be manufactured from hot-rolled carbon steel meeting Society of Automotive EngineersSpecification SAE-1010. Malleable iron connectors shallbe manufactured in accordance with ASTM A 47, Grade 32510.

Each shear plate shall be a circle with a flange aroundthe edge, extending at right angles to the plate face fromone face only.

8.4.2.2.5 Nails and Spikes Nails and spikes shall be manufactured from common

steel wire or high-carbon steel wire that is heat-treated andtempered. When used in withdrawal-type connections, theshank of the nail or spike shall be annularly or helicallythreaded.

8.4.2.2.6 Drift Pins and Bolts

Drift pins and drift bolts shall have a minimum

flexural yield strength of 30.0 ksi.

8.4.2.2.7 Spike Grids

Spike grids shall conform to the requirements of

ASTM A 47, Grade 32510, for malleable iron casting.

8.4.2.2.8 Toothed Metal Plate Connectors

Metal plate connectors shall be manufactured from

galvanized sheet steel that complies with the requirementsof ASTM A 653, Grade A, or better, with the followingminimum mechanical properties: Yield Point .......................................................... 33.0 ksiUltimate Strength ................................................ 45.0 ksiElongation in 2.0 in. ........................................ 20 percent

8.4.2.3 Corrosion Protection

8.4.2.3.1 Metallic Coating

Except as permitted by this Section, all steel hardwarefor wood components shall be galvanized in accordancewith AASHTO M 232 (ASTM A 153) or cadmium platedin accordance with AASHTO M 299 (ASTM B 696).

Except as otherwise permitted, all steel components,timber connectors, and castings other than malleable ironshall be galvanized in accordance with AASHTO M 111 (ASTM A 123).

C8.4.2.3.1

Galvanized nuts should be retapped to allow for the increased diameter of the bolt due to galvanizing.

Protection for the high-strength bars used in stress-laminated decks should be clearly specified. Standard hot-dip galvanizing can adversely affect the properties of high-strength post-tensioning materials. A lower temperature galvanizing is possible with some high-strength bars. The manufacturer of the bars should be consulted on this issue.



8.4.2.3.2 Alternative Coating

Alternative corrosion protection coatings may beused when the demonstrated performance of the coatingis sufficient to provide adequate protection for theintended exposure condition during the design life of thebridge. When epoxy coatings are used, minimumcoating requirements shall comply with AASHTOM 284.

Heat-treated alloy components and fastenings shallbe protected by an approved alternative protectivetreatment that does not adversely affect the mechanicalproperties of the material.

8.4.3 Preservative Treatment

8.4.3.1 Requirement for Treatment

All wood used for permanent applications shall bepressure impregnated with wood preservative inaccordance with the requirements of AASHTO M 133.

Insofar as is practicable, all wood components shouldbe designed and detailed to be cut, drilled, and otherwisefabricated prior to pressure treatment with woodpreservatives. When cutting, boring, or other fabrication isnecessary after preservative treatment, exposed, untreatedwood shall be specified to be treated in accordance withthe requirements of AASHTO M 133.

8.4.3.2 Treatment Chemicals

Unless otherwise approved, all structural components

that are not subject to direct pedestrian contact shall betreated with oil-borne preservatives. Pedestrian railings and nonstructural components that are subject to directpedestrian contact shall be treated with water-borne preservatives or oil-borne preservatives in light petroleumsolvent.

C8.4.3.2

The oil-borne preservative treatments have proven to provide adequate protection against wood attacking organisms. In addition, the oil provides a water repellant coating that reduces surface effects caused by cyclic moisture conditions. Water-borne preservative treatments do not provide the water repellency of the oil-borne treatment, and components frequently split and check, leading to poor field performance and reduced service life.

Direct pedestrian contact is considered to be contact that can be made while the pedestrian is situated anywhere in the access route provided for pedestrian traffic.

Treating of glued laminated timbers with water-borne preservatives after gluing is not recommended. Use of water-borne treatments for glued laminated timber after gluing may result in excessive warping, checking, or splitting of the components due to post-treatment re-drying.

8.4.3.3 Inspection and Marking

Preservative treated wood shall be tested and

inspected in accordance with the requirements ofAASHTO M 133. Where size permits, each piece oftreated wood that meets treatment requirements shall belegibly stamped, branded, or tagged to indicate the name ofthe treater and the specification symbol or specificationrequirements to which the treatment conforms.

When requested, a certification indicating test results andthe identification of the inspection agency shall be provided.



8.4.3.4 Fire Retardant Treatment

Fire retardant treatments shall not be applied unless itis demonstrated that they are compatible with thepreservative treatment used, and the usable resistance andstiffness are reduced as recommended by the productmanufacturer and applicator.

C8.4.3.4

Use of fire retardant treatments is not recommended because the large sizes of timber components typically used in bridge construction have inherent fire resistance characteristics. The pressure impregnation of wood products with fire retardant chemicals is known to cause certain resistance and stiffness losses in the wood. These resistance and stiffness losses vary with specific resistance characteristic, i.e., bending resistance, tension parallel to grain resistance, etc., treatment process, wood species and type of wood product, i.e., solid sawn, glued laminated, or other.

8.4.4 Adjustment Factors for Reference Design Values

8.4.4.1 General Adjusted design values shall be obtained by adjusting

reference design values by applicable adjustment factors in accordance with the following equations:

Fb = Fbo CKF CM (CF or Cv) Cfu Ci Cd Cλ (8.4.4.1-1) Fv = Fvo CKF CM Ci Cλ (8.4.4.1-2) Ft = Fto CKF CM CF Ci Cλ (8.4.4.1-3) Fc = Fco CKF CM CF Ci Cλ (8.4.4.1-4) Fcp = Fcpo CKF CM Ci Cλ (8.4.4.1-5) E = Eo CM Ci (8.4.4.1-6) where: F = applicable adjusted design values Fb, Fv, Ft, Fc, or

Fcp (ksi) Fo = reference design values Fbo, Fvo, Fto, Fco, or Fcpo

specified in Article 8.4 (ksi) E = adjusted modulus of elasticity (ksi) Eo = reference modulus of elasticity specified in

Article 8.4. (ksi) CKF = format conversion factor specified in

Article 8.4.4.2 CM = wet service factor specified in Article 8.4.4.3 CF = size factor for visually-graded dimension lumber

and sawn timbers specified in Article 8.4.4.4 CV = volume factor for structural glued laminated

timber specified in Article 8.4.4.5


SECTION 8: WOOD STRUCTURES 8-21 Cfu = flat-use factor specified in Article 8.4.4.6 Ci = incising factor specified in Article 8.4.4.7 Cd = deck factor specified in Article 8.4.4.8 Cλ = time effect factor specified in Article 8.4.4.9

8.4.4.2 Format Conversion Factor, CKF

The reference design values in Tables 8.4.4.4-1 and 8.4.4.4-2 and reference design values specified in theNDS® shall be multiplied by a format conversion factor, CKF, for use with load and resistance factor design(LRFD). CKF = 2.5/φ, except for compressionperpendicular to grain which shall be obtained bymultiplying the allowable stress by a format conversionfactor of CKF = 2.1/φ.

C8.4.4.2

The conversion factors were derived so that LRFD design will result in same size member as the allowable stress design (ASD) specified in NDS®. For example, a rectangular component in flexure has to satisfy:

1.25 MDL + 1.75 MLL ≤ φ S Fbo CKF CM (CF or Cv) Cfu Ci Cd Cλ CL (C8.4.4.2-1) or:

(1.25 MDL + 1.75 MLL) / (φCKF Cλ) ≤ S Fbo CM (CF or Cv) Cfu Ci Cd CL (C8.4.4.2-2) where: MDL = moment due to dead load MLL = moment due to live load On the other hand, the allowable stress design (ASD) has to satisfy: MDL + MLL ≤ S Fbo CM (CF or Cv) Cfu Ci Cd CD CL or (MDL + MLL) / (CD) ≤ S Fbo CM (CF or Cv) Cfu Ci Cd CL (C8.4.4.2-3)Therefore: (1.25 MDL + 1.75 MLL) / (φCKF Cλ) = (MDL + MLL) / (CD) (C8.4.4.2-4) CKF = [(1.25 MDL + 1.75 MLL)(CD)] / [(MDL + MLL)(φCλ)] (C8.4.4.2-5) The format conversion factor is calculated assuming the ratio of MDL and MLL is 1:10, φ = 0.85, Cλ = 0.8, and CD = 1.15.

8.4.4.3 Wet Service Factor, CM

The dry use reference design values specified in

Tables 8.4.1.1.4-1 and 8.4.1.1.4-2 shall be adjusted formoisture content using the wet service factor, CM, specified below:

C8.4.4.3

An analysis of in-service moisture content should be based on regional, geographic, and climatological conditions. In the absence of such analysis, wet-use conditions should be assumed.



• For sawn lumber with an in-service moisturecontent of 19 percent or less, CM shall be takenas 1.0.

• For glued laminated timber with an in-service moisture content of 16 percent or less, CM shall be taken as 1.0.

• Otherwise, CM shall be taken as specified inTables 1 and 2 for sawn lumber and gluedlaminated timber, respectively.

Reference design values for Southern Pine and MixedSouthern Pine timbers 5 in. × 5 in. and larger shall betaken to apply to wet or dry use.

Reduction for wet-use is not required.

Table 8.4.4.3-1 Wet Service Factor for Sawn Lumber, CM.

Nominal Thickness

FboCF ≤ 1.15 ksi

FboCF > 1.15 ksi Fto

FcoCF≤0.75 ksi

FcoCF > 0.75 ksi Fvo Fcpo Eo

≤4 in. 1.00 0.85 1.00 1.00 0.80 0.97 0.67 0.90 >4.0 in. 1.00 1.00 1.00 0.91 0.91 1.00 0.67 1.00

Table 8.4.4.3-2 Wet Service Factor for Glued Laminated Timber, CM.

Fbo Fvo Fto Fco Fcpo Eo 0.80 0.875 0.80 0.73 0.53 0.833

8.4.4.4 Size Factor, CF, for Sawn Lumber

The size factor, CF, shall be 1.0 unless specified

otherwise herein. For visually-graded dimension lumber of all species

except Southern Pine and Mixed Southern Pine, CF shall be as specified in Table 1.

Reference design values for Southern Pine and MixedSouthern Pine dimension lumber have been size-adjusted;no further adjustment for size shall be applied.

For Southern Pine and Mixed Southern Pinedimension lumber wider than 12.0 in., the tabulatedbending, compression, and tension parallel to grain designvalues, for the 12.0 in. depth, shall be multiplied by thesize factor, CF = 0.9.

C8.4.4.4 CF does not apply to mechanically-graded lumber

(MSR, MEL) or to structural glued laminated timber. Tabulated design values for visually-graded lumber of

Southern Pine and Mixed Southern Pine species groups have already been adjusted for size. Further adjustment by the size factor is not permitted.


SECTION 8: WOOD STRUCTURES 8-23 Table 8.4.4.4-1 Size Effect Factor, CF, for Sawn Dimension Lumber.

Fbo Fto Fco All Other Properties

Thickness

Grade Width (in.) 2.0 in. and

3.0 in. 4.0 in. All All All Structural Light Framing: 2.0 in × 2.0 in. through 4.0 in. × 4.0 in.

Structural Joists and Planks: 2.0 in × 5.0 in. through 4.0 in. × 16.0 in.

≤4 1.5 1.54 1.5 1.15 Sel. Str. 5 1.4 1.4 1.4 1.1 No. 1 6 1.3 1.3 1.3 1.1

No. 2 8 1.2 1.3 1.2 1.05 1.00 10 1.1 1.2 1.1 1.0 12 1.0 1.1 1.0 1.0

≥14 0.9 1.0 0.9 0.9

For sawn beams and stringers with loads applied to

the narrow face and posts and timbers with loads appliedto either face, Fbo shall be adjusted by CF determined as:

• If d ≤ 12.0 in., then

CF = 1.0 (8.4.4.4-1)

• If d > 12.0 in., then

1

912FC

d= ⎛ ⎞

⎜ ⎟⎝ ⎠

(8.4.4.4-2)

where:

d = net width as shown in Figure 8.3-1

For beams and stringers with loads applied to the wideface, Fbo shall be adjusted by CF as specified inTable 2. Table 8.4.4.4-2 Size Factor, CF, for Beams and Stringers with loads applied to the wide face.

Grade Fbo Eo Other Properties SS 0.86 1.00 1.00 No. 1 0.74 0.90 1.00 No. 2 1.00 1.00 1.00

8.4.4.5 Volume Factor, CV, (Glulam)

For horizontally laminated glulam, with loads appliedperpendicular to the wide face of the laminations, Fbo shall be reduced by CV, given below, when the depth, width, orlength of a glued laminated timber exceeds 12.0 in.,5.125 in., or 21.0 ft., respectively:



0.121125.50.12≤⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛=

a

V LbdC (8.4.4.5-1)

where: d = depth of the component (in.) b = width of the component (in.) For layups with

multiple piece laminations (across the width)b = width of widest piece. Therefore: b ≤ 10.75 in.

L = length of the component measured between

points of contraflexure (ft.) a = 0.05 for Southern Pine and 0.10 for all other

species. The volume factor, CV, shall not be applied

simultaneously with the beam stability factor, CL, therefore, the lesser of these factors shall apply.

8.4.4.6 Flat-Use Factor, Cfu

When dimension lumber graded as Structural Light

Framing or Structural Joists and Planks is used flatwise(load applied to the wide face), the bending referencedesign value shall be multiplied by the flat use factorspecified in Table 1.

The flat-use factor shall not apply to dimensionlumber graded as Decking. Table 8.4.4.6-1 Flat-Use Factor, Cfu, for Dimension Lumber.

Thickness (in.) Width (in.) 2 and 3 4

2 and 3 1.0 — 4 1.1 1.0 5 1.1 1.05 6 1.15 1.05 8 1.15 1.05 ≥10 1.2 1.1

C8.4.4.6

Design values for flexure of dimension lumber adjusted by the size factor, CF, are based on edgewise use (load applied to the narrow face). When dimension lumber is used flatwise (load applied to the wide face), the bending reference design value should also be multiplied by the flat use factor specified in Table 1.

Design values for dimension lumber graded as Decking are based on flatwise use. Further adjustment by the flat-use factor is not permitted.

Reference design values for flexure of verticallylaminated glulam (loads applied parallel to wide faces oflaminations) shall be multiplied by the flat use factorsspecified in Table 2 when the member dimension parallelto wide faces of laminations is less than 12.0 in.


SECTION 8: WOOD STRUCTURES 8-25 Table 8.4.4.6-2 Flat-Use Factor, Cfu, for Glulam.

Member dimension parallel to wide faces of laminations

(in.) Cfu

10 3/4 or 10 1/2 1.01 8 3/4 or 8 1/2 1.04

6 3/4 1.07 5 1/8 or 5 1.10 3 1/8 or 3 1.16

2 1/2 or 2 1/8 1.19

8.4.4.7 Incising Factor, Ci

Reference design values for dimension lumber shallbe multiplied by the incising factor specified in Table 1when members are incised parallel to grain a maximumdepth of 0.4 in., a maximum length of 3/8 in., and a density of incisions up to 1100/ft2. Incising factors shall bedetermined by test or by calculation using reduced sectionproperties for incising patterns exceeding these limits. Table 8.4.4.7-1 Incising Factor for Dimension Lumber.

Design Value Ci

Eo 0.95 Fbo, Fto, Fco, Fvo 0.80

Fcpo 1.00

8.4.4.8 Deck Factor, Cd

Unless specified otherwise in this Article, the deck factor, Cd, shall be equal to 1.0.

For stressed wood, nail-laminated, and spike-laminated decks constructed of solid sawn lumber 2.0 in. to 4.0 in. thick, Fbo may be adjusted by Cd as specified in Table 1. Table 8.4.4.8-1 Deck Factor for Stressed Wood and Laminated Decks.

Deck Type Lumber Grade Cd

Stressed Wood Select Structural No. 1 or No. 2

1.30 1.50

Spike-Laminated or Nail-Laminated

All 1.15

C8.4.4.8

Mechanically laminated decks made of stressed wood, spike laminated, or nail-laminated solid sawn lumber exhibit an increased resistance in bending. The resistance of mechanically laminated solid sawn lumber decks iscalculated by multiplying Fbo in Table 8.4.1.1.4-1 by the deck factor.

Deck factor is used instead of the repetitive member factor that is used in NDS®.



For planks 4 × 6 in., 4 × 8 in., 4 × 10 in. and 4 × 12 in., used in plank decks with the load applied to thewide face of planks, Fbo may be adjusted by Cd as specified in Table 2. Table 8.4.4.8-2 Deck Factor for Plank Decks.

Size (in.) Cd 4 × 6 1.10

4 × 8 1.15

4 × 10 1.25

4 × 12 1.50

The deck factors for planks in plank decks shall not beapplied cumulatively with the flat use factor, Cfu, specifiedin Article 8.4.4.6.

The specified deck factors for planks in plank decks are based test results comparing the modulus of rupture (MOR) for plank specimens with load applied in narrow face and wide face (Stankiewicz and Nowak, 1997). These deck factors can be applied cumulatively with the size factor, CF, specified in Article 8.4.4.4.

8.4.4.9 Time Effect Factor, Cλ

The time effect factor, Cλ shall be chosen tocorrespond to the appropriate strength limit state asspecified in Table 1.

Table 8.4.4.9-1 Time Effect Factor.

Limit State Cλ Strength I 0.8 Strength II 1.0 Strength III 1.0 Strength IV 0.6 Extreme Event I 1.0

C8.4.4.9

NDS® and AITC 117-2004 reference design values (based on 10-year loading) multiplied by the format conversion factors specified in Article 8.4.4.2, transform allowable stress values to strength level stress values based on 10-min. loading. It is assumed that a cumulative duration of bridge live load is two months and the corresponding time effect factor for Strength I is 0.8. A cumulative duration of live load in Strength II is shorter and the corresponding time effect factor for Strength II is 1.0. Resistance of wood subjected to long-duration loads is reduced. Load combination IV consists of permanent loads, including dead load and earth pressure.

8.5 LIMIT STATES

8.5.1 Service Limit State

The provisions of Article 2.5.2.6.2 should be considered.

8.5.2 Strength Limit State

8.5.2.1 General

Factored resistance shall be the product of nominalresistance determined in accordance with Article 8.6, 8.7,8.8, and 8.9 and the resistance factor as specified inArticle 8.5.2.2.



8.5.2.2 Resistance Factors Resistance factors, φ, shall be as given below: Flexure .........................................................φ = 0.85Shear ............................................................ φ = 0.75Compression Parallel to Grain ..................... φ = 0.90Compression Perpendicular to Grain ..........φ = 0.90Tension Parallel to Grain .............................φ = 0.80Resistance During Pile Driving....................φ = 1.15Connections ................................................. φ = 0.65

C8.5.2.2 In the case of timber pile foundations, the resistance

factor may be raised to 1.0 when, in the judgment of the Engineer, a sufficient number of piles is used in a foundation element to consider it to be highly redundant. This is indicated to be a judgment issue because there are no generally accepted quantitative guidelines at this writing.

For timber piles, the resistance factor to be applied when determining the maximum allowable driving resistance accounts for the short duration of the load induced by the pile driving hammer.

8.5.2.3 Stability The structure as a whole or its components shall be

proportioned to resist sliding, overturning, uplift, andbuckling.

8.5.3 Extreme Event Limit State

For extreme event limit state, the resistance factor

shall be taken as 1.0.

8.6 COMPONENTS IN FLEXURE

8.6.1 General

The factored resistance, Mr, shall be taken as: = φr nM M (8.6.1-1)

where: Mn = nominal resistance specified herein (kip-in.) φ = resistance factor specified in Article 8.5.2

8.6.2 Rectangular Section

The nominal resistance, Mn, of a rectangularcomponent in flexure shall be determined from: Mn = Fb SCL (8.6.2-1) in which:

( )21 1

1.9 3.61 0.95L

A A AC

+ += − − (8.6.2-2)

b

bEFA

F= (8.6.2-3)

C8.6.2

If lateral support is provided to prevent rotation at the points of bearing, but no other lateral support is provided throughout the bending component length, the unsupported length, Lu, is the distance between such points of intermediate lateral support.



2bE

bE

B

K EF

R= (8.6.2-4)

250e

b

L d

bR = ≤ (8.6.2-5)

where: KbE = 0.76 for visually graded lumber KbE = 0.98 for MEL lumber KbE = 1.06 for MSR lumber KbE = 1.10 for glulam Fb = adjusted design value in flexure specified in

Article 8.4.4 (ksi) E = adjusted modulus of elasticity specified in

Article 8.4.4 (ksi) CL = beam stability factor d = net depth specified in Article 8.4.1.1.2 (in.) b = net width, as specified in Article 8.4.1.1.2 (in.) Le = effective unbraced length (in.) S = section modulus (in.3)

Where the depth of a flexural component does notexceed its width, or where lateral movement of thecompression zone is prevented by continuous support andwhere points of bearing have lateral support to preventrotation, the stability factor, CL = 1.0. For other conditions,the beam stability factor shall be determined in accordancewith the provisions specified herein.

The beam stability factor shall not be appliedsimultaneous with the volume factor for structural gluedlaminated timber, therefore, the lesser of these factors shallapply.

The effective unbraced length, Le, may be determinedas:

• If Lu/d < 7, then Le = 2.06 Lu

• If 7 ≤ Lu/d ≤ 14.3, then Le = 1.63 Lu + 3d

• If Lu/d > 14.3, then Le = 1.84 Lu

where: Lu = distance between point of lateral and rotational

support (in.) d = net depth specified in Article 8.4.1.1.2 (in.)


SECTION 8: WOOD STRUCTURES 8-29 8.6.3 Circular Section

The nominal resistance, Mn, of a circular component

in flexure shall be taken as:

n bM F S= (8.6.3-1)

8.7 COMPONENTS UNDER SHEAR

Shear shall be investigated at a distance away from theface of support equal to the depth of the component. When calculating the maximum design shear, the live load shallbe placed so as to produce the maximum shear at adistance from the support equal to the lesser of either three times the depth, d, of the component or one-quarter of the span L.

The factored shear resistance, Vr, of a component ofrectangular cross-section shall be calculated from:

C8.7

The critical section is between one and three depths from the support.

The critical shear in flexural components is horizontal shear acting parallel to the grain of the component. The resistance of bending components in shear perpendicular to grain need not be investigated.

Note that Eq. 4.6.2.2.2a-1 requires a special distribution factor in the calculation of the live load force effect when investigating shear parallel to the grain.

= φr nV V (8.7-1)

in which:

1.5v

nF bd

V = (8.7-2)

where: φ = resistance factor specified in Article 8.5.2 Fv = adjusted design value of wood in shear, specified

in Article 8.4.1 (ksi)

8.8 COMPONENTS IN COMPRESSION 8.8.1 General

The factored resistance in compression, Pr, shall be taken as:

= φr nP P (8.8.1-1)

where: Pn = nominal resistance as specified in Article 8.8.2

and 8.8.3 (kips) φ = resistance factor specified in Article 8.5.2

8.8.2 Compression Parallel to Grain

Where components are not adequately braced, the nominal stress shall be modified by the column stabilityfactor, Cp. If the component is adequately braced, Cp shall be taken as 1.0.

The nominal resistance, Pn, of a component in thecompression parallel to grain shall be taken as:



=n c pP F AC (8.8.2-1) in which:

( )21 1P

B B BC

c c c

+ += − − (8.8.2-2)

cE

c

FB

F= (8.8.2-3)

2

2

cEcE

e

K EdF

L= (8.8.2-4)

where: c = 0.8 for sawn lumber c = 0.85 for round timber piles c = 0.9 for glulam KcE = 0.52 for visually graded lumber KcE = 0.67 for MEL lumber KcE = 0.73 for MSR lumber KcE = 0.76 for glulam and round piles Fc = adjusted design value in compression parallel to

the grain specified in Article 8.4.4 (ksi) Le = effective length taken as KL (in.) Ag = gross cross-sectional area of the component (in.2)

8.8.3 Compression Perpendicular to Grain

The nominal resistance, Pn, of a component incompression perpendicular to the grain shall be taken as:

=n cp b bP F A C (8.8.3-1) where: Fcp = adjusted design value in compression

perpendicular to grain, as specified inArticle 8.4.4 (ksi)

Ab = bearing area (in.2) Cb = bearing adjustment factor specified in Table 1

When the bearing area is in a location of high flexural stress or is closer than 3.0 in. from the end of thecomponent, Cb shall be taken as 1.0. In all other cases, Cbshall be as specified in Table 1.


SECTION 8: WOOD STRUCTURES 8-31 Table 8.8.3-1 Adjustment Factors for Bearing.

Length of bearing measured along the grain, in. 0.5 1.0 1.5 2.0 3.0 4.0 ≥6.0 Cb 1.75 1.38 1.25 1.19 1.13 1.10 1.00

8.9 COMPONENTS IN TENSION PARALLEL TO GRAIN

The factored resistance, Pr, of a component in tensionshall be taken as:

= φr nP P (8.9-1) in which:

=n t nP F A (8.9-2) where: Ft = adjusted design value of wood in tension

specified in Article 8.4.4 (ksi) An = smallest net cross-sectional area of the

component (in.2) φ = resistance factor specified in Article 8.5.2

8.10 COMPONENTS IN COMBINED FLEXURE AND AXIAL LOADING

8.10.1 Components in Combined Flexure and Tension

Components subjected to flexure and tension shallsatisfy:

* 1.0u u

r r

P M

P M+ ≤ (8.10.1-1)

and

**1.06u u

r

M

M

dP−

≤ (8.10.1-2)

where: Pu = factored tensile load (kips) Pr = factored tensile resistance calculated as specified

in Article 8.9 (kips) Mu = factored flexural moment (kip-in.) Mr* = FbS Mr**= factored flexural resistance adjusted by all

applicable adjustment factors except CV

C8.10.1

Satisfying Eq. 1 ensures that stress interaction on the tension face of the bending member does not cause beam rupture. Mr

* in this formula does not include modification by the beam stability factor, CL.

Eq. 2 is applied to ensure that the bending/tension member does not fail due to lateral buckling of the compression face.


8-32 AASHTO LRFD BRIDGE DESIGN SPECIFICATIONS 8.10.2 Components in Combined Flexure and Compression Parallel to Grain

Components subjected to flexure and compression

parallel to grain shall satisfy:

2

1.0

1

u u

r ur

cE g

P M

PM

PF A

+ ≤

−

⎛ ⎞⎜ ⎟⎝ ⎠ ⎛ ⎞

⎜ ⎟⎝ ⎠

(8.10.2-1)

where: Pu = factored tensile load (kips) Pr = factored tensile resistance calculated as specified

in Article 8.9 (kips) Mu = factored flexural moment (kip-in.) FcE = Euler buckling stress as defined in Eq. 8.8.2-4 Ag = gross cross-sectional area

8.11 BRACING REQUIREMENTS

8.11.1 General

Where bracing is required, it shall prevent both lateral

and rotational deformation.

C8.11.1 In detailing of the diaphragms, the potential for

shrinkage and expansion of the beam and the diaphragm should be considered. Rigidly connected steel angle framing may cause splitting of the beam and diaphragm as the wood attempts to swell and shrink under the effects of cyclic moisture.

8.11.2 Sawn Wood Beams

Beams shall be transversely braced to prevent lateral

displacement and rotation of the beams and to transmitlateral forces to the bearings. Transverse bracing shall beprovided at the supports for all span lengths and atintermediate locations for spans longer than 20.0 ft. The spacing of intermediate bracing shall be based on lateralstability and load transfer requirements but shall notexceed 25.0 ft. The depth of transverse bracing shall not beless than three-fourths the depth of the stringers or girders.

Transverse bracing should consist of solid woodblocking or fabricated steel shapes. Wood blocking shallbe bolted to stringers with steel angles or suspended insteel saddles that are nailed to the blocks and stringersides. Blocking shall be positively connected to the beams.

Transverse bracing at supports may be placed within adistance from the center of bearing equal to the stringer orgirder depth.

C8.11.2 The effectiveness of the transverse bracing directly

affects the long-term durability of the system. The bracing facilitates erection, improves load distribution, and reduces relative movements of the stringers and girders, thereby reducing deck deformations. Excessive deformation can lead to mechanical deterioration of the system.

Bracing should be accurately framed to provide full bearing against stringer sides. Wood cross-frames or blocking that are toe-nailed to stringers have been found to be ineffective and should not be used.


SECTION 8: WOOD STRUCTURES 8-33 8.11.3 Glued Laminated Timber Girders

Transverse bracing should consist of fabricated steel

shapes or solid wood diaphragms. Girders shall be attached to supports with steel shoes

or angles that are bolted through the girder and into orthrough the support.

C8.11.3 Bracing should be placed tight against the girders and

perpendicular to the longitudinal girder axis.

8.11.4 Bracing of Trusses

Wood trusses shall be provided with a rigid system of

lateral bracing in the plane of the loaded chord. Lateral bracing in the plane of the unloaded chord and rigid portaland sway bracing shall be provided in all trusses havingsufficient headroom. Outrigger bracing connected toextensions of the floorbeams shall be used for bracingthrough-trusses having insufficient headroom for a topchord lateral bracing system.

C8.11.4 Bracing is used to provide resistance to lateral forces,

to hold the trusses plumb and true, and to hold compression elements in line.

8.12 CAMBER REQUIREMENTS

8.12.1 Glued Laminated Timber Girders

Glued laminated timber girders shall be cambered a

minimum of two times the dead load deflection at theservice limit state.

C8.12.1 The initial camber offsets the effects of dead load

deflection and long-term creep deflection.

8.12.2 Trusses

Trusses shall be cambered to sufficiently offset the

deflection due to dead load, shrinkage, and creep.

C8.12.2 Camber should be determined by considering both

elastic deformations due to applied loads and inelastic deformations such as those caused by joint slippage, creep of the timber components, or shrinkage due to moisture changes in the wood components.

8.12.3 Stress Laminated Timber Deck Bridge

Deck bridges shall be cambered for three times the

dead load deflection at the service limit state.

8.13 CONNECTION DESIGN

The design of timber connections using mechanical

fasteners including, wood screws, nails, bolts, lag screws,drift bolts, drift pins, shear plates, split rings, and timberrivets shall be in accordance with the 2005 NDS®.



REFERENCES

AF&PA. 2005. National Design Specification® (NDS®) for Wood Construction. American Forest and Paper Association, Washington, DC. AITC. 1996. Standard Specifications for Structural Glued Laminated Timber of Hardwood Species, AITC 119-96. American Institute of Timber Construction, Centennial, CO. AITC. 2001. Standard Appearance Grades for Structural Glued Laminated Timber, AITC 110-2001. American Institute of Timber Construction, Centennial, CO. AITC. 2002. Structural Glued Laminated Timber, ANSI/AITC A190.1. American Institute of Timber Construction, Centennial, CO. AITC. 2004. Standard Specifications for Structural Glued Laminated Timber of Softwood Species, AITC 117-2004. American Institute of Timber Construction, Centennial, CO. Nowak, A. S. 1997. Load Distribution for Plank Decks, UMCEE 97-11. Report submitted to U.S. Forest Service, U.S. Department of Agriculture, Washington, DC, April 1997. Nowak, A. S. 1999. Calibration of LRFD Bridge Design Code, NCHRP Report 368. Transportation Research Board, National Research Council, Washington, DC. Nowak, A. S., C. Eamon, M. A. Ritter, and J. Murphy. 2001. LRFD Calibration for Wood Bridges, UMCEE 01-01. Report submitted to U.S. Forest Service, U.S. Department of Agriculture, Washington, DC, April 2001. Nowak, A. S., P. R. Stankiewicz, and M. A. Ritter. 1999. “Bending Tests of Bridge Deck Planks.” Construction and Building Materials Journal, Vol. 13, No. 4, pp. 221–228. Ritter, M. A. 1990. Timber Bridges, Design, Construction, Inspection, and Maintenance, EM7700-B. U.S. Forest Service, U.S. Department of Agriculture, Washington, DC. Stankiewicz, P. R., and A. S. Nowak. 1997. Material Testing for Wood Plank Decks, UMCEE 97-10. Report submitted to U.S. Forest Service, U.S. Department of Agriculture, Washington, DC, April 1997.


SECTION 11 (SI): ABUTMENTS, PIERS, AND WALLS 11-3

CRu = short-term connection strength reduction factor to account for reduced ultimate strength resulting from the connection (dim.) (11.10.6.4.4b)

Cu = coefficient of uniformity (dim.) (11.10.6.3.2) D = design embedment depth of vertical element (mm); diameter of bar or wire (mm) (11.10.6.3.2)

(C11.8.4.1) D* = diameter of bar or wire corrected for corrosion loss (mm) (11.10.6.4.1) Do = embedment for which net passive pressure is sufficient to provide moment equilibrium (mm) (C11.8.4.1) D60/D10 = uniformity coefficient of soil defined as ratio of the particle size of soil that is 60 percent finer in size to

the particle size of soil that is ten percent finer in size (dim.) (11.10.6.3.2) d = diameter of anchor drill hole (mm); the lateral wall displacement (mm); fill above wall (mm) (C11.6.5)

(11.9.4.2) (11.10.8) Ec = thickness of metal reinforcement at end of service life (mm) (11.10.6.4.1) En = nominal thickness of steel reinforcement at construction (mm) (11.10.6.4.2a) Es = sacrificial thickness of metal expected to be lost by uniform corrosion during service life (mm)

(11.10.6.4.2a) EAE = total active static and seismic force (N/mm) (A11.1.1.1) EPE = total passive static and seismic force (N/mm) (A11.1.1.1) e = eccentricity of load from centerline of foundation (mm) (11.10.8) FT = resultant force of active lateral earth pressure (N/mm) (11.6.3.2) Fy = minimum yield strength of steel (MPa) (11.10.6.4.3a) F* = reinforcement pullout friction factor (dim.) (11.10.6.3.2) g = gravitational acceleration (m/sec.2) (11.9.3.1) Gu = distance from center of gravity of a horizontal segmental facing block unit, including aggregate fill,

measured from the front of the unit (mm) (11.10.6.4.4b) H = height of wall (mm) (11.9.1) Hh = hinge height for segmental facing (mm) (11.10.6.4.4b) Hu = segmental facing block unit height (mm) (11.10.6.4.4b) H1 = equivalent wall height (mm) (11.10.6.3.1) h = vertical distance between ground surface and wall base at the back of wall heel (mm) (11.6.3.2) hi = height of reinforced soil zone contributing horizontal load to reinforcement at level i (mm) (11.10.6.2.1) ib = slope of facing base downward into backfill (°) (11.10.6.4.4b) ka = active earth pressure coefficient (dim.) (11.8.4.1) kaf = active earth pressure coefficient of backfill (dim.) (11.10.5.2) kh = horizontal seismic acceleration coefficient (dim.) (11.8.6) kv = vertical seismic acceleration coefficient (dim.) (A11.1.1.1) kAE = seismic active pressure coefficient (dim.) (A11.1.1.1) kPE = seismic passive pressure coefficient (dim.) (A11.1.1.1) kr = horizontal earth pressure coefficient of reinforced fill (dim.) (11.10.5.2) L = spacing between vertical elements or facing supports (mm); length of reinforcing elements in an MSE

wall and correspondingly its foundation (mm) (11.8.5.2) (11.10.2) La = length of reinforcement in active zone (mm) (11.10.2) Lb = anchor bond length (mm) (11.9.4.2) Le = length of reinforcement in resistance zone (mm) (11.10.2) Lei = effective reinforcement length for layer i (mm) (11.10.7.2) MARV = minimum average roll value (11.10.6.4.3b) Mmax = maximum bending moment in vertical wall element or facing (N-mm or N-mm/mm) (11.8.5.2) N = normal component of resultant on base of foundation (N/mm) (11.6.3.2) PAE = dynamic horizontal thrust (N/mm) (11.10.7.1) Pb = pressure inside bin module (MPa) (11.10.5.1) PH = lateral force due to superstructure or other concentrated loads (N/mm) (11.10.10.1) Pi = factored horizontal force per mm of wall transferred to soil reinforcement at level i; internal inertial

force, due to the weight of the backfill within the active zone (N/mm) (11.10.6.2.1) (11.10.7.2) PIR = horizontal inertial force (N/mm) (11.10.7.1) Pir = horizontal inertial force caused by acceleration of reinforced backfill (N/mm) (11.10.7.1) Pis = internal inertial force caused by acceleration of sloping surcharge (N/mm) (11.10.7.1) Pr = ultimate soil reinforcement pullout resistance per unit of reinforcement width (N/mm) (11.10.6.3.2) Pv = load on strip footing (N/mm) (11.10.10.1) P′v = load on isolated rectangular footing or point load (N) (11.10.10.1)



p = average lateral pressure, including earth, surcharge and water pressure, acting on the section of wall element being considered (MPa) (11.9.5.2)

Qn = nominal (ultimate) anchor resistance (N) (11.9.4.2) QR = factored anchor resistance (N) (11.9.4.2) qs = surcharge pressure (MPa) (11.10.5.2) qmax = maximum unit soil pressure on base of foundation (MPa) (11.6.3.2) R = resultant force at base of wall (N/mm) (11.6.3.2) RBH = basal heave ratio (C11.9.3.1) Rc = reinforcement coverage ratio (dim.) (11.10.6.3.2) Rn = nominal resistance (N or N/mm) (11.5.4) RR = factored resistance (N or N/mm) (11.5.4) RF = combined strength reduction factor to account for potential long-term degradation due to installation

damage, creep and chemical/biological aging of geosynthetic reinforcements (dim.) (11.10.6.4.2b) RFc = combined strength reduction factor for long-term degradation of geosynthetic reinforcement facing

connection (dim.) (11.10.6.4.4b) RFCR = strength reduction factor to prevent long-term creep rupture of reinforcement (dim.) (11.10.6.4.3b) RFD = strength reduction factor to prevent rupture of reinforcement due to chemical and biological degradation

(dim.) (11.10.6.4.3b) RFID = strength reduction factor to account for installation damage to reinforcement (dim.) (11.10.6.4.3b) Sh = horizontal reinforcement spacing (mm) (11.10.6.4.1) St = spacing between transverse grid elements (mm) (11.10.6.3.2) Su = undrained shear strength (MPa) (11.9.5.2) Sv = vertical spacing of reinforcements (mm) (11.10.6.2.1) Srs = ultimate reinforcement tensile resistance required to resist static load component (N/mm) (11.10.7.2) Srt = ultimate reinforcement tensile resistance required to resist transient load component (N/mm) (11.10.7.2) Tac = nominal long-term reinforcement/facing connection design strength (N/mm) (11.10.6.4.1) Tal = nominal long-term reinforcement design strength (N/mm) (11.10.6.4.1) Tcrc = creep reduced connection strength per unit of reinforcement width determined from the stress rupture

envelope at the specified design life as produced from a series of long-term connection creep tests (N/mm) (11.10.6.4.4b)

Tlot = ultimate wide width tensile strength per unit of reinforcement width (ASTM D4595 or D6637) for the reinforcement material lot used for the connection strength testing (N/mm) (11.10.6.4.3b)

Tmd = factored incremental dynamic inertia force (N/mm) (11.10.7.2) Tultconn = ultimate connection strength per unit of reinforcement width (N/mm) (11.10.6.4.4b) Tult = ultimate tensile strength of reinforcement (N/mm) (11.10.6.4.3b) Tmax = applied load to reinforcement (N/mm) (11.10.6.2.1) To = factored tensile load at reinforcement/facing connection (N/mm) (11.10.6.2.2) t = thickness of transverse elements (mm) (11.10.6.3.2) Ttotal = total load on reinforcement layer (static & dynamic) per unit width of wall (N/mm) (11.10.7.2) V1 = weight of soil carried by wall heel, not including weight of soil surcharge (N/mm) (11.6.3.2) V2 = weight of soil surcharge directly above wall heel (N/mm) (11.6.3.2) Wu = unit width of segmental facing (mm) (11.10.2.3.2) W1 = weight of wall stem (N/mm) (11.6.3.2) W2 = weight of wall footing or base (N/mm) (11.6.3.2) x = spacing between vertical element supports (mm) (11.9.5.2) Z = depth below effective top of wall or to reinforcement (mm) (11.10.6.2.1) Zp = depth of soil at reinforcement layer at beginning of resistance zone for pullout calculation (mm)

(11.10.6.2.1) α = scale effect correction factor (dim.) (11.10.6.3.2) β = inclination of ground slope behind face of wall (°) (11.5.5) γEQ = load factor for earthquake loading in Article 3.4.1 (dim.) (11.6.5) γP = load factor for vertical earth pressure in Article 3.4.1 (dim.) (11.10.6.2.1) γs = soil density (kg/m3) γ′s = effective soil density (kg/m3) (C11.8.4.1) γr = density of reinforced fill (kg/m3) (11.10.5.2) γf = density of backfill (kg/m3) (11.10.5.2) ΔσH = horizontal stress on reinforcement from concentrated horizontal surcharge (MPa); traffic barrier impact

stress applied over reinforcement tributary area (MPa) (11.10.6.2.1) (11.10.10.2) Δσv = vertical stress due to footing load (MPa) (11.10.8)



Figure C11.5.5-2 Typical Application of Load Factors for Sliding and Eccentricity.



Figure C11.5.5-3 Typical Application of Live Load Surcharge. 11.5.6 Resistance Factors

Resistance factors for geotechnical design offoundations are specified in Tables 10.5.5.2.2-1, 10.5.5.2.3-1, 10.5.5.2.4-1, and Table 1.

If methods other than those prescribed in theseSpecifications are used to estimate resistance, theresistance factors chosen shall provide the samereliability as those given in Tables 10.5.5.2.2-1, 10.5.5.2.3-1, 10.5.5.2.4-1, and Table 1.

Vertical elements, such as soldier piles, tangent-piles and slurry trench concrete walls shall be treated aseither shallow or deep foundations, as appropriate, forpurposes of estimating bearing resistance, using procedures described in Articles 10.6, 10.7, and 10.8.

C11.5.6

The resistance factors given in Table 1, other than those referenced back to Section 10, were calculated by direct correlation to allowable stress design rather than reliability theory.

Since the resistance factors in Table 1 were based on direct correlation to allowable stress design, the differences between the resistance factors for tensile resistance of metallic versus geosynthetic reinforcement are based on historical differences in the level of safety applied to reinforcement designs for these two types of reinforcements. See Article C11.10.6.2.1 for additional comments regarding the differences between the resistance factors for metallic versus geosynthetic reinforcement.



• Temperature and shrinkage deformationeffects; and

• Earthquake loads, as specified herein, inSection 3 and elsewhere in these Specifications.

The provisions of Articles 3.11.5 and 11.5.5 shallapply. For stability computations, the earth loads shallbe multiplied by the maximum and/or minimum loadfactors given in Table 3.4.1-2, as appropriate.

The design shall be investigated for anycombination of forces which may produce the mostsevere condition of loading. The design of abutments onmechanically stabilized earth and prefabricated modularwalls shall be in accordance with Articles 11.10.11 and11.11.6.

For computing load effects in abutments, the weightof filling material directly over an inclined or steppedrear face, or over the base of a reinforced concrete spread footing may be considered as part of the effectiveweight of the abutment.

Where spread footings are used, the rear projectionshall be designed as a cantilever supported at theabutment stem and loaded with the full weight of thesuperimposed material, unless a more exact method isused.

Cohesive backfills are difficult to compact. Because of the creep of cohesive soils, walls with cohesive backfills designed for active earth pressures will continue to move gradually throughout their lives, especially when the backfill is soaked by rain or rising groundwater levels. Therefore, even if wall movements are tolerable, walls backfilled with cohesive soils should be designed with extreme caution for pressures between the active and at-rest cases assuming the most unfavorable conditions. Consideration must be given forthe development of pore water pressure within the soil mass in accordance with Article 3.11.3. Appropriate drainage provisions should be provided to prevent hydrostatic and seepage forces from developing behind the wall. In no case shall highly plastic clay be used for backfill.

11.6.1.3 Integral Abutments Integral abutments shall be designed to resist and/or

absorb creep, shrinkage and thermal deformations of thesuperstructure.

C11.6.1.3

Deformations are discussed in Article 3.12.

Movement calculations shall consider temperature,creep, and long-term prestress shortening in determiningpotential movements of abutments.

Maximum span lengths, design considerations,details should comply with recommendations outlined inFHWA Technical Advisory T 5140.13 (1980), except where substantial local experience indicates otherwise.

To avoid water intrusion behind the abutment, theapproach slab should be connected directly to theabutment (not to wingwalls), and appropriate provisionsshould be made to provide for drainage of any entrappedwater.

Integral abutments should not be constructed on spread footings founded or keyed into rock unless one end of the span is free to displace longitudinally.

11.6.1.4 Wingwalls Wingwalls may either be designed as monolithic

with the abutments, or be separated from the abutmentwall with an expansion joint and designed to be freestanding.

The wingwall lengths shall be computed using therequired roadway slopes. Wingwalls shall be ofsufficient length to retain the roadway embankment andto furnish protection against erosion.



11.6.1.5 Reinforcement 11.6.1.5.1 Conventional Walls and Abutments Reinforcement to resist the formation of

temperature and shrinkage cracks shall be designed asspecified in Article 5.10.8.

11.6.1.5.2 Wingwalls Reinforcing bars or suitable rolled sections shall be

spaced across the junction between wingwalls and abutments to tie them together. Such bars shall extendinto the masonry on each side of the joint far enough todevelop the strength of the bar as specified for barreinforcement, and shall vary in length so as to avoidplanes of weakness in the concrete at their ends. If bars are not used, an expansion joint shall be provided andthe wingwall shall be keyed into the body of theabutment.

11.6.1.6 Expansion and Contraction Joints Contraction joints shall be provided at intervals not

exceeding 9000 mm and expansion joints at intervals notexceeding 27 000 mm for conventional retaining wallsand abutments. All joints shall be filled with approvedfilling material to ensure the function of the joint. Joints in abutments shall be located approximately midwaybetween the longitudinal members bearing on theabutments.

11.6.2 Movement and Stability at the Service Limit State

11.6.2.1 Abutments The provisions of Articles 10.6.2.4, 10.6.2.5,

10.7.2.3 through 10.7.2.5, 10.8.2.2 through 10.8.2.4, and 11.5.2 shall apply as applicable.

11.6.2.2 Conventional Retaining Walls The provisions of Articles 10.6.2.4, 10.6.2.5,

10.7.2.3 through 10.7.2.5, 10.8.2.2 through 10.8.2.4, and 11.5.2 apply as applicable.

C11.6.2.2

For a conventional reinforced concrete retaining wall, experience suggests that differential wall settlements on the order of 1 in 500 to 1 in 1000 may overstress the wall.



11.6.2.3 Overall Stability

The overall stability of the retaining wall, retainedslope and foundation soil or rock shall be evaluated forall walls using limiting equilibrium methods of analysis.The overall stability of temporary cut slopes to facilitateconstruction shall also be evaluated. Special exploration, testing and analyses may be required for bridgeabutments or retaining walls constructed over softdeposits.

The evaluation of overall stability of earth slopeswith or without a foundation unit should be investigatedat the Service 1 Load Combination and an appropriateresistance factor. In lieu of better information, theresistance factor, φ, may be taken as:

• Where the geotechnical parameters are welldefined, and the slope does not support orcontain a structural element ........................ 0.75

• Where the geotechnical parameters are basedon limited information, or the slope contains orsupports a structural element ...................... 0.65

C11.6.2.3

Figure C11.6.2.3-1 Retaining Wall Overall Stability Failure.

Figure C1 shows a retaining wall overall stability failure. Overall stability is a slope stability issue, and, therefore, is considered a service limit state check.

The Modified Bishop, simplified Janbu or Spencer methods of analysis may be used.

Soft soil deposits may be subject to consolidation and/or lateral flow which could result in unacceptablelong-term settlements or horizontal movements.

11.6.3 Bearing Resistance and Stability at the Strength Limit State

11.6.3.1 General Abutments and retaining walls shall be proportioned

to ensure stability against bearing capacity failure,overturning, and sliding. Safety against deep-seated foundation failure shall also be investigated, inaccordance with the provisions of Article 10.6.2.5.

11.6.3.2 Bearing Resistance Bearing resistance shall be investigated at the

strength limit state using factored loads and resistances,assuming the following soil pressure distributions:

• Where the wall is supported by a soil

foundation:

the vertical stress shall be calculated assuming a uniformly distributed pressure over an effective base area as shown in Figure 1. The vertical stress shall be calculated as

follows:

2v

V B e∑

σ =−

(11.6.3.2-1)

C11.6.3.2

See Figure 11.10.10.1-1 for an example of how to calculate the vertical bearing stress where the loading is more complex. Though this figure shows the application of superposition principles to mechanically stabilized earth walls, these principles can also be directly applied to conventional walls.

See Article C11.5.5 for application of load factors for bearing resistance and eccentricity.



where: ΣV = the summation of vertical forces, and

the other variables are as defined in Figure 1

• Where the wall is supported by a rock

foundation:

the vertical stress shall be calculated assuminga linearly distributed pressure over an effectivebase area as shown in Figure 2. If the resultantis within the middle one-third of the base,

1 6vmaxV eB BΣ ⎛ ⎞σ = +⎜ ⎟

⎝ ⎠ (11.6.3.2-2)

1 6vminV e

B B∑ ⎛ ⎞σ = −⎜ ⎟

⎝ ⎠ (11.6.3.2-3)

where the variables are as defined in Figure 2. If the resultant is outside the middle one-third

of the base,

23[( / 2) )]vmax

VB e∑

σ =−

(11.6.3.2-4)

0vminσ = (11.6.3.2-5)

where the variables are as defined in Figure 2.



Where water seeps beneath a wall, the effects ofuplift and seepage forces shall be considered.

Seepage effects may be investigated by constructing a flow net, or in certain circumstances, by using generally accepted simplified methods.

11.6.3.5 Passive Resistance Passive resistance shall be neglected in stability

computations, unless the base of the wall extends belowthe depth of maximum scour, freeze-thaw or other disturbances. In the latter case, only the embedmentbelow the greater of these depths shall be considered effective.

Where passive resistance is utilized to ensureadequate wall stability, the calculated passive resistance of soil in front of abutments and conventional wallsshall be sufficient to prevent unacceptable forwardmovement of the wall.

C11.6.3.5

The passive resistance shall be neglected if the soilproviding passive resistance is, or is likely to becomesoft, loose, or disturbed, or if the contact between thesoil and wall is not tight.

Unacceptable deformations may occur before passive resistance is mobilized. Approximate deformations required to mobilize passive resistance are discussed in Article C3.11.1, where H in Table C3.11.1-1 is the effective depth of passive restraint.

11.6.3.6 Sliding The provisions of Article 10.6.3.4 shall apply.

11.6.4 Safety Against Structural Failure

The structural design of individual wall elements

and wall foundations shall comply with the provisions ofSections 5, 6, 7, and 8.

The provisions of Article 10.6.1.3 shall be used todetermine the distribution of contact pressure forstructural design of footings.

11.6.5 Seismic Design

The effect of earthquake loading on multi-span

bridges shall be investigated using the extreme event limit state of Table 3.4.1-1 with resistance factorsφ = 1.0, an accepted methodology in Article 4.7.4.3, and the provisions of Article 3.10.9.2, 3.10.9.3, or 3.10.9.4, as appropriate.

Earthquake loading on single-span bridges shall beinvestigated in accordance with Articles 4.7.4.2 and3.10.9.1.

For foundations on soil and rock, the location of theresultant of the reaction forces shall be within the middletwo-thirds of the base for γEQ = 0.0 and within themiddle eight-tenths of the base for γEQ = 1.0.

C11.6.5 In general, the pseudo-static approach developed by

Mononobe and Okabe may be used to estimate the equivalent static forces for seismic loads for gravity and semigravity retaining walls. The estimation of seismic design forces should account for wall inertia forces in addition to the equivalent static-forces. For flexible cantilevered walls, forces resulting from wall inertia effects may be ignored in estimating the seismic design forces. Where a wall supports a bridge structure, the seismic design forces should also include seismic forces transferred from the bridge through bearing supports which do not freely slide, e.g., elastomeric bearings. Refer to Appendix A11.



For values of γEQ between 0.0 and 1.0, therestrictions of the location of the resultant shall beobtained by linear interpolation of the values given inthis Article.

Where all of the following conditions are met, seismic lateral loads may be reduced as provided in Article C11.6.5, as a result of lateral wall movement dueto sliding, from values determined using the Mononobe-Okabe method specified in Appendix A11, Article A11.1.1.1:

• the wall system and any structures supported by

the wall can tolerate lateral movement resultingfrom sliding of the structure.

• the wall base is unrestrained against sliding,other than soil friction along its base andminimal soil passive resistance.

• If the wall functions as an abutment, the top ofthe wall must also be unrestrained, e.g., the superstructure is supported by sliding bearings.

For overall stability of the retaining wall whenearthquake loading is included, a resistance factor, φ , of 0.9 shall be used.

Procedures reducing seismic load due to lateral wall movement are provided in Article A11.1.1.2. In general, this reduction only applies to gravity and semigravity walls. Though the specifications in Article A11.1.1.2 relate to gravity and semigravity walls, these provisions may also apply to other types of walls provided the threeconditions listed in Article 11.6.5 are met.

Kavazanjian et al. (1997) further simplified the relationship provided in Eq. A11.1.1.2-1 of Appendix A11 as follows, assuming that the velocity, in the absence of information on the time history of the ground motion, is equal to 30A:

0.251.66hAk Ad

⎛ ⎞= ⎜ ⎟⎝ ⎠ (C11.6.5-1)

where: A = the maximum earthquake acceleration (dim.) kh = horizontal seismic acceleration coefficient

(dim.) d = the lateral wall displacement (mm)

This equation should not be used for displacements of less than 25 mm or greater than approximately 200 mm, as this equation is an approximation of a more rigorous Newmark analysis. In general, typical practice among states located in seismically active areas is to design walls for reduced seismic pressures corresponding to 50 mm to 100 mm of displacement. However, the amount of deformation which is tolerable will depend on the nature of the wall and what it supports, as well as what is in front of the wall.

In addition to whether or not the wall can tolerate lateral deformation, it is recommended that this simplified approach not be used for walls which have a complex geometry, such as stacked walls, MSE walls with trapezoidal sections, or back-to-back walls supporting narrow ramps, for walls which are very tall (over 15 000 mm), nor for walls where the peak ground acceleration A is 0.3g or higher. In such cases, a specialist should be retained to evaluate the anticipated deformation response of the structure, as potentially unacceptable permanent lateral and vertical wall deformations could occur even if design criteria based on this pseudo static approach are met.

11.6.6 Drainage

Backfills behind abutments and retaining walls shall

be drained or, if drainage cannot be provided, theabutment or wall shall be designed for loads due to earthpressure, plus full hydrostatic pressure due to water inthe backfill.

C11.6.6 Weep holes or geocomposite panel drains at the

wall face do not assure fully drained conditions. Drainage systems should be designed to completely drain the entire retained soil volume behind the retaining wall face.



The presumptive ultimate anchor bond stress values presented in Tables C1 through C3 are intended for preliminary design or evaluation of the feasibility of straight shaft anchors installed in small diameter holes. Pressure-grouted anchors may achieve much higher capacities. The total capacity of a pressure-grouted anchor may exceed 2×106 N in soil or 9×106 to 13×106 N in rock, although such high capacity anchors are seldom used for highway applications. Post-grouting can also increase the load carrying capacity of straight shaft anchors by 20–50 percent or more per phase of post-grouting.

The resistance factors in Table 11.5.6-1, in combination with the load factor EH for apparent earth pressure for anchored walls (Table 3.4.1-2), are consistent with what would be required based on allowable stress design, for preliminary design of anchors for pullout (Sabatini et al., 1999). These resistance factors are also consistent with the results of statistical calibration of full scale anchor pullout tests relative to the minimum values of presumptive ultimate unit bond stresses shown in Tables C1 through C3. Use of the resistance factors in Table 11.5.6-1 and the load factor for apparent earth pressure for anchor walls in Table 3.4.1-2, with values of presumptive ultimate unit bond stresses other than the minimum values inTables C1 through C3 could result in unconservative designs unless the Engineer has previous experience with the particular soil or rock unit in which the bond zone will be established.

Presumptive bond stresses greater than the minimum values shown in Tables C1 through C3 should be used with caution, and be based on past successful local experience, such as a high percentage of passing proof tests in the specified or similar soil or rock unit at the design bond stress chosen, or anchor pullout test results in the specified or similar soil or rock unit. Furthermore, in some cases the specified range of presumptive bond stresses is representative of a range of soil conditions. Soil conditions at the upper end of the specified range, especially if coupled with previous experience with the particular soil unit, may be considered in the selection of anchor bond stresses above the minimum values shown. Selection of a presumptive bond stress for preliminary anchor sizing should consider the risk of failing proof tests if the selected bond stress was to be used for final design. The goal of preliminary anchor design is to reduce the risk of having a significant number of production anchors fail proof or performance tests as well as the risk of having to redesign the anchored wall to accommodate more anchors due to an inadequate easement behind the wall, should the anchor capacities predicted during preliminary design not be achievable.

See Article 11.9.8.1 for guidance on anchor testing.



Significant increases in anchor capacity for anchor bond lengths greater than approximately 12 000 mm cannot be achieved unless specialized methods are used to transfer load from the top of the anchor bond zone towards the end of the anchor. This is especially critical for strain sensitive soils, in which residual soil strength is significantly lower than the peak soil strength.

The anchor load shall be developed by suitableembedment outside of the critical failure surface in theretained soil mass.

Determination of the unbonded anchor length,inclination, and overburden cover shall consider:

• The location of the critical failure surfacefurthest from the wall,

• The minimum length required to ensure minimal loss of anchor prestress due to long-term ground movements,

• The depth to adequate anchoring strata, asindicated in Figure 11.9.1-1, and

• The method of anchor installation and grouting.

Anchor inclination and spacing will be controlled by soil and rock conditions, the presence of geometric constraints and the required anchor capacity. For tremie-grouted anchors, a minimum angle of inclination of about 10° and a minimum overburden cover of about 4500 mm are typically required to assure grouting of the entire bonded length and to provide sufficient ground cover above the anchorage zone. For pressure-grouted anchors, the angle of inclination is generally not critical and is governed primarily by geometric constraints, and the minimum overburden cover is typically 1800–4500 mm. Steep inclinations may be required to avoid anchorage in unsuitable soil or rock. Special situations may require horizontal or near horizontal anchors, in which case proof of sufficient overburden and full grouting should be required.

The minimum horizontal spacing of anchors shouldbe the larger of three times the diameter of the bondedzone, or 1500 mm. If smaller spacings are required todevelop the required load, consideration may be given todiffering anchor inclinations between alternatinganchors.

The minimum horizontal spacing specified for anchors is intended to reduce stress overlap between adjacent anchors.

Anchors used for walls constructed in fill situations, i.e., bottom-up construction, should be enclosed in protective casing to prevent damage during backfill placement, compaction and settlement.

Selection of anchor type depends on anticipated service life, soil and rock conditions, ground water level, subsurface environmental conditions, and method of construction.

11.9.4.3 Passive Resistance The provisions of Articles 11.6.3.5, 11.6.3.6, and

11.8.4.1 shall apply.

C11.9.4.3 It is recommended in Sabatini et al. (1999) that

methods such as the Broms Method or the Wang and Reese method be used to evaluate passive resistance andthe wall vertical element embedment depth needed. However, these methods have not been calibrated for this application for LRFD as yet.



Figure 11.10.10.4-1 Structural Connection of Soil Reinforcement Around Backfill Obstructions. 11.10.11 MSE Abutments

Abutments on MSE walls shall be proportioned tomeet the criteria specified in Article 11.6.2 through11.6.6.

The MSE wall below the abutment footing shall bedesigned for the additional loads imposed by the footingpressure and supplemental earth pressures resulting fromhorizontal loads applied at the bridge seat and from the backwall. The footing load may be distributed asdescribed in Article 11.10.10.1.

The factored horizontal force acting on thereinforcement at any reinforcement level, Tmax, shall be taken as:

max Hmax vT S= σ (11.10.11-1) where: σHmax = factored horizontal stress at layer i, as

defined by Eq. 2 (MPa) Sv = vertical spacing of reinforcement (mm)

Horizontal stresses in abutment reinforced zonesshall be determined by superposition as follows, and asspecified in Article 11.10.10.1:

( )Hmax p v r v r Hk kσ = γ σ + Δσ + Δσ (11.10.11-2) where: γp = load factor for vertical earth pressure in

Table 3.4.1-2

C11.10.11



ΔσH = magnitude of lateral pressure due tosurcharge (MPa)

σv = vertical soil stress over effective base

width (B−2e) (MPa) Δσv = vertical soil stress due to footing load

(MPa) kr = earth pressure coefficient varying as a

function of ka as specified inArticle 11.10.6.2.1

ka = active earth pressure coefficient specified

in Article 3.11.5.8

The effective length used for calculations of internal

stability under the abutment footing shall be asdescribed in Article 11.10.10.1 and Figure 11.10.10.1-2.

The minimum distance from the centerline of thebearing on the abutment to the outer edge of the facingshall be 1070 mm. The minimum distance between theback face of the panel and the footing shall be 150 mm.

Where significant frost penetration is anticipated,the abutment footing shall be placed on a bed ofcompacted coarse aggregate 900 mm thick as describedin Article 11.10.2.2.

The density, length, and cross-section of the soilreinforcements designed for support of the abutmentshall be carried on the wingwalls for a minimumhorizontal distance equal to 50 percent of the height ofthe abutment.

In pile or drilled shaft supported abutments, thehorizontal forces transmitted to the deep foundationelements shall be resisted by the lateral capacity of thedeep foundation elements by provision of additionalreinforcements to tie the drilled shaft or pile cap into thesoil mass, or by batter piles. Lateral loads transmittedfrom the deep foundation elements to the reinforcedbackfill may be determined using a P-Y lateral loadanalysis technique. The facing shall be isolated fromhorizontal loads associated with lateral pile or drilled shaft deflections. A minimum clear distance of 460 mmshall be provided between the facing and deepfoundation elements. Piles or drilled shafts shall bespecified to be placed prior to wall construction andcased through the fill if necessary.

The minimum length of reinforcement, based on experience, has been the greater of 6700 mm or 0.6 (H + d) + 2000 mm. The length of reinforcement should be constant throughout the height to limit differential settlements across the reinforced zone. Differential settlements could overstress the reinforcements.

The permissible level of differential settlement at abutment structures should preclude damage to superstructure units. This subject is discussed in Article 10.6.2.2. In general, abutments should not be constructed on mechanically stabilized embankments if anticipated differential settlements between abutments or between piers and abutments are greater than one-half the limiting differential settlements described in Article C10.5.2.2.

The equilibrium of the system should be checked ateach level of reinforcement below the bridge seat.

Due to the relatively high bearing pressures near thepanel connections, the adequacy and ultimate capacityof panel connections should be determined byconducting pullout and flexural tests on full-sized panels.

Moments should be taken at each level under consideration about the centerline of the reinforced mass to determine the eccentricity of load at each level. A uniform vertical stress is then calculated using afictitious width taken as (B−2e), and the corresponding horizontal stress should be computed by multiplying by the appropriate coefficient of lateral earth pressure.


SECTION 12 (SI)

BURIED STRUCTURES AND TUNNEL LINERS

12-1

12.1 SCOPE This Section provides requirements for the selection

of structural properties and dimensions of buriedstructures, e.g., culverts, and steel plate used to supporttunnel excavations in soil.

Buried structure systems considered herein aremetal pipe, structural plate pipe, long-span structural plate, structural plate box, reinforced concrete pipe,reinforced concrete cast-in-place and precast arch, boxand elliptical structures, and thermoplastic pipe.

The type of liner plate considered is cold-formed steel panels.

C12.1 For buried structures, refer to Article 2.6.6 for

hydraulic design considerations and FHWA (1985) for design methods related to location, length, and waterway openings.

12.2 DEFINITIONS

Abrasion—Loss of section or coating of a culvert by the mechanical action of water conveying suspended bed load of sand, gravel, and cobble-size particles at high velocities with appreciable turbulence. Buried Structure—A generic term for a structure built by embankment or trench methods. Corrosion—Loss of section or coating of a buried structure by chemical and/or electrochemical processes. Culvert—A curved or rectangular buried conduit for conveyance of water, vehicles, utilities, or pedestrians. FEM—Finite Element Method Narrow Trench Width—The outside span of rigid pipe, plus 300 mm. Projection Ratio—Ratio of the vertical distance between the outside top of the pipe and the ground or bedding surface to the outside vertical height of the pipe, applicable to reinforced concrete pipe only. Soil Envelope—Zone of controlled soil backfill around culvert structure required to ensure anticipated performance based on soil-structure interaction considerations. Soil-Structure Interaction System—A buried structure whose structural behavior is influenced by interaction with the soil envelope. Tunnel—A horizontal or near horizontal opening in soil excavated to a predesigned geometry by tunneling methods exclusive of cut-and-cover methods.

12.3 NOTATION

A = wall area (mm2/mm) (12.7.2.3) Aeff = effective wall area (mm2/mm) (12.12.3.5.2) Ag = gross wall area within a length of one period (mm2) (12.12.3.5.3c) AL = axle load, taken as 50 percent of all axle loads that can be placed on the structure at one time (N); sum of

all axle loads in an axle group (N); total axle load on single axle or tandem axles (N) (12.8.4.2) (12.9.4.2) (12.9.4.3)

As = tension reinforcement area (mm2/mm) (C12.10.4.2.4a) (C12.11.3) (C12.11.4) Asmax = minimum flexural reinforcement area without stirrups (mm2/mm) (12.10.4.2.4c) AT = area of the top portion of the structure above the springline (mm2) (12.8.4.2) Avr = stirrup reinforcement area to resist radial tension forces on cross-section of unit width in each line of

stirrups at circumferential spacing, sv (mm2/mm) (12.10.4.2.6) Avs = required area of stirrups for shear reinforcement (mm2/mm) (12.10.4.2.6)



B = width of culvert (mm) (C12.6.2.2.4) B′ = nonuniform stress distribution factor (12.12.3.5.2) Bc = outside diameter or width of the structure (mm) (12.6.6.3) B′c = out-to-out vertical rise of pipe (mm) (12.6.6.3) Bd = horizontal width of trench at top of pipe (mm) (12.11.2.2) BFE = earth load bedding factor (12.10.4.3.1) BFLL = live load bedding factor (12.10.4.3.1) B1 = crack control coefficient for effect of cover and spacing of reinforcement (C12.10.4.2.4d) b = element effective width (mm) (12.10.4.2.4c) (12.12.3.5.3c) CA = constant corresponding to the shape of the pipe (12.10.4.3.2a) Cc = load coefficient for positive pipe projection (12.10.4.3.2a) Cd = load coefficient for trench installation (12.11.2.2) Cdt = load coefficient for tunnel installation (12.13.2.1) CH = adjustment factor for shallow cover heights over metal box culverts (12.9.4.4) CL = live load distribution coefficient (12.12.3.4) Cℓℓ = live load adjusted for axle loads, tandem axles, and axles with other than four wheels; C1 C2 AL (N)

(12.9.4.2) CN = parameter that is a function of the vertical load and vertical reaction (12.10.4.3.2a) Cs = construction stiffness for tunnel liner plate (N/mm) (12.5.6.4) C1 = 1.0 for single axles and 0.5 + S/15 000 ≤ 1.0 for tandem axles; adjustment coefficient for number of

axles; crack control coefficient for various types of reinforcement (12.9.4.2) (12.9.4.3) (C12.10.4.2.4d) C2 = adjustment factor for number of wheels on a design axle as specified in Table 12.9.4.2-1; adjustment

coefficient for number of wheels per axle (12.9.4.2) (12.9.4.3) c = distance from inside face to neutral axis of thermoplastic pipe (mm); distance from inside surface to

neutral axis (mm); distance from neutral axis to extreme fiber (mm) (12.12.3.6) (12.12.3.5.2) (12.12.3.5.4b)

D = straight leg length of haunch (mm); pipe diameter (mm); required D-load capacity of reinforced concrete pipe (N/mm); diameter to centroid of pipe wall (mm) (12.9.4.1) (12.6.6.2) (12.10.4.3.1) (12.12.3.5.4b)

D-load = resistance of pipe from three-edge bearing test load to produce a 0.25-mm crack (N/mm) (12.10.4.3) De = effective diameter of thermoplastic pipe (mm) (12.12.3.6) Df = shape factor (12.12.3.5.4b) Di = inside diameter of pipe (mm) (12.10.4.3.1) Do = outside diameter of pipe (mm) (12.12.3.4) d = required envelope width adjacent to the structure (mm); distance from compression face to centroid of

tension reinforcement (mm) (12.8.5.3) (12.10.4.2.4a) (C12.11.3) d′ = width of warped embankment fill to provide adequate support for skewed installation (mm) (C12.6.8.2) d1 = distance from the structure (mm) (12.8.5.3) E = modulus of elasticity of the plastic (MPa) (12.12.3.3) Em = modulus of elasticity of metal (MPa) (12.7.2.4) E(x) = lateral unbalanced distributed load on culvert below sloping ground and skewed at end wall (N)

(C12.6.2.2.4) E50 = 50-year modulus of elasticity (MPa) (12.12.3.5.3c) F = concentrated load acting at the crown of a culvert (N) (C12.6.2.2.5) Fc = curvature correction factor (12.10.4.2.5) Fcr = factor for adjusting crack control relative to average maximum crack width of 0.25 mm corresponding to

Fcr = 1.0 (12.10.4.2.4d) Fd = factor for crack depth effect resulting in increase in diagonal tension, shear, and strength with decreasing

d (12.10.4.2.5) Fe = soil-structure interaction factor for embankment installations (12.10.2.1) FF = flexibility factor (mm/N) (12.5.6.3) (12.7.2.6) Fn = coefficient for effect of thrust on shear strength (12.10.4.2.5) Frp = factor for process and local materials affecting radial tension strength of pipe (12.10.4.2.3) Frt = factor for pipe size effect on radial tension strength (12.10.4.2.4c) Ft = soil-structure interaction factor for trench installations (12.10.2.1) Fu = specified minimum tensile strength (MPa) (12.7.2.4) Fvp = factor for process and local materials that affect the shear strength of the pipe (12.10.4.2.3) Fy = yield strength of metal (MPa) (12.7.2.3) f′c = compressive strength of concrete (MPa) (12.4.2.2)


SECTION 12 (SI): BURIED STRUCTURES AND TUNNEL LINERS 12-5

γp = maximum load factor for permanent load resulting from Vertical Earth Pressure (EV) for the case of flexible buried structures other than metal box culverts, specified in Table 3.4.1-2

γs = density of backfill (kg/m3); soil density (kg/m3) (C12.9.2) (12.9.4.2) γw = density of water (kg/m3) (12.12.3.4) γWA = load factor for hydrostatic pressure (12.12.3.4) Δ = return angle of the structure (°); haunch radius included angle (°); allowable deflection of pipe, reduction

of vertical diameter due to bending (mm) (12.8.4.2) (12.9.4.1) (12.12.3.5.4b) εbu = factored bending strain = γB εb (mm/mm) (12.12.3.5.4a) εtt = factored long-term tension strain (mm/mm) (12.12.3.5.4a) εt = allowable tension strain (12.12.3.5.4a) ηEV = load modifier, specified in Article 1.3.2, as they apply to vertical earth loads on culverts (12.12.3.4) ηLL = load modifier as they apply to live loads on culverts (12.12.3.4) λ = slenderness factor (12.12.3.5.3c) μ = coefficient of friction between the pipe and soil (12.10.2.1) ρ = effective width factor (12.12.3.5.3c) φ = resistance factor (12.5.1) φf = resistance factor for flexure (12.10.4.2.4c) φfs = coefficient of friction between the fill material and the sides of the trench (12.10.4.3.2a) φr = resistance factor for radial tension (12.10.4.2.4c) φs = resistance factor for soil stiffness, φs = 0.9 (12.12.3.4) Ψ = central angle of pipe subtended by assumed distribution of external reactive force (°) (12.10.4.2.1) ω = spacing of corrugation (mm) (12.12.3.5.3c)

12.4 SOIL AND MATERIAL PROPERTIES

12.4.1 Determination of Soil Properties

12.4.1.1 General Subsurface exploration shall be carried out to

determine the presence and influence of geologic andenvironmental conditions that may affect theperformance of buried structures. For buried structuressupported on footings and for pipe arches and largediameter pipes, a foundation investigation should beconducted to evaluate the capacity of foundationmaterials to resist the applied loads and to satisfy themovement requirements of the structure.

C12.4.1.1 The following information may be useful for

design: • Strength and compressibility of foundation

materials;

• Chemical characteristics of soil and surface waters, e.g., pH, resistivity, and chloride content of soil and pH, resistivity, and sulfate content of surface water;

• Stream hydrology, e.g., flow rate and velocity, maximum width, allowable headwater depth, and scour potential; and

• Performance and condition survey of culverts in the vicinity.

12.4.1.2 Foundation Soils The type and anticipated behavior of the foundation

soil shall be considered for stability of bedding andsettlement under load.

C12.4.1.2 Refer to Article 10.4 for general guidance regarding

foundation soil properties. The performance of rigid pipes is dependent on foundation and bedding stability.



12.4.1.3 Envelope Backfill Soils The type, compacted density and strength properties

of the soil envelope adjacent to the buried structure shallbe established. The backfill soils comprising the soilenvelope shall conform to the requirements of AASHTOM 145 as follows:

• For standard flexible pipes and concretestructures: A-1, A-2, or A-3 (GW, GP, SW, SP,GM, SM, SC, GC),

• For metal box culverts and long-span structures with cover less than 3600 mm: A-1, A-2-4, A-2-5, or A-3 (GW, GP, SW, SP, GM, SM, SC,GC), and

• For long-span metal structures with cover notless than 3600 mm: A-1 or A-3 (GW, GP, SW,SP, GM, SM).

C12.4.1.3 Refer to Sections 26 and 27, AASHTO LRFD

Bridge Construction Specifications, for compaction criteria of soil backfill for flexible and rigid culverts, respectively.

Wall stresses in buried structure are sensitive to the relative stiffness of the soil and pipe. Buckling stability of flexible culverts is dependant on soil stiffness.

In the selection of a type of backfill for the envelope, the quality of the material and its suitability for achieving the requirements of the design should be considered. The order of preference for selecting envelope backfill based on quality may be taken as follows:

• Angular, well-graded sand and gravel;

• Nonangular, well-graded sand and gravel;

• Flowable materials, e.g., cement-soil-fly ash mixtures, which result in low density/low strength backfill, for trench applications only;

• Uniform sand or gravel, provided that placement is confirmed to be dense and stable, but which may require a soil or geofabric filter to prevent the migration of fines;

• Clayey sand or gravel of low plasticity; and

• Stabilized soil, which should be used only under the supervision of an Engineer familiar with the behavior of the material.

12.4.2 Materials 12.4.2.1 Aluminum Pipe and Structural Plate Structures Aluminum for corrugated metal pipe and

pipe-arches shall comply with the requirements ofAASHTO M 196 (ASTM B 745M). Aluminum forstructural plate pipe, pipe-arch, arch, and box structuresshall meet the requirements of AASHTO M 219 (ASTMB 746M).

12.4.2.2 Concrete Concrete shall conform to Article 5.4, except that f′c

may be based on cores.

12.4.2.3 Precast Concrete Pipe Precast concrete pipe shall comply with the

requirements of AASHTO M 170M (ASTM C 76M) and M 242M (ASTM C 655M). Design wall thickness,other than the standard wall dimensions, may be used,provided that the design complies with all applicablerequirements of this Section.



12.13.2 Loading The provisions for earth loads given in

Article 3.11.5 shall not apply to tunnels.

C12.13.2 The earth load to be carried by the tunnel liner is a

function of the type of soil. In granular soil with little or no cohesion, the load is a function of the angle of internal friction of the soil and the diameter of the tunnel. In cohesive soils such as clays, the load to be carried by the tunnel liner is dependent on the shearing strength of the soil above the roof of the tunnel.

12.13.2.1 Earth Loads The provisions of Article 12.4.1 shall apply. When

more refined methods of soil analysis are not employed,the earth pressure may be taken as:

910E dt sW = gC S −×γ (12.13.2.1-1)

where: g = acceleration of gravity (m/sec.2) Cdt = load coefficient for tunnel installation specified

in Figure 1 γs = total density of soil (kg/m3)

C12.13.2.1 Eq. 1 is a form of the Marston formula. It

proportions the amount of total overburden pressure acting on the tunnel based on the internal friction angle of the soil to be tunneled.

In the absence of adequate borings and soil tests, use φf = 0 when calculating WE.

WE = earth pressure at the crown (MPa) S = tunnel diameter or span (mm)

Figure 12.13.2.1-1 Diagram for Coefficient Cdt for Tunnel in Soil.

in which:

H = height of soil over top of tunnel (mm)



12.13.2.2 Live Loads The provisions of Article 12.6.1 shall apply. 12.13.2.3 Grouting Pressure If the grouting pressure is greater than the computed

design load, the design load, WT, on the tunnel liner shallbe the grouting pressure.

12.13.3 Safety Against Structural Failure

12.13.3.1 Section Properties Steel tunnel liner plate shall meet the minimum

requirements of Table 1 for cross-sectional properties,Table 2 for seam strength, and Table 3 for mechanicalproperties.

12.13.3.2 Wall Area The requirements of Articles 12.7.2.2 and 12.7.2.3

shall apply using effective area from Table 12.13.3.1-1.

12.13.3.3 Buckling The requirements of Articles 12.13.2.2 and 12.7.2.4

shall apply, except that the soil stiffness factor, k, may vary from 0.22 to 0.44 depending upon the quality andextent of the backpacking material used.

C12.13.3.3 Wall buckling is a function of the stiffness, k, of the

surrounding soil bearing on the plates. Where portland cement grouting or quality backpacking (meeting the requirements of Section 25, “Steel and Concrete Tunnel Liners,” AASHTO LRFD Bridge Construction Specifications) material fill the void outside the plates, k = 0.22 is applicable. For other soils or in-situ backpacking material, k = 0.44 is suggested. Where tunneled soils slough or voids are left in the backpacking, additional consideration as to the value of k may be required.

12.13.3.4 Seam Strength The requirements of Article 12.7.2.5 shall apply.

12.13.3.5 Construction Stiffness Construction stiffness shall be indicated by a

construction stiffness factor as:

2SEICS

= (12.13.3.5-1)

where:

S = diameter or span (mm) E = modulus of elasticity (MPa) I = moment of inertia (mm4/mm)

The value of CS from Eq. 1 shall not be less than the

values for steel tunnel liner plate as given inArticle 12.5.6.4.

C12.13.3.5 The liner plate ring should have sufficient rigidity to

resist the unbalanced loads of normal construction from grouting, local slough-ins, and miscellaneous concentrated loads.

The minimum construction stiffness required for these loads, CS, can be expressed for convenience by the formula below. It must be recognized, however, that the limiting values given here are only recommended minimums. Actual job conditions may require greater effective stiffness. Final determination of this factor should be based on intimate knowledge of the project and on practical experience.

The construction stiffness, CS, given by Eq. 1,considers the moment of inertia of an individual plate.



12.14.5.2 Distribution of Concentrated Load Effects in Top Slab and Sides Distribution of wheel loads and concentrated loads

for the top slab and sides of three-sided structures withless than 600 mm of fill shall be taken as specified inArticle 12.11.2.1.

Distribution of wheel loads and concentrated loadsfor the top slab and sides for three-sided structures withdepths of fill 600 mm or greater shall be taken asspecified in Article 3.6.1.2.6.

12.14.5.3 Distribution of Concentrated Loads in Skewed Culverts Wheel loads on skewed culverts shall be distributed

using the same provisions as given for culverts withmain reinforcement parallel to traffic. For culvertelements with skews greater than 15°, the effect of theskew shall be considered in analysis.

12.14.5.4 Shear Transfer in Transverse Joints Between Culvert Sections Shear keys shall be provided in the top surface of

the structures between precast units having flat topsunder shallow cover.

C12.14.5.4 Flat top structures with shallow cover may

experience differential deflection of adjacent units, which can cause pavement cracking if a shear key is not utilized.

12.14.5.5 Span Length When monolithic haunches inclined at 45° are taken

into account, negative reinforcement in walls and slabsmay be proportioned on the basis of bending moment atthe intersection of the haunch and uniform depthmember.

12.14.5.6 Resistance Factors The provisions of Articles 5.5.4.2 and 1.3.1 shall

apply as appropriate.

12.14.5.7 Crack Control The provisions of Article 5.7.3.4 for buried

structures shall apply.

12.14.5.8 Minimum Reinforcement The provisions of Article 5.10.8 shall not be taken

to apply to precast three-sided structures. The primary flexural reinforcement in the direction

of the span shall provide a ratio of reinforcement area togross concrete area at least equal to 0.002. Such minimum reinforcement shall be provided at all cross-sections subject to flexural tension, at the inside face ofwalls, and in each direction at the top of slabs of three-sided sections with less than 600 mm of fill.



12.14.5.9 Deflection Control at the Service Limit State The deflection limits for concrete structures

specified in Article 2.5.2.6.2 shall be taken as mandatoryand pedestrian usage as limited to urban areas.

12.14.5.10 Footing Design Design shall include consideration of differential

horizontal and vertical movements and footing rotations. Footing design shall conform to the applicable Articles in Sections 5 and 10.

12.14.5.11 Structural Backfill Specification of backfill requirements shall be

consistent with the design assumptions used. The contract documents should require that a minimumbackfill compaction of 90 percent Standard ProctorDensity be achieved to prevent roadway settlementadjacent to the structure. A higher backfill compactiondensity may be required on structures utilizing a soil-structure interaction system.

12.14.5.12 Scour Protection and Waterway Considerations The provisions of Article 2.6 shall apply as

appropriate.


SECTION 14 (SI): JOINTS AND BEARINGS 14-27

φ A tension = 0.85 φ A shear = 0.85 • For anchors governed by the concrete, the load

factors for Condition B, no supplementalreinforcement, are:

φ B tension = 0.75 φ B shear = 0.75

14.5.6.9.7 Fatigue Limit State Design Requirements

14.5.6.9.7a General

MBJS structural members, including centerbeams,

support bars, connections, bolted and welded splices, andattachments, shall meet the fracture toughnessrequirements in Article 6.6.2. Bolts subject to tensilefatigue shall satisfy the provisions of Article 6.13.2.10.3.

MBJS structural members, including centerbeams,support bars, connections, bolted and welded splices, andattachments, shall be designed for fatigue as specified inArticle 6.6.1.2 and as modified and supplemented herein.

Each detail shall satisfy:

12 THf FΔ = Δ (14.5.6.9.7a-1)

where: Δf = force effect, live load stress range due to the

simultaneous application of vertical andhorizontal axle loads specified inArticle14.5.6.9.4 and distributed as specifiedin Article 14.5.6.9.5, and calculated asspecified in Article 14.5.6.9.7b (MPa)

ΔFTH = constant amplitude fatigue threshold taken

from Table 6.6.1.2.5-3 for the detail categoryof interest (MPa)

The fatigue detail categories for the centerbeam-to-support-bar connection, shop splice, field splice, or othercritical details shall be established by the fatigue testing as required by Article 14.5.6.9.3. All other details shall havebeen included in the test specimen. Details that did notcrack during the fatigue test shall be considerednoncritical. The fatigue detail categories for noncriticaldetails shall be determined using Figure 6.6.1.2.3-1 and Table 6.6.1.2.3-1.

C14.5.6.9.7a

The fatigue strength of particular details in aluminum are approximately one-third the fatigue strength of the same details in steel and, therefore, aluminum is typically not used in MBJS.

Yield strength and fracture toughness and weld quality have not been noted as particular problems for MBJS.

The design of the MBJS will typically be governed by the stress range at fatigue critical details. Static strength must also be checked according to the requirements of Article 14.5.6.9.6, but will typically not govern the design unless the total opening range and the support bar span is very large. Alternate design methods and criteria may be used if such methods can be shown through testing and/or analysis to yield fatigue-resistant and safe designs. Thetarget reliability level for fatigue is 97.5 percent probability of no fatigue cracks over the lifetime of the MBJS.

Provisions are not included for a finite life fatigue design. Typically, most structures that require a modular expansion joint carry enough truck traffic to justify an infinite-life fatigue design approach. Furthermore, uncertainty regarding the number of axles per truck and the number of fatigue cycles per axle would make a finite life design approach difficult. Furthermore, little cost is added to the MBJS by designing for infinite fatigue life.

Division of the constant-amplitude fatigue limit, CAFL, by two is consistent with the fatigue provisions in Article 6.6.1.2.5. This reduction recognizes that, because of the shape of typical truck weight spectra, the fatigue design axle load is approximately one-half of the limit-state fatigue axle load and as such should be compared to one-half the fatigue threshold. The intent of this procedure is to assure that the stress range from the fatigue limit-state load range is less than the CAFL and thereby ensuring essentially an infinite fatigue life.

Fatigue-critical MBJS details include:



Anchors and edgebeams shall be investigated forfatigue considering the force effects from vertical andhorizontal wheel loads. Shear connectors and otheranchors shall be designed for fatigue to resist the verticalwheel loads according to the provisions ofArticle 6.10.10.2. The force effects from the horizontalwheel loads need not be investigated for standard weldedheaded anchors.

Edgebeams shall be at least 9 mm thick. Edgebeamswith standard welded headed anchors spaced at most every300 mm need not be investigated for in-plane bending forfatigue.

• the connection between the centerbeams and the support bars;

• connection of any attachments to the centerbeams (e.g., horizontal stabilizers or outriggers); and

• shop and/or field splices in the centerbeams.

MBJS details can in many cases be clearly associated with analogous details in the bridge design specifications. In other cases, the association is not clear and must be demonstrated through full-scale fatigue testing.

The detail of primary concern is the connection between the centerbeams and the support bars. A typical full-penetration welded connection, which was shown previously, can be associated with Category C. Fillet welded connections have very poor fatigue resistance and should not be allowed.

Bolted connections should be classified as a Category D detail, with respect to the bending stress range in the centerbeam. As in any construction, more than one bolt must be used in bolted connections.

The bolted connections in single-support-bar MBJS usually involve a yoke or stirrup through which the support bar slides and/or swivels. Field-welded splices of the centerbeams and edgebeams are also prone to fatigue. In new construction, it may be possible to make a full-penetration welded splice in the field before the joint is lowered into the blockout. However, in reconstruction work, the joint is often installed in several sections at a time to maintain traffic. In these cases, the splice must be made after the joint is installed. Because of the difficulty in access and position, obtaining a full-penetration butt weld in the field after the joint is installed may be impossible, especially if there is more than one centerbeam. Partial-penetration splice joints have inherently poor fatigue resistance and should not be allowed.

Bolted splices have been used and no cracking of these bolted splice details has been reported. The bolted splice plates behave like a hinge, i.e., they do not take bending moments. As a result, such details are subjected only to small shear stress ranges and need not be explicitly designed for fatigue. However, the hinge in the span creates greater bending moments at the support bar connection, therefore, the span with the field splice must be much smaller than the typical spans to reduce the applied stress ranges at the support bar connection.


SECTION 14 (SI): JOINTS AND BEARINGS 14-41

Rockers should be avoided wherever practical and,when used, their movements and tendency to tip underseismic actions shall be considered in the design anddetails.

Rockers can be suitable for applications in which the horizontal movement of the superstructure, relative to the substructure, is well within the available movement range after consideration of other applicable movements. This might be the case, for example, in Seismic Zone 1, where bridges are founded on rock or stiff competent soils.

14.7.1.2 Materials

Rocker and roller bearings shall be made of stainless

steel conforming to ASTM A 240M, as specified inArticle 6.4.7, or of structural steel conforming toAASHTO M 169 (ASTM A 108), M 102 (ASTM A 668M), or M 270M (ASTM A 709M), Grades 250, 345or 345W. Material properties of these steels shall be takenas specified in Table 6.4.1-1 and Table 6.4.2-1.

C14.7.1.2

Carbon steel has been the traditional steel used in mechanical bearings because of its good mechanical properties. Surface hardening may be considered. Corrosion resistance is also important. The use of stainless steel for the contact surfaces may prove economical when life-cycle costs are considered. Weathering steels should be used with caution as their resistance to corrosion is often significantly reduced by mechanical wear at the surface.

14.7.1.3 Geometric Requirements

The dimensions of the bearing shall be chosen takinginto account both the contact stresses and the movement ofthe contact point due to rolling.

Each individual curved contact surface shall have aconstant radius. Bearings with more than one curvedsurface shall be symmetric about a line joining the centersof their two curved surfaces.

If pintles or gear mechanisms are used to guide thebearing, their geometry should be such as to permit freemovement of the bearing.

C14.7.1.3

The choice of radius for a curved surface is a compromise: a large radius results in low contact stresses but large rotations of the point of contact and vice versa. The latter could be important if, for example, a rotational bearing is surmounted by a PTFE slider because the PTFE is sensitive to eccentric loading.

Bearings shall be designed to be stable. If the bearing has two separate cylindrical faces, each of which rolls on aflat plate, stability may be achieved by making thedistance between the two contact lines no greater than thesum of the radii of the two cylindrical surfaces.

A cylindrical roller is in neutral equilibrium. The provisions for bearings with two curved surfaces achieves at least neutral, if not stable, equilibrium.

14.7.1.4 Contact Stresses

At the service limit state, the contact load, PS, shall satisfy:

• For cylindrical surfaces:

2

1

1

2

8

1

yS

s

FWDP

ED D

⎛ ⎞≤ ⎜ ⎟⎜ ⎟⎛ ⎞ ⎝ ⎠−⎜ ⎟⎝ ⎠

(14.7.1.4-1)

• For spherical surfaces:

C14.7.1.4

The service limit state loads are limited so that the contact causes calculated shear stresses no higher than 0.55 Fy or surface compression stresses no higher than 1.65 Fy. The maximum compressive stress is at the surface, and the maximum shear stress occurs just below it.

The formulas were derived from the theoretical value for contact stress between elastic bodies (Roark and Young, 1976). They are based on the assumption that the width of the contact area is much less than the diameter of the curved surface.

If two surfaces have curves of the opposite sign, the value of D2 is negative. This would be an unusual situation in bridge bearings.



2

31

21

2

401

yS

s

FDP

D ED

⎛ ⎞⎜ ⎟⎜ ⎟≤⎜ ⎟−⎜ ⎟⎝ ⎠

(14.7.1.4-2)

where: D1 = the diameter of the rocker or roller surface (mm)

Eqs. 1 and 2 are more restrictive than similar provisions for line bearing and contact stresses in the AASHTOStandard Specifications. The more conservative design was adopted herein due to the problematic history of some bearings which, in some cases, may be related to small zones of yielding in the bearing or base plate. The increased conservatism is not difficult to handle in new design, but may be a problem in rehabilitation. If careful inspection indicates that existing bearings which do not satisfy these provisions are performing well and there is no evidence of rutting or ridging, which may be evidence of local yielding, then reuse of the bearing may be viable. Evaluation may proceed using the following historical provision:

Bearing per linear inch on expansion rockers and rollers shall not exceed the values obtained by the following formulas: Diameters up to 635 mm

904.14

138yF

p d−

= × (C14.7.1.4-1)

Diameters 635 to 3175 mm

89.50104

138yF

p d−

= (C14.7.1.4-2)

where: p = allowable bearing (N/mm) d = diameter of rocker or roller (mm) Fy = minimum yield point in tension of steel in the

roller or bearing plate, whichever is the smaller (MPa)

If loads are increased significantly by the rehabilitation, complying with the current provisions may be more appropriate.

D2 = the diameter of the mating surface (mm) taken as: • Positive if the curvatures have the same sign, and

• Infinite if the mating surface is flat.

Fy = specified minimum yield strength of the weakeststeel at the contact surface (MPa)

Es = Young’s modulus for steel (MPa) W = width of the bearing (mm)

The two diameters have the same sign if the centers of the two curved surfaces in contact are on the same side of the contact surface, such as is the case when a circular shaft fits in a circular hole.


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