ENCE710 C. C. Fu, Ph.D., P.E. Shear Connectors Design by AASHTO LRFD (LRFD Art. 6.10.10)

In the negative flexure regions, shear connectors shall be provided where the

longitudinal reinforcement is considered to be a part of the composite section.

Otherwise, shear connectors need not be provided in negative flexure regions, but

additional connectors shall be placed in the region of the points of permanent load

contraflexure.

r

srrAC Z

fAn = (LRFD Eq. 6.10.10. 3-1)

(1) Fatigue Limit State

sr

r

VnZp (LRFD Eq. 6.10.10.1.2-1)

Zr = d2 5.5 d2/2; (LRFD Eq. 6.10.10. 2-1) where = 34.5 4.28 log N (LRFD Eq. 6.10.10. 2-2) (2) Strength Limit State

nscr QQ = (LRFD Eq. 6.10.10.4.1-1)

rQ

Pn = (LRFD Eq. 6.10.10.4.1-2)

(a) Nominal Shear Force, Simple&continuous spans that are noncomposite for negative flexure:

22Pp FPP += (LRFD Eq. 6.10.10.4.2-1)

where

++=

fcfcycftftytwyw

sscp tbFtbFDtF

tbfofP

85.0.min

( )( )3-26.10.10.4. Eq. LRFD

2-26.10.10.4. Eq. LRFD

RL

PF ppp = (LRFD Eq. 6.10.10.4.2-4) (For straight spans or segments, Fp may be taken equal to zero)

Continuous spans that are composite for negative flexure:

22TT FPP += (LRFD Eq. 6.10.10.4.2-5)

where

npT PPP += (LRFD Eq. 6.10.10.4.2-6)

++=ssc

fcfcycftftytwywn tbf

tbFtbFDtFofP

45.0.min

( )( )8-26.10.10.4. Eq. LRFD

7-26.10.10.4. Eq. LRFD

RLPF nTT = (LRFD Eq. 6.10.10.4.2-9)

(b) Shear Resistance, Qn

Stud shear connector

Qn = uscccsc FAEfA 5.0 (LRFD Eq. 6.10.10.4.3-1) Channel shear connector

Qn = ( ) cccwf EfLtt + 5.03.0 (LRFD Eq. 6.10.10.4.3-2)

Design Step 5.1 - Design Shear Connectors

Since the steel girder has been designed as a composite section, shear connectors must be provided at the interface between the concrete deck slab and the steel section to resist the interface shear. For continuous composite bridges, shear connectors are normally provided throughout the length of the bridge. In the negative flexure region, since the longitudinal reinforcement is considered to be a part of the composite section, shear connectors must be provided.

Studs or channels may be used as shear connectors. For this design example, stud shear connectors are being used throughout the length of the bridge. The shear connectors must permit a thorough compaction of the concrete to ensure that their entire surfaces are in contact with the concrete. In addition, the shear connectors must be capable of resisting both horizontal and vertical movement between the concrete and the steel.

The following figure shows the stud shear connector proportions, as well as the location of the stud head within the concrete deck.

S6.10.7.4.1

S6.10.7.4.1a

7/8"

14"

8"

5"(Typ.)

AB

C

6"

3"

Figure 5-1 Stud Shear Connectors

Flexure Region A B CPositive 2.875" 3.125" 5.375"Intermediate 2.25" 3.75" 4.75"Negative 1.00 5.00 3.50

Shear Connector Embedment

Table 5-1 Shear Connector Embedment

5-2

The parameters I and Q are based on the short-term composite section and are determined using the deck within the effective flange width.

pn Zr IVsr Q

S6.10.7.4.1b The pitch of the shear connectors must be determined to satisfy the fatigue limit state as specified in S6.10.7.4.2 and S6.10.7.4.3, as applicable. The resulting number of shear connectors must not be less than the number required to satisfy the strength limit states as specified in S6.10.7.4.4.

The pitch, p, of the shear connectors must satisfy the following equation:

OK Heightstud

Diameterstud6.86=

Diameterstud 0.875 in=Heightstud 6.0 in=

S6.10.7.4.1a The ratio of the height to the diameter of a stud shear connector must not be less than 4.0. For this design example, the ratio is computed based on the dimensions presented in Figure 5-1, as follows:

Shear Connector Length

The stud shear connector length is commonly set such that its head is located near the middle of the deck slab. Refer to S6.10.7.4.1d for shear connector embedment requirements.

Shear Connector Layout

It is common to use several stud shear connectors per transverse row along the top flange of the girder. The number of shear connectors per transverse row will depend on the top flange width. Refer to S6.10.7.4.1c for transverse spacing requirements.

5-3

p 10.04 in=p n Zr IVsr Q=

Zr 2.11 K=Therefore,

5.5 d22

2.11= d2 0.48=in d 0.875=

0.626= 34.5 4.28 log N( )=

S6.6.1.2.5(see Design Step 3.14 at location of maximum positive flexure)

N 82125000=

S6.10.7.4.2Zr d2 5.5 d2

2= d

(see live load analysis computer run)

Vsr 34.97K=Vsr 0.75 41.45 K 5.18 K+( )=

In the positive flexure region, the maximum fatigue live load shear range is located at the abutment. The factored value is computed as follows:

Q 1195.8 in3=

Q 8.0 in( ) 103.0 in( )8

62.375 in 50.765 in( )=

S6.10.3.1.1b(see Table 3-4)I 66340.3 in4=(see Figure 5-1)n 3=

In the positive flexure region:

5-4

p 10 in=

Therefore, based on the above pitch computations to satisfy the fatigue limit state, use the following pitch throughout the entire girder length:

p 13.07 in=p n Zr IVsr Q=

(see previous computation) Zr 2.11 K=

S6.10.7.4.2Zr d2 5.5 d2

2=

(see Table 3-1 and live load analysis computer run)

Vsr 34.90K=Vsr 0.75 0.00 K 46.53 K+( )=Q 1807.4 in3=

Q 8.0 in( ) 103.0 in( )8

64.250 in 46.702 in( )=

(see Table 3-5)I 130196.1 in4=

SC6.10.7.4.1bIn the negative flexure region, the parameters I and Q may be determined using the reinforcement within the effective flange width for negative moment, unless the concrete slab is considered to be fully effective for negative moment in computing the longitudinal range of stress, as permitted in S6.6.1.2.1. For this design example, I and Q are assumed to be computed considering the concrete slab to be fully effective.

(see Figure 5-1)n 3=In the negative flexure region:

5-5

The clear depth of concrete cover over the tops of the shear connectors should not be less than 2.0 inches, and shear connectors should penetrate at least 2.0 inches into the deck. Based on the shear connector penetration information presented in Table 5-1, both of these requirements are satisfied.

S6.10.7.4.1d

OK Distanceclear 1.56 in=

(see Figure 5-1)Distanceclear14in

25in d

2=

In addition, the clear distance between the edge of the top flange and the edge of the nearest shear connector must not be less than 1.0 inch.

OK (see Figure 5-1)Spacingtransverse 5.0 in=4 d 3.50 in=

S6.10.7.4.1cFor transverse spacing, the shear connectors must be placed transversely across the top flange of the steel section and may be spaced at regular or variable intervals.

Stud shear connectors must not be closer than 4.0 stud diameters center-to-center transverse to the longitudinal axis of the supporting member.

OK 6 d 5.25 in=d 0.875 in=p 6 d

OK p 24 in

S6.10.7.4.1bIn addition, the shear connectors must satisfy the following pitch requirements:

Shear Connector Pitch

The shear connector pitch does not necessarily have to be the same throughout the entire length of the girder. Many girder designs use a variable pitch, and this can be economically beneficial.

However, for this design example, the required pitch for fatigue does not vary significantly over the length of the bridge. Therefore, a constant shear connector pitch of 10 inches will be used.

5-6

S6.4.4

0.5 0.601 4.0 3834 37.21= K 0.601 60.0 36.06= K Therefore, Qn 36.06 K=

Qr sc Qn=Therefore, Qr 30.65K=

The number of shear connectors provided between the section of maximum positive moment and each adjacent point of 0.0 moment or between each adjacent point of 0.0 moment and the centerline of an interior support must not be less than the following:

S6.10.7.4.4a

nVhQr

= Vh

The total horizontal shear force, Vh, between the point of maximum positive moment and each adjacent point of 0.0 moment is equal to the lesser of the following:

S6.10.7.4.4b

Vh 0.85 f'c b ts= tsor

Vh Fyw D tw Fyt bt tt+ Fyc bf tf+= tf

For the strength limit state, the factored resistance of the shear connectors, Qr, is computed as follows:

S6.10.7.4.4

Qr sc Qn= Qn S6.10.7.4.4asc 0.85= S6.5.4.2

The nominal shear resistance of one stud shear connector embedded in a concrete slab is computed as follows:

S6.10.7.4.4c

Qn 0.5 Asc f'c Ec Asc Fu= Fu

Asc d2

4= Asc 0.601 in2=

f'c 4.0 ksi= (see Design Step 3.1) S5.4.2.1Ec 3834 ksi= (see Design Step 3.3) S5.4.2.4Fu 60.0 ksi=

5-7

Fyc 50 ksi= (see Design Step 3.1) STable 6.4.1-1bf 14 in= (see Design Step 3.18)tf 0.625 in= (see Design Step 3.18)

0.85 f'c b ts 2802 K=Fyw D tw Fyt bt tt+ Fyc bf tf+ 2400 K=Therefore, Vh 2400 K=

Therefore, the number of shear connectors provided between the section of maximum positive moment and each adjacent point of 0.0 moment must not be less than the following:

S6.10.7.4.4a

nVhQr

=

n 78.3=The distance between the end of the girder and the location of maximum positive moment is approximately equal to:

L 48.0 ft= (see Table 3-7) Similarly the distance between the section of the maximum positive moment and the point of dead load contraflexure is approximately equal to:

L 83.6 ft 48.0 ft= (see Table 3-7) L 35.6 ft=

where f'c 4.0ksi= (see Design Step 3.1) S5.4.2.1b 103.0 in= (see Design Step 3.3)ts 8.0 in= (see Design Step 3.1)Fyw 50 ksi= (see Design Step 3.1) STable 6.4.1-1D 54 in= (see Design Step 3.18)tw 0.50 in= (see Design Step 3.18)Fyt 50 ksi= (see Design Step 3.1) STable 6.4.1-1bt 14 in= (see Design Step 3.18)tt 0.875 in= (see Design Step 3.18)

5-8

OK n 131.0=

p 10 in=n 3L 12 in

ft

p=

Using a pitch of 10 inches, as previously computed for the fatigue limit state, the number of shear connectors provided is as follows:

L 36.4 ft=(see Table 3-7) L 120 ft 83.6 ft=

The distance between the point of dead load contraflexure and the centerline of the interior support is approximately equal to:

n 25.0=

nVhQr

=

S6.10.7.4.4aTherefore, the number of shear connectors provided between each adjacent point of 0.0 moment and the centerline of an interior support must not be less than the following:

Vh 766 K=Vh Ar Fyr=

(see Design Step 3.1)Fyr 60 ksi=(see Design Step 3.3)Ar 12.772 in

2=where Vh Ar Fyr= Fyr

S6.10.7.4.4bFor continuous span composite sections, the total horizontal shear force, Vh, between each adjacent point of 0.0 moment and the centerline of an interior support is equal to the following:

OK n 128.2=p 10 in=L 35.6 ft=

n 3L 12 in

ft

p=

Using a pitch of 10 inches, as previously computed for the fatigue limit state, and using the minimum length computed above, the number of shear connectors provided is as follows:

5-9

Therefore, using a pitch of 10 inches for each row, with three stud shear connectors per row, throughout the entire length of the girder satisfies both the fatigue limit state requirements of S6.10.7.4.1 and S6.10.7.4.2 and the strength limit state requirements of S6.10.7.4.4.

Therefore, use a shear stud spacing as illustrated in the following figure.

Symmetrical about L Pier

144 Spaces @ 10" = 120'-0"(3 Stud Shear Connectors Per Row)

L PierCL Bearing AbutmentC

C

Figure 5-2 Shear Connector Spacing

Design Step 5.2 - Design Bearing Stiffeners

Bearing stiffeners are required to resist the bearing reactions and other concentrated loads, either in the final state or during construction.

For plate girders, bearing stiffeners are required to be placed on the webs at all bearing locations and at all locations supporting concentrated loads.

Therefore, for this design example, bearing stiffeners are required at both abutments and at the pier. The following design of the abutment bearing stiffeners illustrates the bearing stiffener design procedure.

The bearing stiffeners in this design example consist of one plate welded to each side of the web. The connections to the web will be designed to transmit the full bearing force due to factored loads and is presented in Design Step 5.3.

S6.10.8.2.1

5-10