Module 4 Frosch

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Chapter 7 - One-Way Slabs

ACI 318-14:Reorganized for Design


One-way slabs

• Similar to beams• Only covering technical changes



Ch. 7 – Minimum flexural reinforcement

Minimum nonprestressed reinforcement clarified by no longer referring to temp. and shrinkage steel *

ACI 318-11, 10.5.4: For structural slabs and footings of uniform thickness, As,min in the direction of the span shall be the same as that required by 7.12.2.1.

ACI 318-14, 7.6.1.1: A minimum area of flexural reinforcement, As,min, shall be provided in accordance with Table 7.6.1.1.


Ch. 7 – Critical section for bar development *

• 318-11, 12.10.2: Critical sections … are … where adjacent reinforcement terminates, or is bent.

• 318-14, 7.7.3.2: Critical locations …are … where bent or terminated tension reinforcement is no longer required to resist flexure.

• Also applies to beams ACI 318-14, 9.7.3.2

≥ ℓd

≥ (d or 12 db)

≥ ℓdBars a Bars b

Bars a no longer required



Ch. 7 – S + T in post-tensioned slabs

• Ag for calculating additional shrinkage and temperature steel from beam face to face *

Fig. R7.7.6.3.2—Plan view at slab edge showing added S and T reinforcement

ACI 318-11

ACI 318-14


Chapter 9 - Beams

ACI 318-14:Reorganized for Design



New member design chapters

• Simplifies code compliance• All requirements in one chapter• Follows normal order of member design

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ACI 318-14 Member Chapter Organization

• Common member chapter sub-headings– 9.1 Scope– 9.2 General– 9.3 Design Limits– 9.4 Required Strength– 9.5 Design Strength– 9.6 Reinforcement Limits– 9.7 Reinforcement Detailing



ACI 318-14 Section content

• 9.1 Scope– Am I in the right chapter?– Do these requirements apply?


Scope of beams

• Nonprestressed concrete• Prestressed concrete• Precast concrete• Composite beams• One-way joists• Deep beams

9.1 Scope9.2 General9.3 Design limits9.4 Required strength9.5 Design strength9.6 Reinforcement limits9.7 Reinforcement detailing




• 9.2 General– Overall information– Materials (general)– Stability (specific)– Connectivity


Materials

• Concrete → Ch. 19• Reinforcing steel → Ch. 20• Embedments → 20.7


Courtesy of PCA



Connections

• Beam-column → Ch. 15• Slab-column → Ch. 15• Precast → 16.2



T-beams• Stability requirements

– Spacing of lateral bracing • T-beams

– Placed monolithic or composite → 16.4– Effective flange widths→ 6.3.2– Flange reinforcing → 7.5.2.3– Torsional section


+ bw *




• 9.3 Design Limits– Constraints on a design– Allowable deflections– Geometry limits– Steel strain limits– Concrete stress limits for

prestressed membersℓ/21, minimum


Design limits

• Minimum depth

• Calculated deflections → 24.2

• Strain ≥ 0.004

• Stress limits in prestressed concrete





• 9.4 Required Strength– What load do I need to resist?– How do I determine the forces and moments?– Where are the critical sections I need to

check?


Required strength

• Loads → Ch. 5• Analysis → Ch. 6• Critical sections for:

– Mu – Face of support– Vu – d from face of support– Tu – d from face of support

• For indeterminate structures– Reduce Tu to φTcr

– Redistribute forces


Critical location for Vu at supports

Beam

Beam




• 9.5 Design Strength– Strength for each limit state– Strength reduction factors– Required steel area

εt

εc = 0.003

c C = 0.85f’cba

T=Asfy

neutral axisa

d


Flexure & shear

• Flexure– φMn ≥ Mu

– φ → 21.2, Mn → 22.3 – For Pu > 0.10f’cAg, Mn → 22.4

• Shear– φVn ≥ Vu

– φ → 21.2, Vn → 22.5




Torsion

• φTn ≥ Tu (if not neglected)• φ → 21.2, Tn → 22.7

• May be neglected for Tu < φTth• Tth → 22.7

• Include transverse and longitudinal torsion reinforcement



Slender precast spandrel beams• Open web reinforcement

permitted to resist torsion on slender precast spandrel beams with h/bt ≥ 4.5 (ACI 318-14, 9.5.4.7) *




• 9.6 Reinforcement Limits– Min. and max. reinforcement


As, min = greater of

3200


Minimum reinforcement • Flexural, As,min

• Shear, Av,min

• Torsion, (Av + 2At)min/s, Aℓ,min





• 9.7 Reinforcement Detailing – Cover, development, splices, bundled bars,

spacing, cutoff points, integrity reinforcement…


Common detailing requirements

• Concrete cover → 20.6.1• Development lengths → 25.4 • Lap splices → 25.5• Bundled bars → 25.6• Bar spacing → 25.2 , 24.3


Courtesy of PCA



Skin reinforcement

• h > 36 in. • Distribute over h/2 from tension face• Smax → 24.3 (crack control)• May include in Mn



Flexural reinforcement

• Bar cutoff points (9.7.3) – Development at critical sections– Extension past point no longer required– Extension into supports– Structural integrity




Transverse reinforcement

• Shear– General requirements → 25.7– Spacing limits in 9.7.6


Stirrups

Max. s = d/2, 24 in.= d/4, 12 in.


Transverse reinforcement

• Shear and torsion– Hoops or closed stirrups → 25.7.1.6– Spacing limits in 9.7.6.3.3


Max. s = ph/8, 12 in.

Hoops Closed stirrups



9.7.7 Structural integrity

• Sometimes overlooked– Section 7.13 of detailing chapter in ACI 318-11

• Intent– Redundancy– Limit disproportionate collapse– Limit to local damage– Minimal, simple detailing changes



Purpose

• Provisions are not– Design for a particular

scenario– A blast-resistant design

(Report ACI 370R-14)• How do they work?

– Continuous reinforcement– Anchored within the

supports and beams– Strategic splicing– Catenary action




Perimeter beams

• 9.7.7 Structural integrity reinf.– Structural integrity bars through column core


As-

As+

1/6 As-,

2 bar min.

1/4 As+,

2 bar min.,Develop at faceof support Hoops Closed stirrups

Class B tension splice


Interior beams

• 9.7.7 Structural integrity reinf.– Interior beams, option 1– Structural integrity bars through column core


As+1/4 As

+, 2 bar min.,Develop at faceof support

Class B tension splice



Interior beams

• 9.7.7 Structural integrity reinf.– Interior beams, option 2


Hoops Closed stirrups


Options

• Can also use – Mechanical or welded splices– Headed bars or straight development in exterior

supports– Strand– WWR transverse reinforcement




Beams (Ch. 9)

• Common sub-headings– 9.1 Scope– 9.2 General– 9.3 Design limits– 9.4 Required strength– 9.5 Design strength– 9.6 Reinforcement limits– 9.7 Reinforcement detailing

• Unique sub-headings– 9.8 Nonprestressed one-way joist systems– 9.9 Deep beams


General requirements

• Rib width > 4 in.• Depth < 3.5 x width• Clear spacing < 30 in. • 10% increase in Vc

• One structural integrity bottom bar continuous

9.1 Scope9.2 General9.3 Design limits9.4 Required strength9.5 Design strength9.6 Reinforcement limits9.7 Reinforcement detailing9.8 One-way joists



Deep beamsGeneral requirements

– Length to height ratio < 4– Concentrated load w/in 2h of support

• Dimensional limit based on Vu– Vu ≤ φ 10 √fc’ (bwd)

• Strut and Tie Model → Ch. 23

9.1 Scope9.2 General9.3 Design limits9.4 Required strength9.5 Design strength9.6 Reinforcement limits9.7 Reinforcement detailing9.8 One-way joists9.9 Deep beams

Section A-A

ℓn


Reinforcement of deep beams

• Reinforcement limits– Minimum transverse, longitudinal,

and flexural tension reinforcement

• Reinforcement details– Cover, spacing, development

requirements

9.1 Scope9.2 General9.3 Design limits9.4 Required strength9.5 Design strength9.6 Reinforcement limits9.7 Reinforcement detailing9.8 One-way joists9.9 Deep beams



Chapter 9 – Beams

• Satisfy sections 9.1 through 9.7 → beam design meets ACI 318 code for SDC A

• Additional requirements in Chapter 18 for SCD B through F


R/C Beam Design Example

6 in

. Sla

b

Design 18 in. × 18 in. beam

f’c = 4 ksi, fy = 60 ksiNormalweight concreteColumns are 18” x 18”

30 ft typical (centerline)

Live load = 50 psf (no red.)SDL = 10 psf

15 ft

15 ft



R/C Beam Geometry

d =

15.5

in.

h =

18”

b = 18 inches


Beam chapter overview

9.1 Scope9.2 General9.3 Design Limits9.4 Required Strength9.5 Design Strength9.6 Reinforcement Limits9.7 Reinforcement Detailing



R/C Beam Design Example9.1 Scope 9.2 General

9.2.4.2T- Beam Flange (midspan) 6.3.2 beff = 2xℓn/8+bw = 100” (midspan); b = 18” (support)

9.3 Design Limits9.3.1.1Deflections hmin = ℓ/21 = 17”< h= 18”9.3.3.1Strain limit εt ≥ 0.004



9.4 Required Strength9.4.1.1Loads & Load Combinations Chapter 5

Dead load slab = 6”/(12’’/ft)*150pcf = 75 psfDead load beam = 15 psfSuperimposed dead load = 10 psfTotal dead load = 100 psf

wu = 1.2 DL+1.6 LL = 200 psfWu = wu x 15’ trib = 3.0 kip/ft




9.4 Required Strength9.4.1.2Required Strength (Analysis) Chapter 6

Use Table 6.5.2 for MomentsNegative Moment (Wuℓn2/11) = 222 k-ftPositive Moment (Wuℓn2/16) = 152 k-ft

9.4.3.2Use Table 6.5.4 for ShearVu = Wu(ℓn)/2 – Wud = 39 k


R/C Beam Design Example9.5 Design Strength9.5.2.1 Moment Strength Mn Section 22.3 (toolbox)Section 22.3 Section 22.2 standard flex. assumptions– Negative Mu at face of support = 222 k-ft= − 2⁄ ; = 0.85⁄ ; = ⁄

As = 3.6 in.2; c = 4.6 in.; εt = 0.007 use 4 No. 9 bars– Positive Mu at midspan = 152 k-ft

As = 2.2 in.2; c = 0.5 in.; εt = 0.09 use 3 No. 8 bars



R/C Beam Design Example9.5 Design Strength

9.5.3.1 Shear Strength Vn Section 22.5 (toolbox)Section 22.3 standard shear assumptions– Factored shear Vu at support = 39 kips– Calculate Vc = 2√f’cbwd = 35 kips– Calculate Vs = Vu /φ – Vc = 17 kips– Calculate Av/s for stirrups = Vs/(fytd) = 0.018 in.2/in.– Select stirrups – try #3 at 7 in.

• Av/s = 2×0.11 in.2/ 7 = 0.031 in.2/in., OK


R/C Beam Design Example9.6 Reinforcement Limits

– 9.6.1 Minimum Flexural Reinforcement• 9.6.1.2 As,min = (200/fy) (bwd) = 1.0 in.2 OK

– 9.6.3 Minimum Shear Reinforcement• 9.6.3.3 Av,min = 50 bw/fyt = 0.015 in.2/in. OK




Summary

h =

18 in

.

b = 18 in.

3#8

4#9

#3@7 in.


R/C Beam Design Example9.7 Reinforcement Detailing• 9.7.1 General

– 9.7.1.1 Concrete Cover Section 20.6.1 – 9.7.1.2 Development Lengths Section 25.4 – 9.7.1.3 Splices Section 25.5

• 9.7.2 Reinforcement spacing– 9.7.2.1 Minimum s Section 25.2– 9.7.2.2 Maximum s Section 24.3



R/C Beam Design Example9.7 Reinforcement Detailing• 9.7.3 Flexural bar cutoff points• 9.7.6 Stirrups

– 9.7.6.1.2 Geometry Section 25.7 – 9.7.6.2 Max. spacing

• 9.7.7 Integrity bars– Provide 2 continuous bottom bars (with Class B laps at

columns)

Chapter 9 Completed100% done with non-seismic design and detailing


Chapter 18 – Earthquake resistant structuresOrdinary Systems (Min. for SDC B)

• Beams • Columns

• Beams• Columns• Two-way slabs• Precast structural

walls

• Beams• Columns• Beam-column joints• Moment frames

using precast concrete

• Diaphragms• Members not part

of seismic force resisting system

• Structural walls• Foundations

Intermediate Systems (Min. for SDC C)

Special Systems (SDC D, E, F)



Ordinary moment frames (SDC B)

• Section 18.3.2

As+

2 bar min.

1/4 As+,

2 bar min.,Develop at faceof support


Intermediate moment frames (SDC C)

• Meet 18.3.2 (ordinary moment frames)• Additional requirements in 18.4.2• Anywhere along beam: Mn

+ and Mn- ≥ 1/5 Mn

at joints

≥ 1/5 Mnat joints

Mn+ ≥ Mn

-/3

Mn- Mn

-

Hoops at smallest of d/4, 8 long. db, 24 hoop db, 12 in.

2h

s ≤ d/2



Intermediate moment frames (SDC C)

• Shear strength, φVn > lesser of:– Shear with nominal

moment capacity at each end

– Seismic load combination with 2.0E


Special moment frames (SDC D, E, or F)

• 18.6.2 Dimensional limits– Depth, ℓn ≥ 4d– Width, bw ≥ lesser of 0.3h

and 10 in.– Beam width on each side

of column ≤ c2 and 0.75 c1

c2



Special moment frames (SDC D, E, F)

• Meet 18.3.2 (ordinary moment frames)• Additional requirements in 18.6.3• Anywhere along beam: Mn

+ and Mn- ≥ 1/4 Mn

at joints

≥ 1/4 Mnat joints

Mn+ ≥ Mn

-/2

Mn- Mn

-

Hoops at smallest of d/4, 6 long. db, 6 in.

2h

s ≤ d/2s ≤ d/4, 4 in.

Hoops or spirals



• Splices prohibited:– Within joints– 2d from joint– 2d from flexural yielding sections

• Hoops required:– 2h from face of support– 2h on either side of sections expected to yield– Must support flexural bars like column ties

(25.7.2.4)




• Shear strength, φVn– Shear with probable

moment capacity at each end (1.25 fy)

– Vc = 0 within 2d from ends and 2d on both sides of yielding sections when:

• Ve ≥ 0.5Vu,max and• Pu ≤ Agf’c/20


Nonparticipating frame beams

• Nonparticipating beams → 18.14– Only applies to SDC D, E, and F– Evaluate for gravity loads at design displacement

• See definition of design displacement in Chapter 2• Requirements in ASCE 7• Design displacement typically greater than from linear-

elastic model



Nonparticipating frame beams• Nonparticipating beams→ 18.14

– If design strength not exceeded• If Pu ≥ Agf’c/10, hoops must meet column tie requirements

ρ ≤ 0.025 top & bot.

Mn- Mn

- s ≤ d/22 bar min. top & bot.


Nonparticipating frame beams

• Nonparticipating beams→ 18.14– If design strength exceeded or beam is not

evaluated• Meet requirements on previous screen• Design shear Ve based on Mpr at each end• Vc = 0 within 2d from ends and 2d on both sides of

yielding sections when:– Ve ≥ 0.5Vu,max and– Pu ≤ Agf’c/20

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Module 4 Frosch