STRC01 ReinforcedConcrete Part1 0715

Structural Engineering Review Course

Reinforced Concrete Design (Part 1)

Reinforced Concrete Design (Part 1) Structural Engineering Review Course

STRC ©2015 Professional Publications, Inc.

© 2015 Professional Publications, Inc.

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Reinforced Concrete Design Part 1

Lesson Overview Reinforced Concrete Design (Part 1) • General Requirements

• Shear in Beams

• Strength Design Principles

• Deep Beams

• Strength Design of Reinforced Concrete • Corbels Beams • Beams in Torsion • Serviceability Requirements for Beams



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Learning Objectives You will learn • reinforced concrete design theory • R/C beam design • R/C corbel design • efficient solution approaches • common terminology and practice • code nomenclature • short‐cuts and rules‐of‐thumb



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Prerequisite Knowledge You should already be familiar with • statics • mechanics of materials • structural analysis • basic reinforced concrete terminology



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Referenced Codes and Standards • International Building Code (IBC, 2012) • Building Code Requirements for Structural Concrete (ACI 318, 2011)



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General Requirements IBC adopts ACI by reference. Sec. 1905 of IBC modifies some sections of ACI.



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General Requirements 2011 ACI follows strength design method • apply factored loads • determine required ultimate strength • calculate nominal strength • multiply by factor to get design strength • design strength ≥ required ultimate strength



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Strength Design Principles required strength • service load × load factor • check all load combinations • most critical combination governs

U   Q = service load U = required strength γ = load factor Q = service load STRC ©2015 Professional Publications, Inc.


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Strength Design Principles loads



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Strength Design Principles load combinations (ACI Sec. 9.2.1) STRM Sec. 1.2



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Example: Strength Design Principles CSCO Example 2.1 dead load

live load or roof live load

wind load



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Example: Strength Design Principles



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Example: Strength Design Principles



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Strength Design Principles design strength nominal strength (theoretical ultimate) × strength reduction factor design strength   Rn

ϕ

= reduction factor

Rn = nominal, or theoretical, strength



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Strength Design Principles reduction factors Multiply nominal strength by these values to get design strength.



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Strength Design of Reinforced Concrete Beams reinforcement bar sizes CSCO Table 1.1 Properties of Standard Reinforcing Bars (no. 14 and no. 18 omitted)



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Strength Design of Reinforced Concrete Beams typical assumptions • rectangular stress block • tension reinforcement has yielded • linear strain • max concrete strain of 0.003 • neglect concrete in tension



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Strength Design of Reinforced Concrete Beams Fig. 1.1 Rectangular Stress Block

Tu = Cu (assumes no axial force) Mu = Tu (d – a/2) = Cu (d – a/2) Cu = 0.85fc’(β1c)(b)

American Concrete Institute. Commentary on Building Code Requirements for Reinforced Concrete. Farmington Hills, MI: American Concrete Institute, 1985.



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Strength Design of Reinforced Concrete Beams nominal flexural strength • two basic concrete strength equations to calculate nominal flexural strength • very important concrete equations



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Strength Design of Reinforced Concrete Beams depth of equivalent rectangular stress block depth of portion of concrete that is effective in compression



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Strength Design of Reinforced Concrete Beams required reinforcement ratio amount of steel required when • concrete dimensions given • moment given



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Strength Design of Reinforced Concrete Beams tension‐controlled section • strain in compression fiber (concrete) = 0.003 • strain in tension steel ≥ 0.005 •

c/d ≤ 0.375

•



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Strength Design of Reinforced Concrete Beams compression‐controlled section • strain in compression fiber (concrete) = 0.003 • strain in tension steel ≤ 0.002 •

c/d ≥ 0.600

•



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Strength Design of Reinforced Concrete Beams transition region between tension‐ and compression‐controlled sections • strain in compression fiber (concrete) = 0.003 • 0.002 < strain in tension steel < 0.005 • 0.375 < c/d < 0.600 •



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Poll Question The reinforced concrete section below is (A) tension‐controlled (B) compression‐controlled



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Poll Question The reinforced concrete section below is (A) tension‐controlled (B) compression‐controlled The answer is (B).



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Strength Design of Reinforced Concrete Beams maximum reinforcement minimum reinforcement • applies to non‐prestressed bending members

•

ACI Sec. 10.5.1

• tension steel strain = 0.004 • c/d = 0.429 •

ACI Sec. 10.3.5



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Example: Strength Design of Reinforced Concrete Beams CSCO Example 3.1



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Example: Strength Design of Reinforced Concrete Beams CSCO Example 3.1



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Example: Strength Design of Reinforced Concrete Beams



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Strength Design of Reinforced Concrete Beams beams with compression reinforcement required when • concrete strength and/or area cannot be increased • factored moment exceeds design strength at steel strain = 0.005 f •   t  0.319 1 c fy Beams with compression reinforcement, when used, also require additional tension reinforcement.



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Example: SD of Reinforced Concrete Beams At what applied factored moment does compression reinforcement become required? fc’ = 4 ksi, fy = 60 ksi



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Example: SD of Reinforced Concrete Beams t  0.319  1

f c fy

 kips   4 in 2    0.319  0.85   kips   60  2 in    0.018 As   bd

  0.01812 in  20 in 

fc’ = 4 ksi, fy = 60 ksi

 4.32 in 2



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Example: SD of Reinforced Concrete Beams  0.59  fy  0.9 Mn  0.9 Asfyd  1   f c   kips     0.9   4.32 in 2   60 20 in  2  in   kips     0.59 0.018 60       in 2     1   kips   4 2   in    3922 in-kips

fc’ = 4 ksi, fy = 60 ksi

The answer is 3922 in‐kips. STRC ©2015 Professional Publications, Inc.


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Strength Design of Reinforced Concrete Beams Fig. 1.3 Flanged Section with Tension Reinforcement

American Concrete Institute. Building Code Requirements for Structural Concrete and Commentary. Farmington Hills, MI: American Concrete Institute, 2011.



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Strength Design of Reinforced Concrete Beams procedure for flanged section with tension reinforcement 1. Calculate the steel required to balance the flange.

2. Determine the moment resisted by the flange.

3. Calculate the residual moment resisted by the web.



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Strength Design of Reinforced Concrete Beams procedure for flanged section with tension reinforcement (continued) 4. Calculate the additional area of reinforcemen required to balance the web.

5. Superimpose the results.



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Serviceability Requirements for Beams overview • control crack widths • limit deflections • service load conditions apply



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Serviceability Requirements for Beams control of crack widths Fig. 1.4 Tension Reinforcement Details

tension reinforcement

skin reinforcement If h > 36 in, provide skin reinforcement Per ACI 10.6.7.



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Serviceability Requirements for Beams deflection limits • allowable immediate deflection (flexural members) • l/180 for flat roofs • l/360 for floors due to applied live load • total deflection after attachment of nonsensitive elements limited to l/240 • total deflection after attachment of sensitive elements limited to l/480



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Serviceability Requirements for Beams service load conditions • apply for the calculation of deflections • rectangular stress block assumption is not made • linearly varying stress distribution assumed



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Serviceability Requirements for Beams Fig. 1.5 Service Load Conditions



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Serviceability Requirements for Beams deflection calculation procedure 1. Calculate moment of inertia of cracked transformed section.

2. Calculate cracking moment.

3. Calculate effective moment of inertia. ACI Eq. 9‐8



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Serviceability Requirements for Beams deflection calculation procedure (continued) 4. Calculate short‐term deflections using effective moment of inertia.

STRM Table 1.3 Values of ξ

5. Calculate additional long‐term deflections. ξ comes from STRM Table 1.3.

ACI Eq. 9‐11



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Serviceability Requirements for Beams deflection calculation procedure (continued) 6. Calculate live load deflection

7. Calculate final deflection



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Example: Serviceability Requirements for Beams Example 1.7



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Example: Serviceability Requirements for Beams Example 1.7



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Example: Serviceability Requirements for Beams



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Elastic Design Method elastic design method overview • also known as the “alternate design method” • allowed by 2011 ACI per Commentary R1.1 • covered in 1999 ACI • service load conditions apply • actual stresses checked against allowable stresses



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Elastic Design Method procedure 1. Determine allowables.

2. Calculate service load condition coefficients.



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Elastic Design Method procedure (continued) 3. Calculate actual stresses. reinforcement: concrete: 4. Check actual stresses against allowable stresses.



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Example: Elastic Design Method CSCO Example 4.1



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Example: Elastic Design Method CSCO Example 4.1



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Example: Elastic Design Method



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Example: Elastic Design Method



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Shear in Beams critical section

Fig. 1.6 Critical Section for Shear

as shown in Fig. 1.6 when • checking near support • reaction produces compressive stress • loads applied at or near top of beam • no concentrated load between support and section location shown otherwise, taken at location of max shear



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Poll Question: Shear in Beams The critical section for shear is at which location?



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Poll Question: Shear in Beams  checking near support  reaction produces compressive stress  loads applied at or near top of beam  no concentrated load between support and section location shown The critical section is located d away from the support. The answer is (B).



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Shear in Beams When is shear reinforcement required? V • For , provide minimum reinforcement. Vu  c 2 ACI Eq. 11‐13

Vs • For , provide reinforcement with a capacity of so that Vu  Vc



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Shear in Beams shear capacity of concrete simplified ACI Eq. 11‐3

refined ACI Eq. 11‐5



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Shear in Beams shear capacity of stirrups for inclined stirrups

Fig. 1.7 Beam with Inclined Stirrups ACI Eq. 11‐16

for vertical stirrups ACI Eq. 11‐15

maximum allowed shear capacity from shear reinforcement



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Shear in Beams spacing of stirrups limited to maximum d/2 or 24 in when

Fig. 1.7 Beam with Inclined Stirrups

limited to maximum d/4 or 12 in when



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Shear in Beams SXST Vertical Breadth Problem 40



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Shear in Beams



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Shear in Beams shear capacity of inclined bars for single, bent‐up bar or group of bars

Fig. 1.8 Beam with Inclined Bars

ACI Eq. 11‐17

for series of equally spaced bent‐up bars ACI Eq. 11‐16

Spacing = s, as shown in Fig. 1.8.



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Shear in Beams spacing of inclined bars typical condition

Fig. 1.8 Beam with Inclined Bars

Vs  4 f cbw d When , use ½ of typical value.



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Example: Shear in Beams Example 1.10

Each U‐stirrup has two vertical legs. STRC ©2015 Professional Publications, Inc.


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Example: Shear in Beams Example 1.10

Each U‐stirrup has two vertical legs. STRC ©2015 Professional Publications, Inc.


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Example: Shear in Beams



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Deep Beams deep beam definition •

clear span 4 depth

Fig. 1.9 Minimum Shear Reinforcement for a Deep Beam

• illustrated in Fig. 1.9 minimum reinforcement • illustrated in Fig. 1.9



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Deep Beams maximum shear strength The maximum achievable shear strength for deep beams is limited.

deep beam action also applies to beams with concentrated loads less than 2h from support



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Deep Beams B‐ and D‐ regions

(beam theory applies)

split beam into D‐regions and B‐regions

Fig 1.10 B‐ and D‐Regions

• D (discontinuity) • Region where traditional beam theory is not applicable • D‐region extends distance h from discontinuity • B (beam) • Treat this region like a typical beam STRC ©2015 Professional Publications, Inc.


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Example: Deep Beams Break the beam shown into D and B regions.



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Example: Deep Beams Though this beam is not a deep beam, it still has D‐ and B‐regions.



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Deep Beams strut‐and‐tie model

Fig. 1.11 Strut‐and‐Tie Model

• ACI App. A • only applies if “compression struts can form” load ≤ 2h from support results θ ≥ 25 deg



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Deep Beams strut nominal strength • governed by transverse tension

Fig. 1.12 Prism and Bottle‐Shaped Struts

• developed by lateral spread of compression force •

•

ACI Eq. A‐2

ACI Eq. A‐3

•



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Deep Beams tie nominal strength • strength of tension reinforcement • •



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Deep Beams nodal zone nominal strength Fig. 1.13 Nodal Zone

•

ACI Eq. A‐7

•

ACI Eq. A‐8

•



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Example: Deep Beams Example 1.11



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Example: Deep Beams



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Example: Deep Beams



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Example: Deep Beams



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Example: Deep Beams



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Example: Deep Beams



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Example: Deep Beams



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Corbels introduction to corbels

Fig. 1.14 Corbel Details

• cantilever bracket supporting a load‐ bearing member • shear span‐to‐depth ratio ≤ 1 • horizontal tension‐to‐vertical shear ratio ≤ 1



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Corbels introduction to corbels (continued)


• shear force (Vu) requires reinforcement area Avf • moment (Vua + Nuc(h − d)) requires reinforcement area Af • tensile force (Nuc) requires reinforcement area An



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Corbels shear in corbels


Avf = shear friction reinforcement factored shear force



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Corbels tension in corbels


Nuc (tension force) ≥ 0.2Vu total tension reinforcement, primary tension reinforcement

minimum closed ties over depth 2d/3 STRM Sec. 1.7 STRC ©2015 Professional Publications, Inc.


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Example: Corbels CSCO Example 5.3



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Example: Corbels CSCO Example 5.3



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Example: Corbels



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Example: Corbels



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Beams in Torsion introduction to torsion Torsion may be neglected if . Otherwise, provide torsion reinforcement to resist Tu . Fig. 1.15 Torsion in Rectangular Section

Fig. 1.16 Torsion in Flanged Section



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Beams in Torsion reinforcement requirements • required area (per leg) of closed stirrup ACI Eq. 11‐21

• required area of longitudinal reinforcement ACI Eq. 11‐22



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Beams in Torsion minimum and maximum reinforcement minimum longitudinal

area

bar size ACI Eq. 11‐24

minimum transverse

area

max spacing ACI Eq. 11‐23



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Example: Beams in Torsion CSCO Example 5.4



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Example: Beams in Torsion



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Example: Beams in Torsion CSCO Example 5.5



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Learning Objectives You have learned • reinforced concrete design theory • R/C beam design • R/C corbel design • how to avoid common exam pitfalls • tricks to speed up problem solving on the exam



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Lesson Overview Reinforced Concrete Design (Part 1) • General Requirements

• Shear in Beams

• Strength Design Principles

• Deep Beams

• Strength Design of Reinforced Concrete • Corbels Beams • Beams in Torsion • Serviceability Requirements for Beams



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STRC01 ReinforcedConcrete Part1 0715

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