strc01 reinforcedconcrete part1 0715

Structural Engineering Review Course Reinforced Concrete Design (Part 1)

© 2015 Professional Publications, Inc. 1

Reinforced Concrete Design (Part 1)Structural Engineering Review Course

STRC ©2015 Professional Publications, Inc.



Reinforced Concrete Design Part 1


Lesson OverviewReinforced Concrete Design (Part 1)

• General Requirements

• Strength Design Principles

• Strength Design of Reinforced Concrete Beams

• Serviceability Requirements for Beams

• Shear in Beams

• Deep Beams

• Corbels

• Beams in Torsion

2





Learning ObjectivesYou 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

3





Prerequisite KnowledgeYou should already be familiar with

• statics

• mechanics of materials

• structural analysis

• basic reinforced concrete terminology

4





Referenced Codes and Standards• International Building Code (IBC, 2012)

• Building Code Requirements for Structural Concrete (ACI 318, 2011)

5





General RequirementsIBC adopts ACI by reference.

Sec. 1905 of IBC modifies some sections of ACI.

6





General Requirements2011 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

7





Strength Design Principlesrequired strength

• service load × load factor

• check all load combinations

• most critical combination governs

= service loadU Q

U = required strength

γ = load factor

Q = service load

8





Strength Design Principlesloads

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Strength Design Principlesload combinations (ACI Sec. 9.2.1)

STRM Sec. 1.2

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Example: Strength Design PrinciplesCSCO 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 Principlesdesign strength

nominal strength (theoretical ultimate) × strength reduction factor

design strength nR

ϕ = reduction factor

Rn = nominal, or theoretical, strength

14





Strength Design Principlesreduction factors

Multiply nominal strength by these values to get design strength.

15





Strength Design of Reinforced Concrete Beamsreinforcement 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 Beamstypical 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 BeamsFig. 1.1 Rectangular Stress Block

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

18

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





Strength Design of Reinforced Concrete Beamsnominal 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 Beamsdepth of equivalent rectangular stress block

depth of portion of concrete that is effective in compression

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Strength Design of Reinforced Concrete Beamsrequired reinforcement ratio

amount of steel required when

• concrete dimensions given

• moment given

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Strength Design of Reinforced Concrete Beamstension‐controlled section

• strain in compression fiber (concrete) = 0.003

• strain in tension steel ≥ 0.005

• c/d ≤ 0.375

•

22





Strength Design of Reinforced Concrete Beamscompression‐controlled section


• strain in tension steel ≤ 0.002

• c/d ≥ 0.600

•

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Strength Design of Reinforced Concrete Beamstransition region between tension‐ and compression‐controlled sections


• 0.002 < strain in tension steel < 0.005

• 0.375 < c/d < 0.600

•

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Poll QuestionThe reinforced concrete section below is

(A) tension‐controlled

(B) compression‐controlled

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Poll QuestionThe reinforced concrete section below is

(A) tension‐controlled

(B) compression‐controlled

The answer is (B).

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minimum reinforcement

•

Strength Design of Reinforced Concrete Beamsmaximum reinforcement

• applies to non‐prestressed bending members

• tension steel strain = 0.004

• c/d = 0.429

• ACI Sec. 10.3.5

ACI Sec. 10.5.1

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Example: Strength Design of Reinforced Concrete BeamsCSCO Example 3.1

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Example: Strength Design of Reinforced Concrete BeamsCSCO Example 3.1

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Example: Strength Design of Reinforced Concrete Beams

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Strength Design of Reinforced Concrete Beamsbeams with compression reinforcement

required when

• concrete strength and/or area cannot be increased

• factored moment exceeds design strength at steel strain = 0.005

•

Beams with compression reinforcement, when used, also require additional tension reinforcement.

10.319 ct

y

ff

31





Example: SD of Reinforced Concrete BeamsAt 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


1

2

2

0.319

kips4 in0.319 0.85 kips60 in

0.018

ct

y

ff

2

0.018 12 in 20 in

4.32 in

sA bd

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Example: SD of Reinforced Concrete Beams

The answer is 3922 in‐kips.

22

2

2

0.590.9 0.9 1

kips0.9 4.32 in 60 20 inin

kips0.59 0.018 60 in1 kips4

in3922 in-kips

ys y

c

fMn A f df


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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.

35





Strength Design of Reinforced Concrete Beamsprocedure 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 Beamsprocedure 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 Beamsoverview

• control crack widths

• limit deflections

• service load conditions apply

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Serviceability Requirements for Beamscontrol of crack widths

tension reinforcement

skin reinforcement

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

Fig. 1.4 Tension Reinforcement Details

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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

Serviceability Requirements for Beams

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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 BeamsFig. 1.5 Service Load Conditions

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Serviceability Requirements for Beamsdeflection 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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4. Calculate short‐term deflections using effective moment of inertia.

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

ACI Eq. 9‐11

deflection calculation procedure (continued)

STRM Table 1.3 Values of ξ

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6. Calculate live load deflection

7. Calculate final deflection

deflection calculation procedure (continued)

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Example: Serviceability Requirements for BeamsExample 1.7

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Example: Serviceability Requirements for BeamsExample 1.7

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Example: Serviceability Requirements for Beams

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50






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Elastic Design Methodelastic 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 Methodprocedure

1. Determine allowables.

2. Calculate service load condition coefficients.

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Elastic Design Methodprocedure (continued)

3. Calculate actual stresses.

reinforcement:

concrete:

4. Check actual stresses against allowable stresses.

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Example: Elastic Design MethodCSCO Example 4.1

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Example: Elastic Design MethodCSCO 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 Beamscritical section

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

Fig. 1.6 Critical Section for Shear

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Poll Question: Shear in BeamsThe 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 BeamsWhen is shear reinforcement required?

• For , provide minimum reinforcement.

• For , provide reinforcement with a capacity of so that

ACI Eq. 11‐13

2c

uVV

u cV V Vs

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Shear in Beamsshear capacity of concrete

simplified

refined

ACI Eq. 11‐3

ACI Eq. 11‐5

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Shear in Beamsshear capacity of stirrups

for inclined stirrups

for vertical stirrups

maximum allowed shear capacity from shear reinforcement

Fig. 1.7 Beam with Inclined Stirrups

ACI Eq. 11‐16

ACI Eq. 11‐15

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Shear in Beamsspacing of stirrups

limited to maximum d/2 or 24 in when

limited to maximum d/4 or 12 in when

Fig. 1.7 Beam with Inclined Stirrups

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Shear in BeamsSXST Vertical Breadth Problem 40

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Shear in Beams

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Shear in Beamsshear capacity of inclined bars

for single, bent‐up bar or group of bars

for series of equally spaced bent‐up bars

Spacing = s, as shown in Fig. 1.8.

ACI Eq. 11‐17

ACI Eq. 11‐16

Fig. 1.8 Beam with Inclined Bars

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Shear in Beamsspacing of inclined bars

typical condition

When , use ½ of typical value.4s c wV f b d

Fig. 1.8 Beam with Inclined Bars

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Example: Shear in BeamsExample 1.10

70

Each U‐stirrup has two vertical legs.





Example: Shear in BeamsExample 1.10

71

Each U‐stirrup has two vertical legs.





Example: Shear in Beams

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Deep Beamsdeep beam definition

•

• illustrated in Fig. 1.9

minimum reinforcement

• illustrated in Fig. 1.9

Fig. 1.9 Minimum Shear Reinforcement for a Deep Beamclear span 4

depth

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Deep Beamsmaximum 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 BeamsB‐ and D‐ regions

split beam into D‐regions and B‐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

(beam theory applies)Fig 1.10 B‐ and D‐Regions

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

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

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Deep Beamsstrut‐and‐tie model

• ACI App. A

• only applies if “compression struts can form”

load ≤ 2h from support

results θ ≥ 25 deg

Fig. 1.11 Strut‐and‐Tie Model

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Deep Beamsstrut nominal strength

• governed by transverse tension

• developed by lateral spread of compression force

•

•

•

ACI Eq. A‐2

ACI Eq. A‐3

Fig. 1.12 Prism and Bottle‐Shaped Struts

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Deep Beamstie nominal strength

• strength of tension reinforcement

•

•

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Deep Beamsnodal zone nominal strength

•

•

•

ACI Eq. A‐7

ACI Eq. A‐8

Fig. 1.13 Nodal Zone

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Example: Deep BeamsExample 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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Corbelsintroduction to corbels

• cantilever bracket supporting a load‐bearing member

• shear span‐to‐depth ratio ≤ 1

• horizontal tension‐to‐vertical shear ratio ≤ 1

Fig. 1.14 Corbel Details

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Corbelsintroduction 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


90






Corbelsshear in corbels

Avf = shear friction reinforcement

factored shear force

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Corbelstension in corbels

Nuc (tension force) ≥ 0.2Vu

total tension reinforcement,

primary tension reinforcement

minimum closed ties over depth 2d/3

STRM Sec. 1.7


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Example: CorbelsCSCO Example 5.3

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Example: CorbelsCSCO Example 5.3

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Example: Corbels

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Example: Corbels

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Beams in Torsionintroduction 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 Torsionreinforcement requirements

• required area (per leg) of closed stirrup

• required area of longitudinal reinforcement

ACI Eq. 11‐21

ACI Eq. 11‐22

98





minimum longitudinal area bar size

minimum transverse area max spacing

Beams in Torsionminimum and maximum reinforcement

ACI Eq. 11‐24

ACI Eq. 11‐23

99





Example: Beams in TorsionCSCO Example 5.4

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Example: Beams in Torsion

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102






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Example: Beams in TorsionCSCO Example 5.5

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Learning ObjectivesYou 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

111





Lesson OverviewReinforced Concrete Design (Part 1)

• General Requirements

• Strength Design Principles

• Strength Design of Reinforced Concrete Beams

• Serviceability Requirements for Beams

• Shear in Beams

• Deep Beams

• Corbels

• Beams in Torsion

112

strc01 reinforcedconcrete part1 0715

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