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Design of Concrete Structure I

Dr. AliTayeh

First Semester 2009

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Lecture 8DESIGN OF

T-Section BEAMS FOR MOMENTS

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Analysis of Flanged Analysis of Flanged SectionSection

• Floor systems with slabs and beams are placed in monolithic pour.

• Slab acts as a top flange to the beam; T-beams, and Inverted L(Spandrel) Beams.

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Analysis of Flanged Analysis of Flanged SectionsSections

Positive and Negative Moment Regions in a T-beam

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Analysis of Flanged Analysis of Flanged SectionsSections

If the neutral axis falls within the slab depth analyze the beam as a rectangular beam, otherwise as a T-beam.

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Analysis of Flanged Analysis of Flanged SectionsSections

Effective Flange WidthPortions near the webs are more highly stressed than areas away from the web.

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Analysis of Flanged Analysis of Flanged SectionsSections

Effective width (beff) beff is width that is stressed uniformly to give the same compression force actually developed in compression zone of width b(actual)

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ACI Code Provisions for ACI Code Provisions for Estimating bEstimating beffeff

From ACI 318, Section 8.10.2T Beam Flange:

eff

f w

actual

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16

Lb

h bb

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ACI Code Provisions for ACI Code Provisions for Estimating bEstimating beffeffFrom ACI 318, Section 8.10.3

Inverted L Shape Flange

eff w

f w

actual w

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6 0.5* clear distance to next web

Lb b

h bb b

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ACI Code Provisions for ACI Code Provisions for Estimating bEstimating beffeff

From ACI 318, Section 8.10

Isolated T-Beams

weff

wf

42bb

bh

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Various Possible Geometries Various Possible Geometries of T-Beamsof T-Beams

Single Tee

Twin Tee

Box

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Analysis of T-BeamAnalysis of T-BeamCase 1Case 1::Equilibrium

fhas y

c eff0.85 A f

T C af b

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Analysis of T-BeamAnalysis of T-BeamCase 1Case 1:: Confirm

fha

005.0cus

1

ys

ccd

ac

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Analysis of T-BeamAnalysis of T-BeamCase 1Case 1:: Calculate Mn

fha

2ysnadfAM

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Analysis of T-BeamAnalysis of T-Beam

Case 2: Assume steel yields fha

ys

wcw

fwcf

85.085.0

fATabfC

hbbfC

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Analysis of T-BeamAnalysis of T-Beam

Case 2: Equilibrium

Assume steel yields

fha

c w fsf

y

0.85 f b b hA

f

The flanges are considered to be equivalent compression steel.

s sf yf w

c w0.85A A f

T C C af b

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Analysis of T-BeamAnalysis of T-Beam

Case 2:Case 2:

Confirmfha

f

1

s cu 0.005

a hac

d cc

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Analysis of T-BeamAnalysis of T-BeamCase 2Case 2: : Calculate nominal moments

fha

n n1 n2

n1 s sf y

fn2 sf y

2

2

M M M

aM A A f d

hM A f d

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Analysis of T-BeamsAnalysis of T-BeamsThe definition of Mn1 and Mn2 for the T-Beam are given as:

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Limitations on Limitations on Reinforcement for Flange Reinforcement for Flange

BeamsBeams• Lower Limits

– Positive Reinforcement

c

ysmin

w

y

4 larger of

1.4

ffA

b df

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Limitations on Limitations on Reinforcement for Flange Reinforcement for Flange

BeamsBeams• Lower Limits

– For negative reinforcement and T sections with flanges in tension

c

y(min)

y

2 larger of

1.4

ff

f

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Example - T-BeamExample - T-BeamFind MFind Mnn and M and Mu u for T-Beam.for T-Beam. hf = 15 cmd = 40cm As = 50cm2 fy = 420Mpa fc = 25Mpabw= 30cm L = 5.5mS=2.15m

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Example of T-BeamExample of T-BeamConfirm beff

eff

f w

550 137 .4 4

16 16 15 30=270cm.

2.15 m 215 .

Lb cm

h b

b cm

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2s y

c eff

1

s

50 4207.21

0.85 0.85 25 137

7.21 8.5 cm0.85

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0.011 0401 0.003 1 0.0038

.005.5

cm mpaA fa cm

f b Mpa cm

ac

t cm ok

dc

Compute the equivalent c value and check the strain in the steel, s

Steel will yield in the tension zone.

Assume a<t.

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2s

w

y

min minc

y

50 cm0.042

30 cm 40 cm

1.4 1.4 0.0033420

0.003325 0.003

4 4 420

0.042 0.0033

Ab d

f

ff

Compute the reinforcement and check to make sure it is greater than min

Section works for minimum reinforcement.

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Compute nominal moment components

n y

4 6

20.072150 10 420 10 0.40

2764295 .

saM A f d

N m

0.9 764295 =688 k .u nM M

N m