A Concrete I Lecture8
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Transcript of A Concrete I Lecture8
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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
4
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
12
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
15
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