Download - Lec-25- Analysis and Design of Slabs
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Plain & Reinforced
Concrete-1CE-313
Lecture # 2516th May 2006
Analysis and Designof Slabs
By Engr. Azhar
Sixth TermCivil Engineering
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Example: Design a cantilever projecting out from a roomslab extending 1.0m and to be used as balcony (LL = 300kg/m2). A brick wall of 250 mm thickness including plasterof 1m height is provided at the end of cantilever.
fc = 17.25 MPa fy = 300 MPa
Slab thickness of room = 125 mm. Slab bottom steel 1in thedirection of cantilever is # 13 @ 190 mm c/c.
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Solution:
1m
125 mm cantilever
2
h1000L
mm10632
1251000L
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Solution: (contd)
mm8912
1063
12
hhmin
Let we use the same thickness as of the room
minhmm125h
d
mm98720125d Main steel in cantilever isat the top
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Solution: (contd)Slab Load
2m/kg30024001000
125Self weight of slab
75 mm brick ballast/ screed2m/kg1351800
1000
75
60 mm floor finishes
2
m/kg13823001000
60
Total dead load2m/kg573138135300
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Solution: (contd)Slab Load
2m/kg300Live Load
100081.93006.15732.1u
2
u m/kN46.11
m/kN46.11u
For a unit strip
1000
81.919301125.02.1Pu
kN65.5Pu
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Solution: (contd)
2
LLPM
2
uuu
kN65.5Pu
1.063m
m/kN46.11u
2
063.111.46063.165.5M
2
u
mkN48.12Mu Per meter width
3.1981000
1048.12
bd
M2
6
2
u
0488.0
f
'f85.0
y
c
0.0052
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Solution: (contd)
2
s 510mm9810000.0052A
d
# 13 @ 380 mm c/calreadyavailable in the form half thebent up bar from the room slab
2
s mm342Ac/c380@13#
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Solution: (contd)
2168mm342-510 Remaining steel required at the top
c/c400@10#
Use
c/c380@10#
Distribution steel 2mm2501251000002.0
c/c280@10#
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Solution: #13 @ 380 c/c
#10 @ 380 c/c
#10 @ 280 c/c
1500 mm
Slab bottom steel
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Two-Way EdgeSupported Slabs
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Two-Way SlabsSlab resting on walls or sufficiently deep and rigid beams on allsides. Other options are column supported slab e.g. Flat slab,waffle slab.
5.0L
Lm
y
x
Two-way slabs have two way bending unlike one-way slab.
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Design Methods1. ACI co-efficient method2. Direct design method3. Equivalent frame method
4. Finite element method
Notes
1. In two-way slabs shorter direction strip carry greater%age of load.
2. Steel will be more in shorter direction.3. Shorter direction steel will be placed near the outer edge
to get more d means more lever arm to get moreflexural capacity.
Lx
Ly
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ACI Co-efficient MethodUnit width strip is taken in both directions. The strip isdesigned separately for +ve and ve moment.
2
nuu LCM C = ACI co-efficientu= Slab load
C depends upon the end conditions of slab and theaspect ratio.Three tables are available for C
Dead load positive moment
Live load positive moment
-ve moment
M+coefficients are increasedby 25 % and M-coefficientsare reduced by 10 % to getthe result more closer toaccurate solution.
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Minimum Depth of 2-Way Slab for DeflectionControl
According to ACI-318-1963
hmin= (inner perimeter of slab panel)/180 90 mm
For fy= 300 MPa180
LL2h
yx
min
For fy= 420 MPa 165
LL2
h yx
min
According to ACI-318-2005
9m36
1500f8.0Lh
yn
min
y
x
L
Lm
Ln = clear span in short direction
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Example: Design the 4 marked slab panels of an ordinaryhouse. Use US customary bars. fc= 17.25 MPa fy= 300 MPa
4500x
7000
6000x
7000
3500x
6000
6000x
6000
1 2
3 4
Wall thickness = 228 mm
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Solution: Panel Edge ConditionsPanel # 1Lx= 4.5m , Ly= 7.0mm = 0.64 > 0.5, 2-way slab
Panel # 2Lx= 6.0m , Ly= 7.0mm = 0.86> 0.5, 2-way slab
Panel # 3
Lx= 3.5m , Ly= 6.0mm = 0.58 > 0.5, 2-way slab
Panel # 4Lx= 6.0m , Ly= 6.0mm = 1 > 0.5,2-way slab
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Solution: (contd)Slab Thickness
Generally same depth is preferred for one monolith slab.Calculate hminfor all the panels and select the largest value.
9m36
1500f8.0Lh
yn
min
Panel # 1
mm140964.036
15003008.04500
hmin
Panel # 2
mm150
986.036
15003008.06000hmin
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Solution: (contd)
Panel # 3
mm117
958.036
15003008.03500hmin
Panel # 4
mm1339136
15003008.06000
hmin
mm150h
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Solution: (contd)Effective depth
mm12327hd1
For longer direction steel
d2 d1
Long direction steel
Short direction steel
mm1122101320hd2
For short direction steel
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Solution: (contd)Slab Load
2m/kg36024001000
150Self weight of slab
75 mm brick ballast/ screed2m/kg1351800
1000
75
60 mm floor finishes
2m/kg13823001000
60
Total dead load2m/kg633138135360
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Solution: (contd)Slab Load
2m/kg200Live Load
1000
81.96332.11.2d
2
d m/kN45.71.2
2L m/kg14.3100081.92006.11.2
2
u m/kN59.1014.345.7
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Solution: (contd)Minimum Steel
bh002.0Amins
1501000002.0Amins
2
mins mm300A For a unit strip
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Concluded