analysis and design of slabs 2
TRANSCRIPT
Plain & Reinforced Concrete-1
CE-313
Analysis and Design of Slabs
Sixth TermCivil Engineering
Plain & Reinforced Concrete-1
Example: Design a cantilever projecting out from a room slab extending 1.0m and to be used as balcony (LL = 300 kg/m2). A brick wall of 250 mm thickness including plaster of 1.0m height is provided at the end of cantilever
fc’ = 17.25 MPa fy = 300 MPa
Slab thickness of room = 125 mm. Slab bottom steel in the direction of cantilever is # 13 @ 190 mm c/c
Plain & Reinforced Concrete-1
Solution:
1m
125 mm
cantilever
2
h1000L
mm10632
1251000L
Plain & Reinforced Concrete-1
Solution: (contd…)
min
106389
12 12
lh mm
Let’s use the same thickness as of the room
minhmm125h
d
mm98720125d Main steel in cantilever is at the top
Plain & Reinforced Concrete-1
Solution: (contd…)
Slab Load
2m/kg30024001000
125Self weight of
slab
75 mm brick ballast/ screed
2m/kg13518001000
75
60 mm floor finishes
2m/kg13823001000
60
Total dead load 2m/kg573138135300
Plain & Reinforced Concrete-1
Solution: (contd…)
Slab Load2m/kg300Live Load
1000
81.93006.15732.1ωu
2u m/kN46.11ω
m/kN46.11ωu For a unit strip
1000
81.919301125.02.1Pu
kN65.5Pu
Plain & Reinforced Concrete-1
Solution: (contd…)
2
LωLPM
2u
uu
kN65.5Pu
1.063m
m/kN46.11ωu
2
063.111.46063.165.5M
2
u
mkN48.12Mu Per meter width
3.1981000
1048.12
bd
M2
6
2u
0488.0f
'f85.0ω
y
c
0.0052ρ
Plain & Reinforced Concrete-1
Solution: (contd…)
2s 510mm9810000.0052A
d
# 13 @ 380 mm c/c already available in the form half the bent up bar from the room slab
2s mm342Ac/c380@13#
Plain & Reinforced Concrete-1
Solution: (contd…)
2168mm342-510 Remaining steel required at the top
c/c400@10#
Use
c/c380@10#
Distribution steel
2mm2501251000002.0
c/c280@10#
Plain & Reinforced Concrete-1
Solution: #13 @ 380 c/c
#10 @ 380 c/c
#10 @ 280 c/c
1500 mm
Slab bottom steel
Plain & Reinforced Concrete-1
Two-Way Edge Supported Slabs
Plain & Reinforced Concrete-1
Two-Way SlabsSlab resting on walls or sufficiently deep and rigid beams on all sides. 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.
Plain & Reinforced Concrete-1Design Methods
1. ACI co-efficient method2. Direct design method3. Equivalent frame method4. 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 more flexural capacity.
Lx
Ly
Plain & Reinforced Concrete-1ACI Co-efficient Method
Unit width strip is taken in both directions. The strip is designed separately for +ve and –ve moment
2nuu LωCM
C = ACI co-efficientωu = Slab load
“C” depends upon the end conditions of slab and the aspect ratioThree tables are available for “C”
• Dead load positive moment
• Live load positive moment
• -ve moment
M+ coefficients are increased by 25 % and M- coefficients are reduced by 10 % to get the result more closer to accurate solution.
Plain & Reinforced Concrete-1
Minimum Depth of 2-Way Slab for Deflection ControlAccording to ACI-318-1963
hmin = (inner perimeter of slab panel)/180 ≥ 90 mm
For fy = 300 MPa
180
LL2h yx
min
For fy = 420 MPa
165
LL2h yx
min
According to ACI-318-2005
9m36
1500f8.0Lh yn
min
y
x
L
Lm
Ln = clear span in short direction
Plain & Reinforced Concrete-1Example: Design the 4 marked slab panels of an ordinary house. Use US customary bars. fc’= 17.25 MPa fy = 300 MPa
4500 x 7000
6000 x 7000
3500 x 6000
6000 x 6000
1 2
3 4
Wall thickness = 228 mm
Plain & Reinforced Concrete-1
Solution: Panel Edge Conditions
Panel # 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 # 3Lx = 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
Plain & Reinforced Concrete-1
Solution: (contd…)
Slab Thickness
Generally same depth is preferred for one monolithic slab Calculate hmin for all the panels and select the largest value
9m36
1500f8.0Lh yn
min
Panel # 1
mm140
964.036
15003008.04500hmin
Panel # 2
mm150986.036
15003008.06000hmin
Plain & Reinforced Concrete-1
Solution: (contd…)
Panel # 3
mm117958.036
15003008.03500hmin
Panel # 4
mm1339136
15003008.06000hmin
mm150h
Plain & Reinforced Concrete-1Solution: (contd…)
Effective depth
mm12327hd1 For longer direction steel
d2 d1
Long direction steel
Short direction steel
mm1122101320hd2
For short direction steel
Plain & Reinforced Concrete-1
Solution: (contd…)
Slab Load
2m/kg36024001000
150Self weight of
slab
75 mm brick ballast/ screed
2m/kg13518001000
75
60 mm floor finishes
2m/kg13823001000
60
Total dead load 2m/kg633138135360
Plain & Reinforced Concrete-1
Solution: (contd…)
Slab Load2m/kg200Live Load
1000
81.96332.11.2ωd
2d m/kN45.71.2ω
2L
9.811.6ω 1.6 200 3.14 /
1000kg m
2u m/kN59.1014.345.7ω
Plain & Reinforced Concrete-1
Solution: (contd…)
Minimum Steel
bh002.0A mins
1501000002.0A mins 2
mins mm300A For a unit strip
Concluded