lec-25- analysis and design of slabs

8/13/2019 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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Plain & Reinforced Concrete-1

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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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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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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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

lec-25- analysis and design of slabs

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