Two Way Slab Design
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Transcript of Two Way Slab Design
PetrofacPetrofac International Limited
PROJECT: Kashagan Development Experimental ProgramDOCUMENT No. DATE
28-05-2006
TITLE : Design Calculation for Two-Way SlabDESIGNED CHECKED SHEET
JJX MNR
Grade of concrete = 25
Grade of reinforcement = 390
Density of concrete = 25
Clear cover to reinforcement = 25 mm
= 3500 mm
= 5500 mm
1.571 < 2. Hence, the slab is two-way.
Thickness of slab = 150 mm
Type of panel (Edge Condition) =
3.1 Dead Load:
Self-weight of slab = 3.75
Load due to floor finish = 1.25
Load due to insulation, if any = 0.5
Other loads, if any = 0
= 5.5
3.2 Live Load:
Live load on slab = 7.5
3.3 Snow Load:
Snow load on slab, if any = 1.5
3.4 Design Load:
Load factor for dead load = 1.4
Load factor for live load = 1.6
Load factor for snow load = 1.6
= 1.4 x 5.5 + 1.6 x 7.5 + 1.6 x 1.5
= 22.1
DESIGN OF TWO-WAY SLAB: (as per BS 8110:Part 1 - 1997)
1.0 GENERAL DATA:
N/mm2
N/mm2
kN/m3
2.0 SIZE OF SLAB:
Length of slab in shorter direction, lx
Length of slab in longer direction, ly
\ ly/lx =
One short edge discontinuous
3.0 LOADING:
kN/m2
kN/m2
kN/m2
kN/m2
\ Total dead load kN/m2
kN/m2
kN/m2
\ Total design load, n
kN/m2
PetrofacPetrofac International Limited
PROJECT: Kashagan Development Experimental ProgramDOCUMENT No. DATE
28-05-2006
TITLE : Design Calculation for Two-Way SlabDESIGNED CHECKED SHEET
JJX MNR
Refer Clause 3.5.3.4 of BS 8110-1:1997.
Maximum design ultimate moments (for unit width),
Refer Table 3.14 of BS 8110-1:1997 for bending moment coefficients.
Bending Moment (kN-m/metre width)
Direction Location Coefficient Moment, kN-m
X directionSupport 0.059 15.973
Mid span 0.044 11.912
Y directionSupport 0.037 10.017
Mid span 0.028 7.58
Refer Clause 3.5.3.7 of BS 8110-1:1997.
Maximum design ultimate shear force (for unit width),
Refer Table 3.15 of BS 8110-1:1997 for bending moment coefficients.
Shear Force (kN/metre width)
Direction Edge Coefficient Shear Force, kN
X directionContinuous 0.479 37.051
Discontinuous 0.000 0
Y directionContinuous 0.360 27.846
Discontinuous 0.240 18.564
4.0 CALCULATION OF BENDING MOMENTS:
for span lx, msx = bsx n lx2
for span ly, msy = bsy n lx2
msxS =
msxM =
msyS =
msyM =
5.0 CALCULATION OF SHEAR FORCE AT EDGES:
for span lx, vsx = bvx n lx
for span ly, vsy = bvy n lx
vsxC =
vsxD =
vsyC =
vsyD =
PetrofacPetrofac International Limited
PROJECT: Kashagan Development Experimental ProgramDOCUMENT No. DATE
28-05-2006
TITLE : Design Calculation for Two-Way SlabDESIGNED CHECKED SHEET
JJX MNR
6.1 Design for Bending Moment:
Refer 3.4.4.4 of BS 8110:Part 1 - 1997 K' = 0.156 (no redistribution of moments)
Moment redistribution ratio, 1
Considering unit width of slab, b = 1000 mm
Minimum reinforcement required, 0.0013 x 1000 x 150 (0.13%, Refer Table 3.25
= 195 of BS 8110:Part 1 - 1997)
a) Calculation of Bottom Reinforcement in X direction:
Design Bending Moment = 11.912 kN-m
d = 120 mm
K =
= 0.033 (Compression reinf. is not required)
z = d {0.5 + sqrt(0.25 - K/0.9)}
= 114 mm
= 283
283
Diameter of reinforcement = 10 mm
Required spacing of reinforcement = 277 mm
Maximum spacing of reinforcement allowed = Refer 3.12.11.2.3 of
= 190 BS 8110:Part 1 - 1997
Provide 10 T @ 175 mm c/c (at the bottom of slab along X direction).
449
Hence, percentage of reinforcement provided 0.299 %
b) Calculation of Bottom Reinforcement in Y direction:
Design Bending Moment = 7.58 kN-m
d = 111 mm
K =
= 0.025 (Compression reinf. is not required)
6.0 DESIGN OF SLAB:
bb =
Astmin =
mm2
Mu/bd2 fcu
(zmax = 0.95d)
Ast = Mu/(0.95 fy z)
mm2
Comparing with Astmin,
\ Area of reinforcement required Astreq = mm2
70000 bb/fy + dia. of bar
\ Area of reinforcement provided, Astprovided = mm2
Mu/bd2 fcu
PetrofacPetrofac International Limited
PROJECT: Kashagan Development Experimental ProgramDOCUMENT No. DATE
28-05-2006
TITLE : Design Calculation for Two-Way SlabDESIGNED CHECKED SHEET
JJX MNR
z = d {0.5 + sqrt(0.25 - K/0.9)}
= 105.45 mm
= 195
195
Diameter of reinforcement = 8 mm
Required spacing of reinforcement = 257 mm
Maximum spacing of reinforcement allowed = Refer 3.12.11.2.3 of
= 188 BS 8110:Part 1 - 1997
Provide 8 T @ 175 mm c/c (at the bottom of slab along Y direction).
287
Hence, percentage of reinforcement provided 0.191 %
c) Calculation of Top Reinforcement in X direction:
Design Bending Moment = 15.973 kN-m
d = 120 mm
K =
= 0.044 (Compression reinf. is not required)
z = d {0.5 + sqrt(0.25 - K/0.9)}
= 113.81 mm
= 379
379
Diameter of reinforcement = 10 mm
Required spacing of reinforcement = 207 mm
Maximum spacing of reinforcement allowed = Refer 3.12.11.2.3 of
= 190 BS 8110:Part 1 - 1997
Provide 10 T @ 175 mm c/c (at the top of slab along X direction).
449
Hence, percentage of reinforcement provided 0.299 %
(zmax = 0.95d)
Ast = Mu/(0.95 fy z)
mm2
Comparing with Astmin,
\ Area of reinforcement required Astreq = mm2
70000 bb/fy + dia. of bar
\ Area of reinforcement provided, Astprovided = mm2
Mu/bd2 fcu
(zmax = 0.95d)
Ast = Mu/(0.95 fy z)
mm2
Comparing with Astmin,
\ Area of reinforcement required Astreq = mm2
70000 bb/fy + dia. of bar
\ Area of reinforcement provided, Astprovided = mm2
PetrofacPetrofac International Limited
PROJECT: Kashagan Development Experimental ProgramDOCUMENT No. DATE
28-05-2006
TITLE : Design Calculation for Two-Way SlabDESIGNED CHECKED SHEET
JJX MNR
d) Calculation of Top Reinforcement in Y direction:
Design Bending Moment = 10.017 kN-m
d = 111 mm
K =
= 0.033 (Compression reinf. is not required)
z = d {0.5 + sqrt(0.25 - K/0.9)}
= 105.45 mm
= 257
257
Diameter of reinforcement = 8 mm
Required spacing of reinforcement = 195 mm
Maximum spacing of reinforcement allowed = Refer 3.12.11.2.3 of
= 188 BS 8110:Part 1 - 1997
Provide 8 T @ 175 mm c/c (at the top of slab along Y direction).
287
Hence, percentage of reinforcement provided 0.191 %
6.2 Check for Shear Stress:
Refer 3.5.5 of BS 8110:Part 1 - 1997.
Maximum shear force, V = 37.051 kN
Average effective depth, d = 115.5 mm
Design shear stress, v = V/bd
= 0.321
Refer 3.5.5.2 of BS 8110:Part 1 - 1997.
Maximum allowable shear stress =
= 4 Hence Ok.
Refer Table 3.8 of BS 8110: Part 1 - 1997.
Mu/bd2 fcu
(zmax = 0.95d)
Ast = Mu/(0.95 fy z)
mm2
Comparing with Astmin,
\ Area of reinforcement required Astreq = mm2
70000 bb/fy + dia. of bar
\ Area of reinforcement provided, Astprovided = mm2
N/mm2
0.8 (fcu)0.5 or 5 N/mm2, whichever is less
N/mm2
PetrofacPetrofac International Limited
PROJECT: Kashagan Development Experimental ProgramDOCUMENT No. DATE
28-05-2006
TITLE : Design Calculation for Two-Way SlabDESIGNED CHECKED SHEET
JJX MNR
=
Factor for characteristic strength of concrete = where,
= 1
0.191
1.364 (without shear reinforcement)
Partial safety factor for material 1.25 (Refer 2.4.4.1 of BS 8110:Part 1 - 1997)
0.496
Shear stress is less than the design concrete shear stress, hence Ok.
6.3 Check for Deflection:
Refer 3.5.7 of BS 8110:Part 1 - 1997.
Span/effective depth, 3500/120
= 29.167
Refer Table 3.9 & Cl. 3.4.6.4 of BS 8110: Part 1 - 1997.
Basic span/effective depth ratio = 26 (Continuous Support)
Refer equations 7 & 8 of BS 8110: Part 1 - 1997.
Modification factor for tension reinforcement =
Design service stress, 1
Refer 3.4.6.2 of BS 8110: Part 1 - 1997.
1
163.88
0.827
2
Refer equation 9 of BS 8110: Part 1 - 1997.
Modification factor for compression reinf. =
= 1.091
Hence, modified span/effective depth ratio = 2 x 1.091 x 26
= 56.732 > 29.167, hence Ok.
Design concrete shear stress, nc 0.79 {100 As/(bv d)}1/3 {400/d}1/4 /gm
(fcu/25)1/3 fcumax = 40 N/mm2
100 As/bv d =
{400/d}1/4 =
gm =
\ nc = N/mm2
lx/dx =
0.55 + (477 - fs) < 2
120 [0.9 + M/bd2]
fs = 2 fy As req
3 As prov bb
As no redistribution of moment is done, bb =
\ fs = N/mm2
Mu/bd2 =
\ Modification factor for tension reinforcement =
1 + 100A's prov/bd < 1.5
3 + 100A's prov/bd
PetrofacPetrofac International Limited
PROJECT: Kashagan Development Experimental ProgramDOCUMENT No. DATE
28-05-2006
TITLE : Design Calculation for Two-Way SlabDESIGNED CHECKED SHEET
JJX MNR
CONTENTS
S. No. Description Page No.
1.0 General Data 1
2.0 Size of Slab 1
3.0 Loading 1
3.1 Dead Load 1
3.2 Live Load 1
3.3 Snow Load 1
3.4 Design Load 1
4.0 Calculation of Bending Moments 2
5.0 Calculation of Shear Force at Edges 2
6.0 Design of Slab 3
6.1 Design for Bending Moment 3
6.2 Check for Shear Stress 5
6.3 Check for Deflection 6
PetrofacPetrofac International Limited
PROJECT: Kashagan Development Experimental ProgramDOCUMENT No. DATE
28-05-2006
TITLE : Design Calculation for Two-Way SlabDESIGNED CHECKED SHEET
JJX MNR
PetrofacPetrofac International Limited
PROJECT: Kashagan Development Experimental ProgramDOCUMENT No. DATE
28-05-2006
TITLE : Design Calculation for Two-Way SlabDESIGNED CHECKED SHEET
JJX MNR