Week 6 Challenge
Aim :
- To Summarize your study for the bending moment, shear force and deflection diagrams for the raft foundation in stadd and compare them with manual calculation for different set of loads. Fill of 1 m on top slab.
1) Earth pressure, 2) self-weight, 3) Surcharge, 4) 70R load.
- Based on the analysis design the members and outline the thought process in selecting the member sizes along with the raft foundation design.
- Detailing of reinforcement in the base slab.
Also, what will be the change in shear in base slab if there is
a)5 m fill
b)1 m fill on top of bridge
Introduction : The given box structure is of 12m clear span and 5.5m clear height with top slab thickness 0.85m, vertical wall thickness 0.9m & base slab thickness 0.9m. Depth of fill in top slab 1m.
Procedure :
- Staad creation:
Manual Calculation
- Self Weight of the bottom Slab
The thickness of the bottom slab = 0.9m
Width of the Underpass = 12.0m
Thickness of wall = 0.9m
Volume of slab = (12+2 x 0.9) x 0.9 x 1 = 12.42 m3
Slf wt of slab = 12.42 x 2.5 = 31.05 t
- Earth Pressure Calculation
θ = 30 degree
earth pressure co-efficient(c) = 0.5
Density of soil = 20 Kn/m3
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Height from top (m) |
Intensity of Earth pressure(KN/m2) |
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1.400 |
1.400 |
0.5 *20*1.4 |
= |
14.00 |
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0.450 |
1.850 |
0.5 *20*1.85 |
= |
18.50 |
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0.150 |
2.000 |
0.5 *20*2 |
= |
20.00 |
|
5.175 |
7.175 |
0.5 *20*7.175 |
= |
71.75 |
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0.150 |
7.325 |
0.5 *20*7.325 |
= |
73.25 |
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0.450 |
7.775 |
0.5 *20*7.775 |
= |
77.75 |
- Live load surcharge
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Equivalent height |
= |
1.0 |
m |
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Uniform Intensity of loading |
= |
1.2*20*0.5 |
= |
10.00 |
KN/m2 |
- 70R load
For 70R loading 70ton of vehicular loading is being applied on the structure
Applying in staad model
- Self Weight
Self wt has been applied to the structure by inputing the self wt. as -1 in staad.
- Earth Pressure
The Earth pressure applied to the structure from top to bottom in Linear varying load.
- Live load surcharge
- 70R load
Bending Moment, SFD & Deflection
BM
SFD
DEFLECTION
2.Based on the analysis design the members and outline the thought process in selecting the member sizes along with the raft foundation design.
ANS:
4.Also, what will be the change in shear in base slab if there is
a)5 m fill
It is being analyzed by applying the load in Staad pro
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Height of fill |
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= |
5 |
m |
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Load (UDL) on top slab |
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= |
100.0 |
KN/m |
Applying the load
Shear Force Diagram
- As per the analysis the maximum shear force for design is = 1102KN
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Maximum SF (VNS) |
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= |
1102 |
KN |
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Shear design |
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Shear force VEd |
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= |
0.5*bw*d*ν*fcd |
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= |
90411.1 |
KN |
> |
1102 KN |
Safe |
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Where ν is a strength reduction factor |
= |
0.6(1-fck/310)fck |
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= |
16.26 |
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Longitudinal force (NEd) |
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= |
0 |
KN |
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Sh. Force by shear reinforcement (V Rd.s) |
= |
Aswzfywdcotθ/s |
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Shear resistance of section without shear reinforcement (VRd.c) |
= |
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[0.12K(80ρ1.fck)0.33+0.15σcp]bw.d |
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Where |
K= |
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200 |
= |
1.490881 |
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d |
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νmin= |
0.031K3/2fck1/2 |
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= |
0.309091 |
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σcp= |
NEd/Ac |
<= |
0.2fcd |
= |
0 |
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ρ1= |
Asl/bw.d |
<= |
0.02 |
= |
0.004 |
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VRd.c |
= |
317.52 |
KN |
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Subject to a Minimum shear resistance (νRd.c) |
= |
(νmin+0.15σcp)bw.d |
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= |
256.55 |
KN |
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VRd.c |
= |
317.52 KN |
> |
1102 KN |
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Shear Reinforcement required |
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If required |
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VNS |
= |
VRd.max |
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= |
acwbwzν1fcd/(cotθ+tanθ) |
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= |
acwbwzν1fcd/(2/sin2θ) |
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sin2θ |
= |
VNS/acwbwzν1fcd/2 |
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= |
0.338 |
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θ |
= |
9.89 |
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Cotθ |
= |
5.735258828 |
<= 2.5 |
>= 1 |
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Dia of bar used as shear reinforcement |
= |
12 |
mm |
2 |
Legged |
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Shear Force by shear reinforcement (V Rd.s) |
= |
Aswzfywdcotθ/s |
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= |
VNS |
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Sapcing, s |
= |
Aswzfywdcotθ/s |
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= |
145 |
mm |
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Provide Shear reinforcement vertically |
2 |
Legged |
12 |
mm dia @ |
125 |
mm C/C |
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b)1 m fill on top of bridge
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Maximum SF (VNS) |
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= |
497 |
KN |
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Shear design |
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Shear force VEd |
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= |
0.5*bw*d*ν*fcd |
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= |
90411.1 |
KN |
> |
497 KN |
Safe |
|||||||||||||||
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Where ν is a strength reduction factor |
= |
0.6(1-fck/310)fck |
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|||||||||||||||||||
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= |
16.26 |
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Longitudinal force (NEd) |
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= |
0 |
KN |
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Sh. Force by shear reinforcement (V Rd.s) |
= |
Aswzfywdcotθ/s |
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Shear resistance of section without shear reinforcement (VRd.c) |
= |
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[0.12K(80ρ1.fck)0.33+0.15σcp]bw.d |
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Where |
K= |
|
200 |
= |
1.490881 |
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d |
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νmin= |
0.031K3/2fck1/2 |
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= |
0.309091 |
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σcp= |
NEd/Ac |
<= |
0.2fcd |
= |
0 |
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ρ1= |
Asl/bw.d |
<= |
0.02 |
= |
0.004 |
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VRd.c |
= |
317.52 |
KN |
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Subject to a Minimum shear resistance (νRd.c) |
= |
(νmin+0.15σcp)bw.d |
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= |
256.55 |
KN |
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VRd.c |
= |
317.52 KN |
> |
497 KN |
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Shear Reinforcement required |
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If required |
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VNS |
= |
VRd.max |
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= |
acwbwzν1fcd/(cotθ+tanθ) |
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= |
acwbwzν1fcd/(2/sin2θ) |
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sin2θ |
= |
VNS/acwbwzν1fcd/2 |
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= |
0.153 |
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θ |
= |
4.39 |
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Cotθ |
= |
13.02665484 |
<= 2.5 |
>= 1 |
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|||||||||||||||
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Dia of bar used as shear reinforcement |
= |
8 |
mm |
2 |
Legged |
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|
|||||||||||||||
|
Shear Force by shear reinforcement (V Rd.s) |
= |
Aswzfywdcotθ/s |
|
|
||||||||||||||||||||
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|
|
|
|
|
= |
VNS |
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|
|||||||||||||||
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Sapcing, s |
= |
Aswzfywdcotθ/s |
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= |
142 |
mm |
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|
|||||||||||||||
|
Provide Shear reinforcement vertically |
2 |
Legged |
8 |
mm dia @ |
125 |
mm C/C |
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