Week 6 Challenge
Aim :-To analyze and design the raft foundation considering earth pressure , seft weight , surcharge , 70R loads.
Modeling in Staad Pro:- The bridge is modeled as a plan frame structure taking the centerline dimension of the structure in Staad -pro . As the length of the bridge is more than twice its width , the box will be analyzed for unit length and the design will be adopted for the entire length . Loads corresponding to the unit length are evaluated and the structure analyzed and designed.Since the box is fully resting on the soil, discrete spring supports are provided below the base on a sub -grade modulus of the soil available at the base. The sizes of the member are assigned accordingly in the model.
Loading on the structure
Self - weight of the base slab
The Sizes of the members are given below :-
The thickness of the top slab =0.85m
Assumed Height of top haunch =0.15m
The thickness of the Bottom slab =0.9m
Assumed Height of bottom haunch =0.15m
Clear Height =5.5m
Clear weight =12m
The Volume of the bottom Slab is =0.9*1*(12*0.9*0.9)
=12.42m^3
Weight of bottom Slab =12.45*25
=310.5kN
Earth Pressure :-
Angle of repose =30 degree
At rest earth pressure co-efficient= 0.5
Density of soil=20 kN/m^3
Height from the top
The intensity of earth pressure (kN/m^2)=rest earth pressure *density of soil*height
| Height from top (m) | The intensity of earth pressure (kN/m^2) |
| 0.425 | 0.5*20*0.425=4.25 |
| 0.85 | 0.5*20*0.85=8.5 |
| 1 | 0.5*20*1=10 |
| 6.2 | 0.5*20*6.2=62 |
| 6.35 | 0.5*20*6.35=63.5 |
| 6.8 | 0.5*20*6.8=68 |
The earth pressure acting on the structure is ssigned as trapezoidal on the both sides of the box structure in staad.
Similarly , the live load surcharge and braking loads are applied using specific load commands
Live load surcharge:-
Equivalent height=12
Intensity of loading=1.2*20*0.5
=12kN/m^2
Braking load
Max. Live load on the box =700 kN
Width of the box = 12m
Braking Load =14.58 kN
Load Combination
Partial Safety Factors for the ulitmate limit state are considered as per IRC 6. The following loaded combinations are used.
The Analysis is carried out using STAAD-PRO.
From the analysis results, a critical case of the load values is adopted for the design.The bending moment will be maximum at the center of the base slab . For the worst combination design has to be carried out. The critical section for shear will be at the distance "d" from the face of the support. The bending moment, shear force and deflection daigram are given below.
Analysis Results:-
| Load | Bending Moment Mz,(kN.m) | Shear Force Fy, (kN) |
| Dead Load | 398.83 | 232.11 |
| Earth Pressure | 41.38 | 1.07 |
| Live Load Surcharge | 12.98 | 17.8 |
| Braking Load | 11.94 | 6.06 |
2.Design of the member based on the analysis and indicate the selection of the member size.
The members of the underpass i.e, the top and bottom slabs and vertical walls are designed as the beam members subjected to axial thrust and flexure.The assumed dimensions of the selections are for adequacy of the Reinforcement provided and stresses in the concrete and reinforcing steel.
Using the load combination, bending Moment envelops for the structures are obtained. for the Maximum B.M corresponding,axial forces are picked out from the STAAD post-Processor.
Max factored bending moment =470kN.m
Max factored shear force 320kN
Depth of base slab,D 900m
Width of base slab ,b 1000mm
Grade of concrete M30
Grade of steel Fe500
Es = 2*10*5Mpa
Ecm 31000Mpa
DEsign yeild strength of shear reinforcement Fywd=0.87fyk/ys
=0.8*500*/1.15
=348 Mpa
material Safety factor
COncrete 1.5
Steel = 1.15
Ulimate compressive strain in concrete 0.035 up to fck
Modular ratio 6.45
Long trem modulr ratio 12.9
Ulimate tensile strain in steel =0.00217
Coefficient, 0.67
Factor 0.8
1
The design value of concrete comressive strength fcd=a*fck/ym
13.4 Mpa
Fav= 10.72
The effective depth of the member 900-50-10
=840mm
M/(bd^2*Fav)
470*10^6/(1000*840^2*10.72)
0.062
518.52 mm
Force in compression =Force in Tension
fy*As/Ys=n*fcd*a`lamda`x*b =Fav*x*b
M=Fav*x*b*(d-bx)
which gives , x=d(1-(1-4bkav)^(1/2)/2b
53.44mm<518.52 mm
Reinforcement area ,
1317.6mm^2
Provide 10 mm reiforcement=1963mm^2>1317.6mm^2
Hence ok
Netural axis depth, 79.62 mm <518.58 mm
Hence ok
Xlim/d
518/840
0.617
Rlim4.98
Effective depth required( Mu/(Rlim*b))
307mm<900 mm
Hence Safe
Selection of member Size:-
The size of the base slab depends upon factors such as the height of the bridge, uplift pressure acting on the foundation, soil fill on the top of the box.
When the height of the bridge is more, the size of the member required will be more because of the increase in lever arm as well as force. In such cases, the forces can be reduced by reducing the height of the structure and providing fill on top.The hydrological parameter should be taken into account in this case.
To avoid uplift, the size of the base slab can be increased. Alternately, the lenght of the raft slab can be increased. This will result in an increased in uplift but can be compensated by the earth from the top. The more the fill on top slab , the proportion of the raft foundation is more. Generally, span /10 is adopted for selection of base slab thickness , later it can be optimized seeing design and economy. While determining the member sizes feasibility , safety , hydrology, and site criteria also be oberved.
4 .To analyze the change in shear in the base slab if there is a 5m fill SIDL due to earth fill
The thickness of the earth fill on top is 5m
The density of fill material 20 kN/m^3
UDL due to earthfill 100kN/m
It is applied as a dead load on top, Uniformly distributed throughout the weigth of underpass.
After analysis, the design shear force is taken as
Shear design :-
Shear force=0.5*1000*840*16.26*13.4
Where v is the strength reduction factor
Longitudinal force=0 kN
Shear force by shear reinforcement
Shear resistance of the section without shear reinforcement
Vrdc=0.12k(80plfck)^0.33+0.15ac*p*bw*d
=100.937 Kn
Hence shear reinforcement is required
The diameter of the bar used as shear reinforcement is 2
Shear force by shear reinforcement Vns
Provide shear reinforcement vertically
To analyze the change in shear in the base slab if there is a 0m fill SIDL due to earth fill
After analysis, the design shear force is taken as
Shear design :-
Shear force=91511.3 kN
Where v is the strength reduction factor
Longitudinal force=0 kN
Shear force by shear reinforcement
=100.937 kN
Shear resistance of the section without shear reinforcement
Hence shear reinforcement is required and should be provided as per IRC 112-2020.