Footings And Rafts

FOOTINGS AND RAFTS

 P₁=800kN

P₂ =1000kN

q_o =20 t/m²,M15,  f_y=415kN/m²

Fig. 4.51 Loading on combined footing

Column size: 400x400mm.

See Fig 4.54 for details of footing.  Column design

Let pt=0.8%

A_x =.008A;  A_x=0.992A

Clause.39.3 of IS 456-2000

A=146763.8mm²

A_x =1174.11 mm²,  =145589.746mm²

Provide footing of 400x400size for both columns.

Using 8-16 j as main reinforcement and 8   j  @250c/c as lateral tie

Design of Footing

Fig. 4.52 Forces acting on the footing

Resultant of Column Load

R =1800 kN acting 3.08m from the boundary.

Area of the footing :

Taking length L=6m, Depth of footing  D_f=0.9m,

Width of footing,  =1.549m.

Therefore, provide footing of dimension 6m x 1.6m

Soil Pressure q = 180/ 6 x 1.6 =18.75 t/m²< 20 t/m² OK.

q_u=28.125 t/m²

Soil pressure intensity acting along the length =B x  =1.6x28.125 =45t/m.

R_B =119.88kN, R_C =150.12kN.

Thickness of Footing

 i. Wide beam shear:

Maximum shear force is on footing C,SF=115.02KN

 for percentage reinforcement P_t =0.2%

0.32 x d x 1.6=45 [2.556-0.2-d]

d=1.1m

 for percentage reinforcement  =0.6% 0.6 x d x 1.6=45 [2.556-0.2-d] d=0.847m.D=900mm.OK.

ii.Two way Shear Thickness of Footing

 i. Wide beam shear:

Maximum shear force is on footing C,SF=115.02KN

for percentage reinforcement  P_t=0.2%

0.32 x d x 1.6=45 [2.556-0.2-d]

d=1.1m

 for percentage reinforcement P_t =0.6%

0.6 x d x 1.6=45 [2.556-0.2-d]

d=0.847m.D=900mm.OK.

ii.Two way Shear

Column B

d=0.415m.

Column A

2d[(0.4+d)+(0.42+d/2)] x 96.8=120-28.125[(0.4+d)(0.42+d/2)] d=0.3906m

d_reqd =0.85mm

D_provided =900mm, d_reqd =850mm.OK.

 Flexural reinforcement

Along Length Direction

 M_u/bd²=1.15N/mm²

 Table 1of SP16

P_t  =0.354%

 P_tprovided=0.6% 

A_strequired=5100 mm²/mm

Provide 28 j @120mmc/c at top and bottom of the footing

Along width direction

 Raft Footing Design the raft footing for the given loads on the columns and spacing between the columns as shown below.

Fig 4.57 column locations and intensity of loads acting on the raft

a) Column sizes

 Take size of the columns are as: 300*450 mm for load of less than 115 ton

450*450 mm for a load of greater than 115 ton

Thickness of raft

Two way shear

The shear should be checked for every column, but in this case because of symmetry property checking for 115 t, 150 t, and 55 t is enough.

For 150 t column

Fig 4.58 section for two way shear for 150 t column

IS: 456-1978, 

b_c=450/450=1.0 

4(0.45+d)*d*96.8=150*1.5-5.607(0.45+d)2

Therefore d=0.562 m

For 115 t column

Fig 4.59 section for two way shear for 115 t column

2(0.45+d+0.15+0.3+d/2) d*96.8=115*1.5-5.607(0.45+d)(0.3+0.15+0.5d)

Therefore d=0.519 m

For 55 t column

Fig 4.60 section for two way shear for 55 t column

2(0.45+0.075+0.5d+0.15+0.3+0.5d) d*96.8=55*1.5-5.607(0.45+0.5d+0.075)(0.3+0.5d+0.15)

Therefore d=0.32 m

The guiding thickness is 0.562m and code says that the minimum thickness should not be less than 1.0m.

let provide a overall depth of 1.1m=D

d_pdv =1100-75-20/2=1015mm.

To calculate k &  l Stiffness factors

There are two criterions for checking the rigidity of the footing:

Plate size used is 300*300 mm.

For clays:  Mus=0.5,

If column spacing is less than 1.75/ l, then the footing is said to be rigid.

Therefore the given footing is rigid.

One criterion showing the footing is flexible and another showing that the given footing is rigid. Both are contradicting each other, so design the footing for both criterions.

Reinforcement in width direction

From SP-16 graphs

P_t =0.102%, but minimum is 0.12%.

A_dx =(0.12*1000*1015)/100=1218 mm²

Provide 20 mm diameter bars @250 c/c along shorter direction in bottom.

Reinforcement in length direction

Provide 20 mm diameter bars @250 c/c in longer direction.

Clause 33.3.1

Provide 20 mm diameter bars @ 200 c/c in central band and 20 mm diameter bars @300 c/c at other parts along shorter direction at bottom.

Shear (wide beam shear criterion)

In width direction

=0.235 N/mm² <  r(0.27 N/mm²)

Therefore no shear reinforcement is required.

Along the width direction

Fig. 4.63 Shear Force and Bending Moment Diagrams of strips 1 and 4

In width direction: Strip1/4:-  =141.2tm

Strip2/3

Fig. 4.64 Shear Force and Bending Moment Diagrams of strips 2 and 3

Strip 2/3

M_u =282.36tm

M/bd² = 0.364N/mm²

Minimum  P_t=0.12%has to be provided.

Provide 20  j @200c/c in centre band and 20 j @300c/c at other parts along the shorter direction.

1. Shear check

Along width direction:-

For strip1/4:

V_a=76.35t            

For strip 2/3:                

V_a=159.14 t         

Hence no shear reinforcement is required.

Development Length

At the ends, length of bar provided=150mm.

Extra length to be provided=1128.3-150-8x20=818.3mm.

Provide a Development length of 850mm

3. Transfer of load at the base of the column:-

For end column;            

A1=2650X2725=7.22125x106mm²     

A2=300x450=135000mm²