Ex: Design of a mat foundation following rigid design method.

Allowable bearing capacity for the foundation soil, qallowable=180kPa.

Young’s Modulus of concrete, Econcrete=20x106kPa, Coefficient of Subgrade

reaction, ks=3000kN/m3.

Load Factor, LF=1.6.

fc’= 25 Mpa and fy= 420 MPa for the column and the footing, Column

dimensions 40 x 40 cm.

Design the mat foundation with the column

loads given in the figure.

a) Calculate eccentricity of the resultant

load and soil pressures at points A, B, C,

D, E and F.

b) Determine thickness of the foundation

pad by diagonal tension shear check at

Column F.

c) Check rigidity of the mat. Use a strip

width of 2m.

d) Calculate adjusted average soil pressure

and the adjusted column loads for strip

ABC. Use a strip width of 2m.

e) Plot Shear and Moment diagrams for

strip ABC and indicate design moments

for top steel and bottom steel in the

longitudinal direction.

3m 3m

4m

A B C

D E F

TOTAL LOADS (kN)

A 500

B 600

C 650

D 400

E 500

F 700

a) eccentricity of the resultant load and soil pressures at points A, B, C, D, E and F.

Soil pressures. All less than allowablebearing pressure.

b)thickness of the foundation pad by diagonal tension shear check at Column F.

c) Checking rigidity of the mat using a strip width of 2m.

d) adjusted average soil pressure and the adjusted column loads for strip ABC, using a strip width of 2m.

Due to eccentricity of R for strip ABC, the pressure distribution needs to be reconsidered.

e) Plot of Shear and Moment diagrams for strip ABC, design moments for longitudinal direction.

65.926

-724.139

425.643

-522.405

920.351

-106.639

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

0 1 2 3 4 5 6 7V (

kN)

x-distance (m)

6.538

-514.186

2.677

-729.265

-820.462

-1000

-800

-600

-400

-200

0

200

0 1 2 3 4 5 6 7

M (

kNm

)

Example exact solution using Microsoft Excel.

References

• J. N. Cernica, Foundation Design, Wiley.