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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.
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