Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939



Principles of Geotechnical Enginee...

9th Edition
Braja M. Das + 1 other
ISBN: 9781305970939
Textbook Problem

A square footing is subjected to an inclined load as shown in Figure 16.19. If the size of the footing, B = 2.25 m, determine the gross allowable inclined load, Q, that the footing can safely carry. Given: α = 12° and Fs = 3.5.


Figure 16.19

To determine

Find the gross allowable inclined load (Q) that the footing can safely carry.


Given information:

The width of footing B is 2.25 m.

The unit weight of the soil γ is 16.8kN/m3.

The saturated unit weight of the soil γsat is 19kN/m3.

The value of cohesion c is 38kN/m2.

The soil friction angle ϕ is 27°.

The depth of foundation Df is 2 m.

The depth of foundation above the water table D is 1 m.

The inclination of the load on the foundation with respect to the vertical α is 12°.

The factor of safety Fs is 3.5.


Determine the shape factor λcs using the relation.


Here, Nq is the contribution of surcharge, Nc is the contribution of cohesion,

Refer Table 16.2, “Bearing-capacity factors Nc, Nq, and Nγ” in the textbook.

Take the Nc as 23.94, Nq as 13.20, and Nγ as 14.47 for the ϕ value of 27°.

Substitute 2.25 m for B, 2.25 m for L, 13.20 for Nq, and 23.94 for Nc.


Determine the depth factor λcd using the relation.


Substitute 2 m for Df and 2.25 m for B.


Determine the inclination factor λci using the relation.


Substitute 12° for α.


Determine the shape factor λqs using the relation.


Substitute 2.25 m for B, 2.25 m for L, and 27° for ϕ.


Determine the depth factor λqd using the relation.


Substitute 27° for ϕ, 2 m for Df, and 2.25 m for B.


Determine the shape factor λγs using the relation.


Substitute 2.25 m for B and 2.25 m for L.


Determine the inclination factor λγi using the relation.


Substitute 12° for α and 27° for ϕ.


Determine the magnitude of q using the relation.

q=γ(DfD)+γD=γ(DfD)+(γsatγw)D (1)

Here, γ is the effective unit weight of soil and γw is the unit weight of water

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