   Chapter 16, Problem 16.12P Principles of Geotechnical Enginee...

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

Solutions

Chapter
Section 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.

Explanation

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.

Calculation:

Determine the shape factor λcs using the relation.

λcs=1+(BL)(NqNc)

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.

λcs=1+(2.252.25)(13.2023.94)=1.55

Determine the depth factor λcd using the relation.

λcd=1+0.4(DfB)

Substitute 2 m for Df and 2.25 m for B.

λcd=1+0.4(22.25)=1.355

Determine the inclination factor λci using the relation.

λci=λqi=(1α90°)2

Substitute 12° for α.

λci=(112°90°)2=0.751

Determine the shape factor λqs using the relation.

λqs=1+(BL)tanϕ

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

λqs=1+(2.252.25)tan27°=1.509

Determine the depth factor λqd using the relation.

λqd=1+2tanϕ(1sinϕ)2(DfB)

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

λqd=1+2tan27°(1sin27°)2(22.25)=1.27

Determine the shape factor λγs using the relation.

λγs=10.4(BL)

Substitute 2.25 m for B and 2.25 m for L.

λγs=10.4(2.252.25)=0.6

Determine the inclination factor λγi using the relation.

λγi=(1αϕ)2

Substitute 12° for α and 27° for ϕ.

λγi=(112°27°)2=0.308

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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