A six-story building with plan dimensions of 150 ft × 150 ft has a 12 ft deep basement. This building is subjected to horizontal wind loads, and the structural engineer wishes to transfer these loads into the ground through the basement walls. The maximum horizontal force acting on the basement

Question

A six-story building with plan dimensions of 150 ft × 150 ft has a 12 ft deep basement. This building is subjected to horizontal wind loads, and the structural engineer wishes to transfer these loads into the ground through the basement walls. The maximum horizontal force acting on the basement wall is limited by the passive pressure in the soil. Using Rankine's theory, compute the maximum force between one of the basement walls and the adjacent soil assuming full passive conditions develop, then convert it to an allowable force using a factor of safety of 3. The soil is a silty sand with [latex]c^{\prime }= 0[/latex], [latex]Φ^{\prime }= 30°[/latex], and [latex]γ= 119 lb/ft^{3}[/latex], and the ground surface surrounding the building is essentially level.

Accepted Answer

[latex]K_{p}= an ^{2}\left(45° + \Phi ^{\prime }/2 ight) = an^{2}\left(45° + 30°/2 ight) =3.00[/latex]

[latex]P_{p}/b=\frac{\gamma H^{2}K_{p}\cos \beta }{2} =\frac{\left(119 lb/ft^{3} ight) \left(12 ft ight)^{2} \left(3.00 ight) \cos 0}{2} =25,700 lb/ft[/latex]

[latex]P_{p}=\frac{\left(25.700 lb/ft ight) \left(150 ft ight) }{1000 lb/k} =3860 k[/latex]

The allowable passive force, [latex](P_{p})_{a}[/latex], is:

[latex](P_{p})_{a}=\frac{P_{p}}{F} =\frac{3860 k}{3} =[/latex] 1290 k

Note: The actual design computations for this problem would be more complex because they would need to consider the active pressure acting on the opposite wall, sliding friction along the basement floor, lateral resistance in the foundations, and other factors. In addition, the horizontal displacement required to develop the full passive resistance may. be excessive, so the design value may need to be reduced accordingly. Finally, to take advantage of this resistance, the wall would need to be structurally designed to accommodate this large load, which is much greater than that due to the active or at-rest pressure.

Question 16.3: A six-story building with plan dimensions of 150 ft × 150 ft...

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