Principles of Foundation Engineering (MindTap Course List)
Principles of Foundation Engineering (MindTap Course List)
9th Edition
ISBN: 9781337705028
Author: Braja M. Das, Nagaratnam Sivakugan
Publisher: Cengage Learning
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Chapter 13, Problem 13.1P
To determine

Find the percentage of load carried by the shaft.

Expert Solution & Answer
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Answer to Problem 13.1P

The percentage of load carried by the shaft is 0.62%_.

Explanation of Solution

Given information:

The diameter of the base (Db) is 5ft.

The total length (L) is 27.0 ft.

Unit weight of loose sand (γ) is 110lb/ft3.

Unit weight of dense sand (γ) is 115lb/ft3.

The diameter of the shaft (Ds) is 2.5ft.

The length of the shaft (L1) is 24.0ft.

The value of factor of safety (FOS) is 4.

Consider δ'=0.6ϕ'.

Calculation:

Find the area of the base (Ap) as follows:

Ap=π4Db2

Substitute 5ft for Db.

Ap=π4×(5ft)2=19.64ft2

From given Figure, find the effective stress of soil.

q'=24ft×110lb/ft3+3ft×115lb/ft3=2,985lb/ft2

Find the ratio LDb as follows:

Substitute 27 ft for L and 5 ft for Db.

LDb=27ft5ft=5.4

Refer Table 13.3. “Berezantzev et al.’s value of ω ” in the textbook.

The value of ω is 0.83 for the soil friction angle of 38°.

Find the bearing capacity factor (Nq*) using the relation:

Nq*=0.21e0.17ϕ'

Substitute 38° for ϕ'.

Nq*=0.21e0.17×38°=134.2

Find the net ultimate load carrying capacity at the base (Qp(net)) using the relation:

Qp(net)=Apq'(ωNq*1)

Substitute 19.64ft2 for Ap, 2,985lb/ft2 for q', 0.83 for ω, and 134.2 for Nq*.

Qp(net)=19.64ft2×2,985lb/ft2(0.83×134.21)=6,471.4×103lb=6,471.4kip

Find the shaft load (Qs) as follows:

Find the perimeter of the shaft (p) as follows:

p=πDs

Substitute 2.5 ft for Ds.

p=π×2.5ft=7.85ft

Find the value of (Ko) using the relation:

Ko=1sinϕ'

Substitute 31° for ϕ'.

Ko=1sin31=0.485

Find the value of δ' using the relation:

δ'=0.6ϕ'

Substitute 31° for ϕ'.

δ'=0.6(31°)=18.6°

Find the critical depth (L') using the relation:

L'=15Ds

Substitute 2.5 ft for Ds.

L'=15×2.5ft=37.5ft

The value of critical depth 37.5 ft is more than the length L1=24ft.

Find the frictional resistance (f) along the pile shaft using the relation:

f=Kσo'tanδ'

At depth z=0:

f=0

At depth z=24ft:

Substitute 0.485 for K, 24ft×110lb/ft3 for σo', and 18.6° for δ'.

f=0.485×24ft×110lb/ft3×tan18.6°=430.9lb/ft2

Find the load carrying capacity of the shaft (Qs) using the above calculated values as follows:

Qs=favpL=(0+430.9lb/ft22)×7.85ft×24ft =40.6×103lb=40.6kip

Find the ultimate load (Qu) using the relation:

Qu=Qp+Qs

Substitute 6,471.4kip for Qp and 40.6kip for Qs.

Qu=6,471.4kip+40.6kip=6,512kip

Find the allowable load (Qall) using the relation:

Qall=QuFOS

Substitute 6,512kip for Qu and 4 for FOS.

Qall=6,512kip4=1,628kip

Find the percentage of load carried by the shaft:

%ofloadcarriedbytheshaft=QsQu×100

Substitute 6,512kip for Qu and 40.6kip for Qs.

%ofloadcarriedbytheshaft=40.6kip6,512kip×100=0.62%

Therefore, the percentage of load carried by the shaft is 0.62%_.

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