Answered: A structural engineer finished a design…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

A structural engineer finished a design of a library. They determine that each column will carry 1000 lbs. the soil beneath the footing has the properties: gamma= 130 pcf, c= 75psf, phi= 40 degrees. The groundwater table is of great depth so it’s no concern. Sketch figures. What is the minimum size of the footing for a factor of safety of 3? Case 1: assume square footing Case 2: assume round footing

Case II: Assume round footing
No, No, N
1000
100
10
0.1
0
Na
10
N
20
o' (degrees)
30
0
40
50

Expert Solution

Step 1: Case 1- square footing:

To calculate the minimum footing size, we need to use the following equation:

q_a = q_u / FOS

where:

q_ais the allowable bearing capacity (psf)
q_u is the ultimate bearing capacity (psf)
FOS is the factor of safety and (3)

The ultimate bearing capacity of a square footing can be calculated using the following equation:

q_u = N_c * c + N_q * γ * D + N_γ * γ * D_f

where,

N_{c ,}N_{q ,}N_γ are bearing capacity factors,

which depend on the soil friction angle and the depth of the footing

c is the soil cohesion (psf)
γ is the soil unit weight (pcf)
D is the depth of the footing (ft)
D_f is the depth to the groundwater table (ft)

Using the given soil properties and a bearing capacity factor chart, we can calculate the following bearing capacity factors:

N_c = 30

N_q = 20

N_γ = 0

Substituting these values,

q_u = 30 * 75 + 20 * 130 * D

To calculate the allowable bearing capacity:

q_a = (30 * 75 + 20 * 130 * D) / 3

1000 = (30 * 75 + 20 * 130 * D) / 3

Solving this equation for D, we get:

D = 2.6 ft

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