Concept explainers
The following table shows the boring log at a site where a multi-story shopping center would be constructed. Soil classification and the standard penetration number, N60, are provided in the boring log. All columns of the building are supported by square footings which must be placed at a depth of 1.5 m. Additionally, the settlement (elastic) of each footing must be restricted to 20 mm. Since the column loads at different location can vary, a design chart is helpful for quick estimation of footing size required to support a given load.
- a. Prepare a chart by plotting the variation of maximum allowable column loads with footing sizes, B = 1 m, 1.5 m, 2 m, and 3 m. Use a factor of safety of 3.
- b. If the gross column load from the structure is 250 kN, how would you use this chart to select a footing size?
- c. What would be the design footing size for the column in Part (b) if you use Terzaghi’s bearing capacity equation? For the well graded sand, assume that ϕ′ = 33°. Use Fs = 3.
- d. Compare and discuss the differences in footing sizes obtained in Parts b and c.
(a)
Plot the variation of maximum allowable column loads with size of footings to prepare a chart.
Explanation of Solution
Given information:
The location of depth of footing
The given size of the footing B is 1 m, 1.5 m, 2 m, and 3 m.
The settlement of each footing
The given factor of safety
Calculation:
For B value is 1 m:
Determine the depth factor using the relation.
Substitute 1.5 m for
The
The field standard penetration number
Determine the depth of foundation for the field standard penetration number gets averaged.
Substitute 1.5 m for
Determine the averaged
Here,
Substitute 12 for
Determine the net allowable bearing capacity of the soil
Substitute 10 for
Determine the maximum allowable column load
Substitute
For B value is 1.5 m:
Determine the depth factor using the relation.
Substitute 1.5 m for
The field standard penetration number
Determine the depth of foundation for the field standard penetration number gets averaged.
Substitute 1.5 m for
Determine the averaged
Here,
Substitute 7 for
Determine the net allowable bearing capacity of the soil
Substitute 8 for
Determine the maximum allowable column load
Substitute
For B value is 2 m:
Determine the depth factor using the relation.
Substitute 1.5 m for
The field standard penetration number
Determine the depth of foundation for the field standard penetration number gets averaged.
Substitute 1.5 m for
Determine the averaged
Substitute 12 for
Determine the net allowable bearing capacity of the soil
Substitute 9 for
Determine the maximum allowable column load
Substitute
For B value is 3 m:
Determine the depth factor using the relation.
Substitute 1.5 m for
The field standard penetration number
Determine the depth of foundation for the field standard penetration number gets averaged.
Substitute 1.5 m for
Determine the averaged
Here,
Substitute 12 for
Determine the net allowable bearing capacity of the soil
Substitute 12 for
Determine the maximum allowable column load
Substitute
Summarize the calculated values as in Table (1).
Width B (m) | Column load (kN) |
1 | 71 |
1.5 | 115 |
2 | 198 |
3 | 507.5 |
Plot the graph between the size of the footing and the column load as in Figure (1).
(b)
Find the footing size for the given gross column load of 250 kN.
Answer to Problem 16.1CTP
The footing size for the given gross column load of 250 kN is
Explanation of Solution
Given information:
The location of depth of footing
The given size of the footing B is 1 m, 1.5 m, 2 m, and 3 m.
The settlement of each footing
The given factor of safety
Calculation:
Refer Figure (1).
The size of the footing is 2.25 m for the gross column load of 250 kN.
Therefore, the footing size for the given gross column load of 250 kN is
(c)
Find the design column load for the footing size of 2.25 m using the Terzaghi’s bearing capacity equation.
Answer to Problem 16.1CTP
The design column load for the footing size of 2.25 m using the Terzaghi’s bearing capacity equation is
Explanation of Solution
Given information:
The value of cohesion
The soil friction angle
The location of depth of footing base
The width of the footing B is 2.25 m.
The given factor of safety
Calculation:
Determine the net ultimate bearing capacity of the soil
Here,
Take the unit weight of the soil
Refer Table 16.1, “Terzaghi’s bearing-capacity factors–
Take the
Substitute
Determine the net allowable bearing capacity
Substitute
Therefore, the design column load for the footing size of 2.25 m using the Terzaghi’s bearing capacity equation is
(d)
Compare and discuss the differences in footing sizes obtained in parts (b) and (c).
Explanation of Solution
Given information:
The soil friction angle
The location of depth of footing base
The width of the footing B is 2.25 m.
The given factor of safety
Calculation:
The net allowable column load obtained by using Terzaghi’s bearing capacity equation (2,173 kN) is significantly higher than the method based on the
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Chapter 16 Solutions
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