A 1350 kN column load is to be supported on a square spread footing founded in a clay with su = 150 kPa. The depth of embedment, D, will be 500 mm, and the soil has a unit weight of 18.5 kN/m^3. The groundwater table is at a depth below the bottom of the footing. Using a factor of safety of 3.0,

Question

A 1350 kN column load is to be supported on a square spread footing founded in a clay with [latex]s_{u} = 150 kPa[/latex]. The depth of embedment, D, will be 500 mm, and the soil has a unit weight of [latex]18.5 kN/m^{3}[/latex]. The groundwater table is at a depth below the bottom of the footing. Using a factor of safety of 3.0, determine the required footing width.

Accepted Answer

Per Table 17.1,

[latex]\Phi ^{\prime }[/latex] (deg)	[latex]N_{c}[/latex]	[latex]N_{q}[/latex]	[latex]N_{\gamma }[/latex]
0	5.7	1.0	0.0
1	6.0	1.1	0.1
2	6.3	1.2	0.1
3	6.6	1.3	0.2
4	7.0	1.5	0.3
5	7.3	1.6	0.4
6	7.7	1.8	0.5
7	8.2	2.0	0.6
8	8.6	2.2	0.7
9	9.1	2.4	0.9
10	9.6	2.7	1.0
11	10.2	3.0	1.2
12	10.8	3.3	1.4
13	11.4	3.6	1.6
14	12.1	4.0	1.9
15	12.9	4.4	2.2
16	13.7	4.9	2.5
17	14.6	5.5	2.9
18	15.5	6.0	3.3
19	16.6	6.7	3.8
20	17.7	7.4	4.4
21	18.9	8.3	5.1
22	20.3	9.2	5.9
23	21.7	10.2	6.8
24	23.4	11.4	7.9
25	25.1	12.7	9.2
26	27.1	14.2	10.7
27	29.2	15.9	12.5
28	31.6	17.8	14.6
29	34.2	20.0	17.1
30	37.2	22.5	20.1
31	40.4	25.3	23.7
32	44.0	28.5	28.0
33	48.1	32.2	33.3
34	52.6	36.5	39.6
35	57.8	41.4	47.3
36	63.5	47.2	56.7
37	70.1	53.8	68.1
38	77.5	61.5	82.3
39	86.0	70.6	99.8

[latex]N_{c} = 5.7[/latex], [latex]N_{q}= 1.0[/latex], [latex]N _{γ}= 0.0[/latex] for [latex]Φ=0[/latex]

[latex]σ^{\prime }_{D}=γD - u=(18.5 kN/m^{3})(0.5 m) - 0=9 kPa[/latex]

[latex]q_{ult}=1.3cN_{c} + σ_{D}N_{q} + 0.4γ^{\prime }BN_{γ}=1.3(150 kPa)(5.7) + (9 kPa)(1.0) + 0=1121 kPa[/latex]

[latex]q_{a}=\frac{q_{ult}}{F} =\frac{1121 kPa}{3.0} =374 kPa[/latex]

[latex]q_{a}=q=\frac{P}{B^{2}} +\gamma _{c}D - u[/latex]
[latex]374 kPa=\frac{1350 kN}{B^{2}} +\left(23.6 kN/m^{3}\right) \left(0.5 m\right) - 0[/latex]
[latex]B =1.93 m[/latex]

Normally spread footing dimensions are expressed as multiples of 3 in or 100 mm. Therefore, round up to B = 2.0 m

Question 17.3: A 1350 kN column load is to be supported on a square spread ...

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