ABCD is a raft foundation of a multi-story building [Fig. 6. 9(b)] wherein AB = 65.6 ft, and BC = 39.6 ft. The uniformly distributed load q over the raft is 73 10 lb/ft^2. Determine σz at a depth of 19.7 ft below point O [Fig. 6.9(b)] wherein AA1 = 13.12 ft and A1O = 19.68 ft. Use Fig. 6.8.

Question

ABCD is a raft foundation of a multi-story building [Fig. 6. 9(b)] wherein AB = 65.6 ft, and BC = 39.6 ft. The uniformly distributed load q over the raft is 73 10 [latex]lb / ft ^{2} ext {. Determine } \sigma_{z}[/latex] at a depth of 19.7 ft below point O [Fig. 6.9(b)] wherein [latex]A A_{1}=13.12 ft ext { and } A_{1} O=19.68 ft[/latex]. Use Fig. 6.8.

Accepted Answer

Rectangles are constructed as shown in [Fig. 6.9(b)].

[latex] ext { Area } A B C D=O B_{1} C D_{1}-O B_{1} B D_{2}-O D_{1} D A_{1}+O A_{1} A D_{2}[/latex]

Rectangle	l	b	m	n	I
	(ft)	(ft)
[latex]O B_{1} C D_{1}[/latex]	85.28	52.72	2.67	4.33	0.245
[latex]O B_{1} B D_{2}[/latex]	85.28	13.12	0.67	4.33	0.168
[latex]O D_{1} D A_{1}[/latex]	52.72	19.68	1	2.67	0.194
[latex]O A_{1} A D_{2}[/latex]	19.68	13.12	0.67	1	0.145

Per Eq. (6.17)

[latex]\sigma_{z}=q\left(I_{1}-I_{2}-I_{3}+I_{4} ight)[/latex] (6.17)

[latex]\sigma_{z}=q\left(I_{1}-I_{2}-I_{3}+I_{4} ight)=7310(0.245-0.168-0.194+0.145)=204.67 lb / ft ^{2}[/latex]

The same value can be obtained using Fig. 6.7.

Question 6.5: ABCD is a raft foundation of a multi-story building [Fig. 6....

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