An L-shaped reinforced concrete slab 3.6 m 3.6 m, with a 1.8 m 1.8 m cut-out and thickness t = 230 mm, is lifted by three cables attached at O, B, and D, as shown in the figure. The cables are are...

An L-shaped reinforced concrete slab 3.6 m

3.6 m, with a 1.8 m

1.8 m cut-out and thickness t = 230 mm, is lifted by three cables attached at O, B, and D, as shown in the figure. The cables are are combined at point Q, which is 2.1 m above the top of the slab and directly above the center of mass at C. Each cable has an effective cross-sectional area of A_e
= 77 mm².

(a) Find the tensile force T_i
(I = 1, 2, 3) in each cable due to the weight W of the concrete slab (ignore weight of cables).

(b) Find the average stress

_i
in each cable. (See Table I-1 in Appendix I for the weight density of reinforced concrete.)

(c) Add cable AQ so that OQA is one continuous cable, with each segment having force T₁, which is connected to cables BQ and DQ at point Q. Repeat parts (a) and (b). Hint: There are now three forced equilibrium equations and one constraint equation, T₁
= T₄.