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Theory of Structures

Q1: If a concrete column 200 x 200 mm in cross-section is reinforced with four steel bars of 1200 mm2 total cross-sectional area. Calculate the safe load for the column if permissible stress in concrete is 5 N/mm2 and Es is 15 Ec

A 264 MN

B 274 MN

C 284 MN

D 294 MN

E None of these.

ANS:C - 284 MN

As = 1200.
Ac = 38800. 6c=5.
Es = Ec.

We know that,
dL = PL/AE = 6L/E.

Here,
dLs = dLc.
6sLs/Es = 6cLc/Ec. Ls = Lc.
6s/Es = 6c/Ec.
6s/15Ec = 5/Ec.
6s = 5/Ec * 15Ec.
6s = 75.

Now,
P = 6sAs + 6cAc.
P = 75 * 1200 + 5 * 38800.
P = 284000N.



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