# Civil Engineering - Theory of Structures - Discussion

Discussion Forum : Theory of Structures - Section 3 (Q.No. 1)
1.
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
264 MN
274 MN
284 MN
294 MN
None of these.
Explanation:
No answer description is available. Let's discuss.
Discussion:
16 comments Page 1 of 2.

Avinash said:   3 years ago
It's 284KN not 284MN.

Nuuui said:   3 years ago
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.
(1)

Akshat kumar said:   4 years ago
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.
(1)

Govind Singh said:   4 years ago
Thank you, Nishant Jain, for giving an answer with placid explanation.

Roy said:   4 years ago
So,modular ratio is m=Es/Ec=15.

Stress in steel, t=mc=15*5 = 75mpa.

RAJU said:   4 years ago
Thank you @Maniesh.

Abhishek said:   5 years ago
Thank you for explaining.

Kisan prasad gaire said:   5 years ago
Excellent explanation, Thanks @Maniesh.

Maniesh said:   6 years ago
Stress in steel = load / area of steel and likewise same for concrete,

Es= permissible stress in steel/ strain in steel and likewise same for concrete,
strain in concrete and steel are same = permissible stress in steel/ Es= permissible stress in concrete/ Ec.

Es= 15Ec.
=permissible stress in steel= permissible stress in concrete/ Ec xEs =( 5 /Ec)x 15Ec= 75Mpa for steel.
Load = permissible Stress in steel x area of steel +permissible stress in concrete x area of concrete.
= 75 x 1200+ 5 x (200X200 -1200)= 284kN.

Chulbul said:   6 years ago
As the elongations are equal, use the formula.

Strain= stress/Young's modulus.