Correct Answer - Option 2 : 13 MPa
Concept:
The loss of stress due to creep in concrete is given as
Fc = θmfcs
Where,
θ is the ultimate creep coefficient
m is the modular ratio and it is given as
\({\rm{m}} = \frac{{{\rm{Modulus\;of\;Elasticity\;of\;steel}}}}{{{\rm{Modulus\;of\;Elasticity\;of\;Concrete\;}}}}\)
fcs is the stress in concrete at the level of steel.
The loss of stress due to shrinkage in concrete is given as
Fs = Es × ϵ
Where,
Es is the Modulus of elasticity of steel
ϵ is the shrinkage strain in concrete
Calculation:
Given,
θ = 1.6, ϵ = 200 × 10-6 ; f1 = 3f2; Es = 200 GPa and Ec = 35.35 GPa
m = 200/35.35 = 5.66
f1 = 1.6 × 5.66 × fcs = 9.05fcs N/mm2
f2 = 200 × 1000 × 200 × 10-6 = 40 N/mm2
It is given that
f1 = 3f2
9.05fcs = 3 × 40
⇒ fcs = 13.26 ≈ 13 N/mm2