Question

For a pre-tensioned beam, young’s Modulus of steel and concrete are 200 GPa and 35.35 GPa. if ultimate shrinkage strain and Ultimate Creep Coefficient are 200 microns and 1.6, respectively, what is the level of sustained stress in concrete at the level of ‘steel if the loss due to creep is three times the loss due to shrinkage?
1. 9 MPa
2. 13 MPa
3. 11 MPa
4. 15 MPa

Answer 1

Correct Answer - Option 2 : 13 MPa

Concept:

The loss of stress due to creep in concrete is given as

F_c = θmf_cs

Where,

θ is the ultimate creep coefficient

m is the modular ratio and it is given as

\({\rm{m}} = \frac{{{\rm{Modulus\;of\;Elasticity\;of\;steel}}}}{{{\rm{Modulus\;of\;Elasticity\;of\;Concrete\;}}}}\)

f_cs is the stress in concrete at the level of steel.

The loss of stress due to shrinkage in concrete is given as

F_s = E_s × ϵ

Where,

E_s 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; E_s = 200 GPa and E_c = 35.35 GPa

m = 200/35.35 = 5.66

f₁ = 1.6 × 5.66 × f_cs = 9.05f_cs­ N/mm²

f₂ = 200 × 1000 × 200 × 10^-6 = 40 N/mm²

It is given that

f₁ = 3f₂

9.05f_cs­ = 3 × 40

⇒ f_cs = 13.26 ≈ 13 N/mm²