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

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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

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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