250+ TOP MCQs on Loss Due to Elastic Deformation and Answers

Basic Prestressed Concrete Structures Questions and Answers on “Loss Due to Elastic Deformation”.

1. The loss of prestress due to elastic deformation of concrete depends on ____________
a) Modular ratio and average stress
b) Modular elasticity and shear
c) Prestress in concrete
d) Modulus of elasticity of steel
Answer: a
Clarification: The loss due to elastic deformation of concrete depends on the modular ratio and the average stress in concrete at the level of steel, consider a post tensioned member which is prestressed by a single tendon and the shortening of concrete occurs till the tendon is jacked and no shortening of concrete is observed after it.

2. The term E_c in losses developed by elastic deformation is expressed as ____________
a) P_e/A
b) P_c/E_a
c) P/A_cE_c
d) E_a/E_l
Answer: c
Clarification: The term E_c is defined as strain in concrete and the equation for loss due to elastic deformation is given as E_c = P_c/E_c = P/A_c×1/E_c, the tension in the tendon is obtained after the elastic shortening of concrete and therefore, there will not be losses due to elastic shortening.

3. The term E_s in losses developed by elastic deformation is defined as ____________
a) Shear in steel
b) Torsion in steel
c) Strain loss in steel
d) Loading in steel
Answer: c
Clarification: The term Es is defined as strain loss in steel, E_s = Δf_s/E_s,
Δf_s = Loss of stress in steel, Es = strain loss in steel.

4. The loss of stress in steel due to elastic shortening or deformation is ____________
a) α_ef_c
b) α_cf_c
c) α_c/f_c
d) α_e/f_c
Answer: a
Clarification: Loss of stress in steel due to elastic shortening is α_ef_c,
α_e = E_s/E_c = modular ratio, f_c = prestress in concrete at the level of steel, E_s = modulus of elasticity of steel, E_c = modulus of elasticity of concrete.

5. A pretensioned concrete beam, 100mm wide and 300mm deep in prestressed by straight wires and modulus of elasticity of steel and concrete are 210 and 35n/mm2. Find modular ratio?
a) 14
b) 7
c) 6
d) 10
Answer: c
Clarification: b = 100mm, d = 300mm, E_s = 210kn/mm², E_c = 35n/mm²
α_e = E_s/E_c = (210/35) = 6n/mm².

6. A pretensioned concrete beam 200mm wide and 300mm deep, is prestressed by straight wires carrying an initial force of 150kn at eccentricity of 50mm, area of steel wires is 188mm². Find initial stress in steel?
a) 1400
b) 800
c) 200
d) 100
Answer:b
Clarification: b = 200mm, d = 300mm, p = 150kn = 150×103, e = 50mm, a = 188n/mm²,
Initial stress in steel = (150×10³/188) = 800n/mm².

7. A pre tensioned concrete beam 100mm wide and 300mm deep, initial force of 150kn at an eccentricity of 50mm, moment of inertia is 225×10⁶mm⁴, initial stress in steel is 400n/mm², modular ratio is 8. Estimate the percentage loss?
a) 10%
b) 5%
c) 14%
d) 20%
Answer: c
Clarification: P = 150kn, y = d/6 = 300/6 = 50mm, a = (100×300) = 3×10⁴, I = 225×10⁶, α_e = 8, initial stress = 400n/mm², Stress in concrete, f_c = (150×10³/3×10⁴)+(150×10³×50×50/225×10⁶) = 6.66n/mm²,
Loss of stress due to elastic deformation of concrete = α_ef_c = (8×6.66) = 53n/mm²,
Percentage of loss of stress in steel = (53×100/400) = 13.25% = 14%.

8. A rectangular concrete beam 360mm deep and 200mm wide, is prestressed by means of fifteen 5mm diameter wires located 65mm from the bottom of the beam and three 5mm wires, located 275mm from top of the beam, initial tension stress is 840n/mm². Calculate prestressing force?
a) 504×10²kn
b) 500×10²kn
c) 620×10²kn
d) 400×10²kn
Answer: a
Clarification: Position of the centroid of wires from soffit of the beam y = ((15×65)+(3×25)/(15+3)) = 100mm, e = (150-100) = 50mm, area of concrete A = (200×300) = 6×10⁴mm², I = (200×300³)/12 = 45×10⁷mm⁴, Prestressing force = initial stress×area = 840×6×10⁴ = 504×10⁵N = 500×10²kn.

9. A post tensioned concrete beam, 100mm wide and 400mm deep is prestressed by three cables, each with a cross sectional area of 50mm², initial stress of 1200n/mm². Calculate the stress in concrete at level of steel?
a) 2.4n/mm²
b) 2.0n/mm²
c) 2.7n/mm²
d) 1.5n/mm²
Answer: c
Clarification: Force in each cable, p = (50×1200) = 60×10³n = 60kn, A = 3×10⁴mm², I = 225×10⁶mm⁴, e = 50mm, y = 50mm stress in concrete at the level of steel f_c = (60×10³/3×10⁴)+(60×10³×50×50/225×10⁶) = 2.7n/mm².

10. The loss of stress due to successive tensioning of curved cables in elastic deformation of concrete is estimated by considering ___________
a) Initial stress
b) Average stress
c) Bondage stress
d) Anchorage stress
Answer: b
Clarification: In most bridge girders, the cables are curved with maximum eccentricity in center of the span in such cases loss of stress due to elastic deformation of concrete is estimated by considering stress in concrete at the level of steel.

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