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 Ec in losses developed by elastic deformation is expressed as ____________
a) Pe/A
b) Pc/Ea
c) P/AcEc
d) Ea/El
Answer: c
Clarification: The term Ec is defined as strain in concrete and the equation for loss due to elastic deformation is given as Ec = Pc/Ec = P/Ac×1/Ec, 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 Es 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, Es = Δfs/Es,
Δfs = 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) αefc
b) αcfc
c) αc/fc
d) αe/fc
Answer: a
Clarification: Loss of stress in steel due to elastic shortening is αefc,
αe = Es/Ec = modular ratio, fc = prestress in concrete at the level of steel, Es = modulus of elasticity of steel, Ec = 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, Es = 210kn/mm2, Ec = 35n/mm2
αe = Es/Ec = (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, αe = 8, initial stress = 400n/mm2, Stress in concrete, fc = (150×103/3×104)+(150×103×50×50/225×106) = 6.66n/mm2,
Loss of stress due to elastic deformation of concrete = αefc = (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 fc = (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.
To practice basic questions and answers on all areas of Prestressed Concrete Structures,