1. 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
Explanation: b = 100mm, d = 300mm, Es = 210kn/mm2, Ec = 35n/mm2
αe = Es/Ec = (210/35) = 6n/mm2.
2. 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
Explanation: b = 200mm, d = 300mm, p = 150kn = 150×103, e = 50mm, a = 188n/mm2,
Initial stress in steel = (150×103/188) = 800n/mm2.
3. 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%
Explanation: 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%.
4. 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
Explanation: 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
5. 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
Explanation: 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.
6. 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
Explanation: 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.
7. The shrinkage of concrete in prestressed members results in __________
a) Shortening
b) Elongation
c) Bulking
d) Stressing
Explanation: The shrinkage of concrete in prestressed members is due to the gradual loss of moisture which results in changes in volume, rich mixes exhibit relatively greater shrinkage than lean mixes since the contraction of the cement gel increases with the cement content, the shrinkage also depends upon the degree of hardening of the concrete at the commencement of drying and the shrinkage of concrete in prestressed members results in a shortening of tensioned wires and hence contributes to the loss of stress.
8. The shrinkage of concrete is influenced by ___________
a) Type of cement
b) Type of chemical
c) Type of admixtures
d) Type of retarders
Explanation: The shrinkage of concrete is influenced by the type of cement and aggregates and the method of curing used, the rate and amount of shrinkage of the structural member under ambient conditions will depend very much upon the ratio of surface area to volume of the member, as the exchange of moisture between the concrete and the atmosphere must take place through the surface.
9. Which of the following is used to reduce shrinkage of concrete?
a) High strength concrete
b) Admixtures
c) Boulders
d) Low water cement ratio
Explanation: The use of high strength concrete with low water cement ratios results in a reduction in shrinkage and consequent loss of prestress, aggregates of rock type having high modular of elasticity and low values of deferred strain are more effective in restraining the contraction of the cement paste and their use reduces the shrinkage of concrete.
10. The rate of shrinkage is higher at __________
a) End
b) Surface
c) Middle
d) Edges
Explanation: The rate of shrinkage is higher at the surface of the member and the primary cause of drying shrinkage is the progressive loss of water from concrete, the phenomena of shrinkage being time dependant only the total anticipated or residual shrinkage strain is considered in the computation of loss of prestress to be used in design.