# Prestressed Concrete Structures Questions and Answers – Bond Stresses

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This set of Prestressed Concrete Structures Multiple Choice Questions & Answers (MCQs) focuses on “Bond Stresses”.

1. The magnitude of bond stresses is developed between ____________
a) Concrete and steel
b) Aggregates and steel
c) Water and steel
d) Bricks and steel

Explanation: The magnitude of bond stresses developed between concrete and steel and its variation in the transfer zone of pretensioned beam, the deformation of concrete shrinkage depends on environmental conditions, age of concrete, size of concrete, concrete composition, etc.

2. The bond stress is zero at the distance equal to the ____________
a) Tensile length
b) Span length
c) Transmission length
d) Anchorage length

Explanation: The bond stress is zero at the end but builds up rapidly to a maximum over a very short length and this value decreases as the stress in the wire builds up at a distance equal to the transmission length, the bond stress is almost zero while the stress in steel and concrete reach their maximum values.

3. The relations proposed by Marshall for bond stress are given as ____________
a) (τ bp)x = (τ bp)maxe-4ψx/ϕ
b) (τ bp)x = (τ bp)maxe-4ψx
c) (τ bp)x = (τ bp)maxe-4ψ
d) (τ bp)x = (τ bp)maxe-4

Explanation: Based on tests conducted at the university of leeds, the following relations have been proposed by marshall (τ bp)x = (τ bp)maxe-4ψx/ϕ, fx = fsc(1-e-4ψx/ϕ), (τ bp)x = maximum value of bond stress, (τbp)max = bond stress of a distance x from the free end, ϕ = diameter of wire, fx = stress in steel a distance x from the free end, fse = effective stress in steel at the ends of transfer zone, ψ = constant, x = distance measured from the free end in mm.

4. According to Marshall the wires of 2 and 5mm diameter are stressed to ____________
a) 1500 and 1700n/mm2
b) 1575 and 1100n/mm2
c) 1400 and 1800n/mm2
d) 1250 and 1600n/mm2

Explanation: Based on tests conducted according to Marshall using wires of 2 and 5mm diameter stressed to 1575 and 1100n/mm2 respectively in conjunction with a concrete having cube strength of 80n/mm2, the values of maximum bond stress and constant ψ found to be 7.42n/mm2 and 0.00725 respectively.

5. The magnitude of the average bond stress compared to the maximum local bond stress is considerably ____________
a) Less
b) More
c) Zero
d) Constant

Explanation: The magnitude of the average bond stress is considerably less than the maximum local bond stress but according to the investigations of Ros, the average bond stress varied from 3.25 to 1n/mm2 for round wires of 1.5 to 5mm diameter in the case of wires initially tensioned to a stress of 1200n/mm2 and tensile stress shall not be allowed at any loading stage up to cracking in case of members assembled out of precast blocks.

6. The stress in a steel wire gradually increases from zero to the ____________
a) Middle
b) Bottom
c) End
d) Top

Explanation: The stress in a steel wire gradually increases from zero at the end of the beam to 100 percent of the effective stresses at the end of the transmission length, after the beam is placed the slab is casted and different rates of shrinkage imposed forces are developed because a moment is induced if the slab is not at the neutral axis of section.

7. The prestressing force of 90 to 95 percent is obtained at about ____________
a) Half of the transmission length
b) Three fourth of transmission length
c) Four third of transmission length
d) 1.5 of transmission length

Explanation: The effective prestressing force of 75 to 80 percent develops to about half of the transmission length, 90 to 95 percent of the prestressing force is attained at about three fourths of the transmission length from the end face of the beam.

8. A pre tensioned beam is prestressed with the cube strength of concrete at transfer is 30n/mm2 (β = 0.0235) calculate the transmission length?
a) 645mm
b) 1100mm
c) 485mm
d) 1600mm

Explanation: β = 0.0235, cube strength of concrete is 30n/mm2,
Transmission length (Lt) = ((fcu)1/2 x 103/β)1/2
= ((30)1/2 x 103/0.0235) = 485mm.

9. A pretensioned beam is prestressed using 5mm diameter wires, τ bp = 7.42, ϕ = 0.00725, Lt = 485mm. Calculate the bond stress at l/4 and l/2 the transmission length from the end?
a) 3.7n/mm2 and 1.82n/mm2
b) 2.2n/mm2 and 5.8n/mm2
c) 4.8n/mm2 and 10.5n/mm2
d) 1.5n/mm2 and 7.4n/mm2

Explanation: Bond stress given by (τ bp)x = (τ bp)maxe-4ψx/ϕ = 7.42 e-(4×0.00725xX)/5
τ bp = 7.42e-0.0058X
Bond stress at L/4 is given by: τ bp = 7.42e-0.0058×121.25 = 8.7n/mm2, τ bp = 7.42e-0.0058×242.5 = 1.82n/mm2.

10. A pre tensioned beam is prestressed using 5mm diameter wires with an initial stress of 80 percent of the ultimate strength of steel fpu = 1600n/mm2. Calculate average bond stress?
a) 4.20n/mm2
b) 3.30n/mm2
c) 2.0n/mm2
d) 4.9n/mm2

Explanation: fpu = 1600n/mm2, d = 5mm, initial stress = 80% = 0.08,
Average bond stress = (τ bp)average
= (19.6×0.8×1600/πx5x485) = 3.30n/mm2.

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