# Design of RC Structures Questions and Answers – Prestressed Concretes Basics – Set 2

This set of Design of RC Structures Multiple Choice Questions & Answers (MCQs) focuses on “Prestressed Concretes Basics – Set 2”.

1. Which of the following is not an immediate loss of prestress for pre – tensioning?
a) Loss due to friction
b) Loss in tendon force
c) Loss due to relaxation of tendons
d) Loss due to elastic deformation

Explanation: Immediate losses of prestress for pre – tensioning are:
i. Loss due to friction at the bends and loss due to wedge draw – in of the anchorage devices.
ii. Loss due to relaxation of pretensioning tendons.
iii. Loss due to elastic deformation of concrete.
Immediate losses of prestress for post – tensioning are loss in tendon force corresponding to the deformation of concrete.

2. What is the value of loss of prestress due to elastic shortening of concrete?
a) (mP / Ag)
b) (mP / Ac)
c) (mP / As)
d) (m / Ag)

Explanation: When prestress is applied to the concrete, an elastic shortening of the concrete takes place. This results in an equal and simultaneous shortening of the prestressing steel. The loss of prestress due to elastic shortening can be easily determined. The loss of prestress Δσ is:
Δσ = (mP / Ag)
Here m is modular ratio,
P is initial prestressing force.

3. What is the value of loss of prestress due to creep of concrete?
a) (2mθσc)
b) 1 / 2(mθσc)
c) (θσc)
d) (mθσc)

Explanation: Creep is the property of concrete by which it continues to deform with time under sustained loads at unit stresses within the accepted elastic range. This inelastic deformation increases at a decreasing rate during the time of loading and its total magnitude may be several times as large as the short – term elastic deformation. The loss of prestress due to creep is:
Δσ = (mθσc)
Here θ is coefficient of creep.

4. What is the value of loss of prestress due to shrinkage of concrete?
a) 2.5(εshEs)
b) 2(εshEs)
c) 0.5(εshEs)
d) (εshEs)

Explanation: Shrinkage is defined as change in volume of concrete members. It is dependent on humidity in atmosphere, type of cement and aggregate and passage of time. The shrinkage strain varies due to several factors and may be taken between 0.0002 and 0.0003 for computing prestress loss. The loss due to shrinkage is given by:
Δσ = (εshEs)
Here εsh is shrinkage strain in concrete.

5. Which of the following is not a value of creep coefficient (θ) in the equation of loss of prestress due to creep?
a) 1.6
b) 1.5
c) 1.1
d) 2.2

Explanation: The value of creep coefficient θ is equal to 2.2, 1.6 or 1.1 depending on if the age of concrete at loading is 7 days, 28 days or 1 year. It takes about 12 months to develop full creep strains. Pre – tensioned beams will exhibit more creep than post – tensioned beams because, in the former, the prestress is imposed when concrete is in its early stage.

6. What is value of shrinkage strain in determining the loss of prestress due to shrinkage of concrete for pre – tensioned members?
a) 3 × 10-4
b) (2 × 10-4) / log10(t + 2)
c) 2 × 10-4
d) (3 × 10-4) / log10(t + 2)

Explanation: The Clause 5.2.4 of IS: 1343 – 1980 recommends the values for total shrinkage strains:
εsh = 3 × 10-4 for pre – tensioned members
= (2 × 10-4) / log10(t + 2) for post – tensioned members
Here t is age of concrete at transfer in days.

7. What is value of loss of prestress for prestressing steel at 1000 hours at 20°C due to relaxation of steel for initial stress 0.6 σp?
a) 0
b) 35
c) 70
d) 90

Explanation: Relaxation is assumed to mean the loss of stress in steel under nearly constant strain at constant temperature. The relaxation of steel depends on the concrete deformation due to creep and shrinkage. This loss is generally of the order of 2 to 5% of the initial stress at the end of 1000 hours. The values of loss of prestress for prestressing steel at 1000 hours at 20°C due to relaxation of steel may be taken as:
For initial stress 0.5 σp, Relaxation loss 0 MPa,
For initial stress 0.6 σp, Relaxation loss 35 MPa,
For initial stress 0.7 σp, Relaxation loss 70 MPa,
For initial stress 0.8 σp, Relaxation loss 90 MPa.
Here σp is characteristic strength of prestressing steel.

8. The loss of prestress due to friction occurs only in post – tensioned members.
a) True
b) False

Explanation: The loss of prestress due to friction occurs only in post – tensioned members. There are small friction losses in the jacking equipment. The friction between tendons and surrounding materials is not small and may be considered partly a length effect or wobble effect and partly a curvature effect. In straight lengths it occurs due to wobble effect and in curved lengths, it occurs due to curvature effect and wobble effect.

9. A beam is prestressed by a cable carrying initial prestress of 500 N/mm2. Which of the following is the percentage of loss of prestress due to shrinkage of concrete if the beam is pre – tensioned? (age of concrete at transfer is 7 days).
a) 8.38%
b) 8.40%
c) 12%
d) 12.5%

Explanation: For pre – tensioned beams:
Δσ = (εshEs),
εsh = 3 × 10-4, (Es) = 200 kN/mm2
Loss of prestress Δσ = 3 × 10-4 × 200 × 1000 = 60 N/mm2
Percentage loss of prestress = (60 / 500) × 100 = 12%

10. A beam of 150 mm × 300 mm is prestressed by a force of 250 kN by steel cables located at an eccentricity of 60 mm. What will be the loss of prestress due to creep of concrete for following data?
σck = 45 N/mm2,
cables = 6 Nos. – 7 mm,
creep coefficient θ = 2,
Es = 200 kN/mm2,
Ec = 4500√σck = 30190 N/mm2.
a) 20%
b) 10%
c) 12%
d) 9%

Explanation: Area of section = 150 × 130 = 45000 mm2
Moment of inertia = 150 × 3003 / 12 = 337.5 × 106 mm4
Loss of prestress Δσ = mθσc
Stress in concrete at the level of steel
σc = (P / A) + (Pey / I)
= [(250 × 1000) / 45000] + [(250 × 1000 × 60 × 60) / (337.5 × 106)]
= 8.23 N/mm2
m = (Es / Ec) = (200 × 1000) / 30190 = 6.62
Loss of prestress Δσ = 6.62 × 2 × 8.23 = 109 N/mm2
Prestress = P / As = (250 × 1000) / [6(π / 4) × 72] = 1083 N/mm2
Percentage loss of prestress = (109 × 100) / 1083 = 10%.

11. Which of the following formula is correct combined stress formula in homogeneous beam concept of limit state of serviceability for prestressed concrete?
a) σ = (P / 2A) ± (My / I)
b) σ = (P / 3A) ± (My / I)
c) σ = (P / A) ± (2My / I)
d) σ = (P / A) ± (My / I)

Explanation: In the elastic analysis of stresses, that is, limit state of serviceability in prestressed concrete, the combined stress formula in the homogeneous beam concept is given by:
σ = (P / A) ± (My / I)
The above formula can be used to determine stresses due to prestress and bending moment in section.
Here σ = bending stress at the fiber under consideration,
P = axial force of prestress,
A = area of cross – section,
M = bending moment due to prestress = Pe
y = distance of the fiber from the centroidal axis and
I = moment of inertia.

12. The load balancing concept of limit state of serviceability in prestsressed concrete, prestressing is treated primarily as the process of balancing loads on the member.
a) True
b) False

Explanation: In load balancing concept, prestressing is primarily treated as the process of balancing loads on the member. The tendons are placed so that eccentricity of prestressing force varies in the same fashion as moments from the applied loads. The flexural stresses would be zero, if this could be exactly achieved. The section will be then subjected to axial stress (P / A).

13. Which of the following is not an assumption in the load balancing concept for limit state of serviceability in prestressed concrete?
a) A plane section before bending remains plane after bending
b) Within the range of working stress both concrete and steel behave elastically
c) Any change in the loading produces no change of stress in concrete
d) The purpose of prestressing tendon is to maintain prestress at the same level

Explanation: The following assumptions are made in the elastic analysis of prestressed concrete sections:
i. A plane section before bending remains plane after bending,
ii. Within the range of working stress both concrete and steel behave elastically, and
iii. Any change in the loading produces a change of stress in concrete only up to the limit state of modulus of rupture of concrete. The purpose of prestressing tendon is to impart and maintain the prestress at the same level without any change due to the change in stress in concrete surrounding it.

14. In pre – tensioned members if the area of prestressing tendons is small, it is important to account for them in calculating centroid.
a) True
b) False

Explanation: In pre – tensioned members if the area of prestressing tendons is relatively small, there is no need to account for them in calculating area, centroid and inertia of a cross – section. Otherwise the allowance should be made on the basis of (m – 1) times the area of prestressing tendons where m is the modular ratio.

15. The stresses computed from the combined stress formula for prestressed concrete, positive stresses are taken as compressive and negative stresses are taken as tensile.
a) True
b) False

Explanation: In the homogeneous beam concept the combined stress formula is given as:
σ = (P / A) ± (My / I)
Here the positive stresses are taken as compressive and negative stresses are taken as tensile. The eccentricity (e) is taken positive when measured below the centroidal axis.
The stresses due to prestress are as follows:
Tensile stress at top pσtt = (P / A) [1 – (eyt / r2)]
Compressive stress at the bottom pσbc = (P / A) [1 + (eyb / r2)]
pσij = the first subscript i = t or b represents top or bottom fiber
the second subscript j = t or c represents tension or compression
yt = distance of top fiber from the centroidal axis
yb = distance of bottom fiber from the centroidal axis
The subscript p represents prestress.

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