Analysis of Prestress MCQ Quiz - Objective Question with Answer for Analysis of Prestress - Download Free PDF

Explanation:

As per IS 456: 2000,

• A standard hook has an anchorage value equivalent to a straight length of 16ϕ.
• The anchorage value of the standard U-type hook shall be 16 times the diameter of the bar. 
• The anchorage value of the standard bend shall be considered as 4 times the diameter of the bar for each 45o bend subject to a maximum value of 16 times the diameter of the bar.

Calculation:

Given:  

Diameter = ϕ = 25 mm

Anchorage value for 45° = 25 × 4 = 100 mm

Anchorage value for 90° = 25 × 8 = 200 mm

Explanation:

Prestressed Concrete

Prestressed concrete is a form of concrete construction where compressive stresses are deliberately induced in the concrete before any external loads are applied. This is done to counteract the tensile stresses that will develop under service loads, thus improving the concrete's performance and durability.

Analyzing the Given Options

1. Option 1: "Compressive stress induced in concrete before bending." (Correct Answer)

   • In prestressed concrete, compressive stress is introduced in the concrete using prestressing techniques like pre-tensioning or post-tensioning.

   • This compressive stress counteracts the tensile stresses that occur when the concrete is subjected to external loads.

2. Option 2: "Compressive stress induced in steel before bending." (Incorrect Answer)

   • In prestressed concrete, compressive stress is not applied to steel. Instead, tensile stress is applied to steel tendons.

   • Steel tendons are stretched and anchored to induce compressive forces in the concrete.

3. Option 3: "Tensile stress induced in steel before bending." (Incorrect Answer)

   • Tensile stress is indeed applied to the steel tendons in prestressed concrete, but this is not the same as the compressive stress induced in concrete.

   • The question specifically asks about the stress in the concrete, not in the steel.

   • Therefore, this option is not correct in the context of the question.

4. Option 4: "Tensile stress induced in concrete before bending." (Incorrect Answer)

   • In prestressed concrete, compressive stress is induced in the concrete, not tensile stress.

   • Tensile stress is undesirable in concrete because it is weak in tension and prone to cracking under tensile loads.

Explanation:

Transmission length:

• Prestress is transferred over a certain length from each end of a member which is called transmission length or transfer length. (L_t).
• The stress in the tendon is Zero at the ends of the members and increases over the transmission length to the effective prestress under the service loads.
• Then, remains constant, after the transmission length.

As per IS: 1343 - 1980, Clause 19.6

• These values are recommended by codes in absence of test data.
• These values are applicable when the concrete is well compacted
• Also, its strength is not less than 35 N/mm² at the transfer, and tendons are released gradually.

Explanation:

• High-strength concrete is necessary for prestressing concrete as the material offers
• High resistance in tension, shear bond, and bearing.
• High-strength concrete is invariably preferred to minimize the cost.
• High-strength concrete is less liable to shrinkage cracks and has a lighter modulus of elasticity and smaller ultimate creep strain.
• Resulting in a smaller loss of prestress in steel.

Additional Information 

Minimum grade of concrete for different purposes

• PCC – M15
• RCC – M20
• Post-tensioned PSC – M30
• Pre-tensioned PSC – M40

The correct answer is longs spans.Key Points

• Post tensioning is a construction technique that involves the use of high-strength steel strands or cables to reinforce concrete structures.
• The suitability of post tensioning depends on various factors such as span length, design requirements, and construction constraints.
• Post tensioning allows for longer spans to be achieved without the need for intermediate supports.
• This is because the high-strength steel cables can provide the necessary tensile strength to counteract the weight of the structure and any applied loads.
• Longer spans can result in more open and flexible interior spaces, which can be beneficial for certain building types such as sports arenas, exhibition halls, and airports.
• Post tensioning can also help reduce the overall weight of the structure, which can lead to cost savings in materials and construction.
• The use of post tensioning can improve the durability and resilience of concrete structures, as the cables can help prevent cracking and deformation due to temperature changes, shrinkage, and other factors.

Additional Information

• End spans refer to the sections of a structure that are adjacent to a support, such as a column or a wall.
  • Post tensioning can be used for end spans, but it may not be as necessary as for long spans.
• Break spans are sections of a structure that are interrupted by an expansion joint or a construction joint.
  • Post tensioning can be used for break spans, but it may require additional design considerations and construction techniques.
• Edge spans are sections of a structure that are located at the perimeter, such as a balcony or a cantilevered slab.
  • Post tensioning can be used for edge spans, but it may require additional reinforcement to account for wind loads and other lateral forces.

The correct answer is longs spans.Key Points

• Post tensioning is a construction technique that involves the use of high-strength steel strands or cables to reinforce concrete structures.
• The suitability of post tensioning depends on various factors such as span length, design requirements, and construction constraints.
• Post tensioning allows for longer spans to be achieved without the need for intermediate supports.
• This is because the high-strength steel cables can provide the necessary tensile strength to counteract the weight of the structure and any applied loads.
• Longer spans can result in more open and flexible interior spaces, which can be beneficial for certain building types such as sports arenas, exhibition halls, and airports.
• Post tensioning can also help reduce the overall weight of the structure, which can lead to cost savings in materials and construction.
• The use of post tensioning can improve the durability and resilience of concrete structures, as the cables can help prevent cracking and deformation due to temperature changes, shrinkage, and other factors.

Additional Information

• End spans refer to the sections of a structure that are adjacent to a support, such as a column or a wall.
  • Post tensioning can be used for end spans, but it may not be as necessary as for long spans.
• Break spans are sections of a structure that are interrupted by an expansion joint or a construction joint.
  • Post tensioning can be used for break spans, but it may require additional design considerations and construction techniques.
• Edge spans are sections of a structure that are located at the perimeter, such as a balcony or a cantilevered slab.
  • Post tensioning can be used for edge spans, but it may require additional reinforcement to account for wind loads and other lateral forces.

Explanation:

As per CI. 19.5.1 of IS 1343 At the time of initial tensioning, the maximum tensile stress, f_pi immediately behind the anchorages shall not exceed 76 percent of the ultimate tensile strength, f_pu of the wire or bar or strand.Important Points 

Grade of concrete:

• M 40 for pre-tensioned members
• M 30 for post-tensioned members

Concept:

Prestress concrete is the concrete in which internal stresses are produced due to compression or tension applied before applying external load and these stresses are counter balanced by the applied load to the desired degree.

Calculation:

Given,

Prestressing force = 2500 KN

Effective span length = 10 m

Total external load = 40 kN/m

We know that,

 \(M = P.e = {WL^2 \over 8}\)

\(e = {WL^2 \over 8P} = {40\times10^2 \over 8\times2500} = 0.2 m = 200 mm\)

Concept:

Shrinkage loss

Time-dependent strain measured in an unloaded and unrestrained specimen at a constant temperature.

Loss of pre-stress (Δf_p) due to shrinkage = E_P × ϵsh

Where E_p is the modulus of pre-stressing steel and

ϵsh is shrinkage strain

The approximate value of shrinkage strain for design shall be assumed as follows (IS 1383):

For pre-tensioning = 0.0003

Calculation:

Given, 

initial Prestressing force, P_o = 300 kN, Area = 300 mm²

Assume, E_p of steel = 2 × 10⁵ N/mm²

Initial stress, f = P_o/A = 300000/300 = 1000 N/mm²

Loss of pre-stress due to shrinkage, (Δfp) = EP × ϵsh

(Δfp) = 2 × 10⁵ × 0.0003 = 60 N/mm²

Loss of stress (%) = \(\frac{{{\Delta f_p}}}{f} \times 100 = \frac{{60}}{{1000}} \times 100 = 6\%\)

So, the percentage of loss of stress due to shrinkage in pre-tensioned members is 6 %. Hence the most appropriate option is 1 i.e 6.3 %.

Concept:

Stress at top fibre at midspan due to prestress in compression = \(\frac{{\bf{P}}}{{\bf{A}}} - \frac{{{\bf{P}}.{\bf{e}}}}{{\bf{Z}}}\)

Calculation:

Given,

b= 300 mm, d = 900 mm, e = 350 mm, P = 700 kN 

Where, Z = \(\frac{{\bf{I}}}{{\bf{y}}}\) = \(\frac{{\frac{{{\bf{b}}{{\bf{d}}^3}}}{{12}}}}{{\frac{{\bf{d}}}{2}}} = \frac{{{\bf{b}}{{\bf{d}}^2}}}{6} = \frac{{300 \times {{900}^2}}}{6} = 40.5 \times {10^6}{\bf{m}}{{\bf{m}}^3}\)

Stress at top fibre at midspan due to prestress = \(\frac{{\bf{P}}}{{\bf{A}}} - \frac{{{\bf{P}}.{\bf{e}}}}{{\bf{Z}}}\)

= \(\frac{{700 \times {{10}^3}}}{{300 \times 900}}- \frac{{700 \times {{10}^3} \times 350}}{{40.5 \times {{10}^6}}}\)

= 2.593 - 6.049

= 3.456 MPa (tensile)

Concept:

A minimum grade of concrete to be used in the design of the prestressed concrete structure as per IS 1343 is as below:

1. For Post-tensioning minimum grade of concrete used is M-30.

2. For Pre-tensioning minimum grade of concrete used is M-40.

Additional Information

Cover to be used in the design of the prestressed concrete structure as per IS 1343 is as below:

1. For Post-tensioning minimum cover to be used is 30 mm.

2. For Pre-tensioning minimum cover to be used is 20 mm.

Explanation:

• As per CI. 18.5.1 of IS 1343 at the time of initial tensing, the maximum tensile stress immediately behind the anchorages shall not exceed 80% of the ultimate tensile strength of wire or bar or strand.

As per the given option, we should take 76% (for the safer side)

Important Points

•  Grade of concrete:
  • M 40 for pre-tensioned members
  • M 30 for post-tensioned members

Concept:

Advantages of the Freyssinet system:

• Securing wires is not an expensive process.
• The required force for stretching the wires can be obtained very quickly.
• The plugs if placed in the concrete then it do not project beyond the ends of the member.​

Disadvantage of the Freyssinet  system:

• All the wires of cable should be stretched together in this system and therefore the stresses in the wires developed may not be exactly the same.
• The greatest stretching force which is applied in the range of 250 kN to 500 kN and this may not sufficient in many cases.
• The jack arrangements used in the system are very heavy and expensive, therefore practical difficulties are associated with it.

Explanation:

Some Important Codes:

I. IS 456 : 2000 : Code of practice for plain and Reinforced concrete

II. IS 800 : 2007 : Code of practice for general construction in steel

III. IS 875 (Part-1) : 1987 : Dead loads

IV. IS 875 (Part-2) : Imposed loads

V. IS 875 (Part-3) : Wind loads

VI. IS 875 (Part-4) : Snow loads

VII. IS 1343 : Code of practice for Prestressed concrete

VIII. IS 13920 : Code of practice for ductile detailing of reinforced concrete structure subjected to seismic forces.

Additional Information The pre-stressing steel, as per the IS code – 1343:1980, should be any one of the following types:

• Plain hard-drawn steel wires - Available in sizes of 2.5, 3, 4, 5, 7 and 8 mm diameter.
• Cold-drawn indented wire
• High tensile steel bar  - - Available in sizes of  10, 12, 16, 20, 22, 25, 28 and 32 mm diameter
• Uncoated stress relieved strand.

Explanation:

Given that

The span of beam, L = 5m

Prestressing force, P = 750 kN

Live Load, W­ = 5 kN/m

Cross-section size = 150 × 250 mm

The cable profile is parabolic with eccentricity at the center, e = 50 mm and at supports, e = 0

The BMD of the simply supported beam due to live load and prestressing cable is shown below:

The BM due to live load at supports will be zero as both end supports are hinged i.e. M_L = 0

The BM due to pre-stressing force at any point is given as – M_p = Pe;

Since at supports e = 0 so BM at supports is also zero due to pre-stressing force or M_p = 0

The stress in any fiber at any point is given as:

σ_b = {Direct stress due to Pre-stressing force, P} + {flexure stress due to BM caused by live load}  + { flexure stress due to BM caused by eccentricity of pre-stressing cable}

or

\(σ_b = \frac{P}{A} + \frac{M}{Z} + \frac{Pe}{Z}\)

Where- Z is section modulus at that section

For end support as we already concluded that M_p = M_L = 0; therefore, the stress at extreme fiber at end support is due to only the direct pre-stressing force which is uniform throughout the entire section and compressive in nature.  

σ_b  = P/A

σ_b = 750000/(150 × 250)

σ_b = 20 MPa

∴ The stress at extreme bottom fiber at end support is 20 MPa (compressive).