VTU Civil Engineering (Semester 7)
Design of Pre-stressed Concrete Structures
December 2014
Total marks: --
Total time: --
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

1 (a) Define pre-stressed concrete. State its advantage over reinforced concrete.
6 M
1 (b) Explain with neat sketches, 'Fryssinet' system of pre-stressing.
6 M
1 (c) A pre-stressed concrete beam supports a live load of 4kN/m over a simply supported span of 8m. The beam has an 1-section with an overall depth of 400 mm. The thickness of flanges and web are 60 and 80 mm respectively. The width of the flanges is 200mm. The beam is to be pre-stressed by an effective force of 235 kN at a suitable eccentricity such that the resultant stresses at the soffit of the beam at the centre of span is zero.
i) Find the eccentricity required for the force.
ii) If the tendon in concentric, what should be the magnitude of the pre-stressing force for the resultant stress to be zero at the bottom fibre of the central span section?
8 M

2 (a) Explain concept o load balancing in pre-stressed concrete design.
6 M
2 (b) A concrete beam with a 'double overhang' has the middle span equal to 10m and the equal overhanging on either side is 2.5m. Determine the profile of the pre-stressing cable with an effective force of 250 kN which can balance a uniformly distributed load of 8 kN/m on the beam, which includes the self-weight of the beam. Sketch the cable profile marking the eccentricity of cable at the support and mid-span.
14 M

3 (a) List the various types of losses in pre-stressed concrete members and the equations used to determine them.
6 M
3 (b) A rectangular beam 180mm wide by 400mm deep is simply supported over a span of 8m and is reinforced with 3 wires of 8mm dia meter. The wires are located at a constant eccentricity of 80mm and are subjected to an initial stress of 1200 N/mm2. Calculate the percentage loss of stress in the wires if the beam is i) pre tensioned ii) post tensioned. Take Es=210 kN/mm2, modular ratio =6, slip at anchorage =0.8 mm, friction coefficient = 0.002/m, relaxation of steel stress = 6%. Adopt creep and shrinkage co-efficient as per IS: 1343 code specifications.
14 M

4 (a) Explain the significance of long term deflections in PSC beams and indicate how it is calculated.
6 M
4 (b) What are the factors influencing the deflection of PSC beams? Briefly discuss them.
4 M
4 (c) A concrete beam having a rectangular section 150 mm wide by 300 mm deep is pre stressed by a parabolic cable having an eccentricity of 75 mm at centre of span towards the soffit and an eccentricity of 25 mm towards the top at support sections. The effective force in the cable is 350 kN. The beam supports a concentrated load of 20 kN at the centre of span in addition to the self-weight. If the modulus of elasticity of concrete is 38 kN/mm2 and span is 8m calculate:
i) Short term deflection at centre of span under prestress, self wight and live load
ii) Long term deflection assuming the loss ratio as 0.8 and creep co-efficient as 1.6.
10 M

5 (a) What are the different types of flexural failures observed in a pre-stressed concrete beam? Explain with sketches.
6 M
5 (b) A double Tee section having a flange 1200 mm wide and 150 mm thick is pre-stressed by 4700 mm2 of high tensile steel located at an effective depth of 1600mm. The ribs have a thickness of 1500 mm each. The cube strength of concrete is 40 N/mm2 and tensile strength of steel is 1600 N/mm2. Determine the flexural strength of the double tee girder using IS: 1343 code provisions.
7 M
5 (c) A post - tensioned beam with 'unbounded tendors' is of rectangular cross section 500mm × 1000mm. The cross sectional area of pre-stressing steel is 3000 mm2. The effective pre-stress after considering all losses is 1000 Mpa. The effective span of the beam made. M40 concrete is 15m. Estimate the ultimate moment of resistance of the section using codal provisions.
7 M

6 (a) Discuss briefly the modes of failure due to shear.
5 M
6 (b) A concrete beam of rectangular section, 200mm wide and 600 mm deep, is pre-stressed by a parabolic cable located at an eccentricity of 100mm at mid-span and zero at the supports. If the beam has a span of 10m and carries a uniformly distributed live load of 4 kN/m, find the effective force necessary in the cable for zero shear stress at the support section. For this condition calculate the principle stresses. The density of concrete is 24 kN/m3.
7 M
6 (c) A PSC beam 250 mm wide and 150 mm deep is subjected to a shearing force of 900 kN. The fibre stress under working loads is 4N/mm2. If the effective pre-stresses is 1000 N/mm2 and area of cables 1500 mm2. Design the shear reinforcement . The cables are inclined at an angle of sin-1 (1/6) with horizontal.
8 M

7 (a) Explain Marginal method of end block design.
8 M
7 (b) The end block of a post tensioned beam is 300mm wide by 300mm deep and is pre-stressed concentrically by a fryssinet cylindrical anchorage of 150 mm diameter with a jacking force of 800kN. Design suitable anchorage zone reinforcement and sketch the details.
12 M

8 Design a pre-tensioned symmetrical I-beam for an effective span of 7 m to support a super imposed load of 6 kN/m. The beam is to be pre cast in factory and is to be designed for handling at any point along length during transport and erection, Load factors against failure by bending or shear, For dead load = 1.5, for live load = 2.5
Permissible stresses:
At trasfer,
       Compressive stress = 1.4 N/mm2
       Tensile stress = 1.4 N/mm2
At working load,
      Compressive stress = 16 N/mm2
      Tensile stress = 1.4 N/mm2.
20 M

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