PRESTRESSED CONCRETE

Tutorial Problems

Note :Use IS 1343-1980 to solve problems

1. A concrete beam with a single overhang is simply supported at A and B over a span

of 8 m and the overhang BC is 2 m. The beam is of rectangular section 300 mm

wide and 900 mm deep and supports a uniformly distributed live load of 4 kN/m over

the entire span in addition to its self-weight. Determine the profile of the prestressing

cable with an effective force of 500 kN which can balance the dead and live loads

on the beam. Sketch the profile of the cable along the length of the beam.

2. A PSC pile of 300 mm x 300 mm in section and is provided with 40 wires of 3 mm

diameter distributed uniformly over the section. Initially the wires are tensioned in

the prestressing beds with a total pull of 450 kN. Determine the final stress and the

percentage loss of stress in the wires. Take Es = 2.08 x 105 N/mm2 ; Ec = 3.20 x 104

N/mm2; creep shortening – 36 x 10-6 mm/mm per N/ mm2 of stress; total shrinkage

strain = 200 x 10-6; relaxation loss of stress in steel – 4.5% of the initial stress.

3. The initial prestressing force transmitted by a cable to a prestressed concrete beam

is 390 kN. The sectional area of the prestressing wires is 325 mm2. Find the

percentage loss of stress in the wires due to shrinkage of concrete only (i) if the

beam is post-tensioned (ii) if the beam is prestensioned. Assume age of concrete at

transfer = 7 days; Es = 2.1 x 105 N/mm2.

4. A rectangular beam 180 mm wide and 400 mm deep is simply supported over a

span of 8 m and is reinforced with 3 wires of 8 mm diameter. The wires are located

at a constant eccentricity of 80 mm 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; fck = 45 N/mm2 and 35

N/mm2 respectively for pre-tensioned and post-tensioned concrete; slip at

anchorage – 0.8 mm; friction co-efficient due to wave effect – 0.002 per m;

relaxation of steel stress – 6 %; Adopt creep and shrinkage co-efficients as per

codal provisions.

5. A post-tensioned prestressed concrete beam of span length 10 m has a rectangular

section 300 mm wide and 800 mm deep. The beam is prestressed by a parabolic

cable concentric at the supports and with an eccentricity of 250 mm at the centre of

span. The cross-sectional area of high tensile wires in the cable is 500 mm2. The

wires are stressed by using a jack at the left end so that the initial force in the cable

at the right end is 250 kN. Calculate (i) the total loss of stress in the wires (ii) the

jacking force required at the left end. Use the following data - Coefficient of friction

for curvature effect – 0.55; friction co-efficient due to wave effect – 0.003/m;

anchorage slip at the jacking end – 3 mm; relaxation of steel stress – 4%; shrinkage

of concrete – 0.0002; creep coefficient – 2.2; Es = 210 kN/mm2 ; Ec = 35 kN/mm2.

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