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JE – 947

*JE947*

First Semester M.E. (Civil) Degree Examination, July/August 2013 2K8PC101 : PRESTRESSED CONCRETE Prestressed Concrete Structures (Common to PSC/Str) Time : 3 Hours

Max. Marks : 100

Instructions : 1) Answer any five full questions. 2) Reference to IS-1343 permitted. 3) Any missing data may be suitably assumed. 1. A simply PS.C. member has a cross-section 300 mm × 600 mm and it is 12 m long. It carries a line load of 15 KN/m in addition to its self weight. It is prestressed with 2000 mm2 high tensile steel located at 175 mm from soffit. The cable profile is straight for full length of the beam and it is stressed to a level of 1000 N/mm2. It is bonded to concrete. Determine the stresses in the beam at end, quarter span and mid-span sections. Also locate the position of the thrust line using force concept. 20 2. a) Explain variation of stresses in steel at various load stages in a prestressed concrete element subjected to flexure, with a neat sketch.

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b) An unsymmetrical I-S/C having top flange – 500 mm × 200 mm, bottom flange – 400 mm × 200 mm and web of 200 mm × 600 mm is designed to carry a line load bending moment of 700 KN/m at mid-span. It is prestressed with a force of 1600 KN at 150 mm from soffit. Evaluate the stresses at transfer stage and at service load stage at top and bottom fibres. Assume 15 % loss in prestress at service load stage. Evaluate also the limitations of position of cable if the permissible stresses in concrete in compression and tension are limited to 16 N/mm2 and 1.0 N/mm2. 14 3. Evaluate the losses in forces due to elastic shortening in cables 1, 2, 3 and 4 of a PS.C. beam of cross-section 300 × 600 mm, it is post-tensioned with 12 nos of 12.72 mm dia strand in all the above, 4 cable ducts. 3 strands form one cable. 40 mm duct is provided for each cable of 3 strands. Two cable ducts are located at a level of 100 mm from soffit and two more cable ducts at 200 mm from soffit. Each cable with 3 strands is prestressed at one stretch with a force of 3 × 130 KW. The bottom cables 1 and 2 stressed first and then the second level cables 3 and 4 are stressed. The cables have straight profile. Evaluate the loss in force of prestress due to elastic shortening. Assume m = 6. 20 P.T.O.

JE – 947

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4. A pretensioned PS.C beam has a rectangular section of 200 × 500 mm. The high tensile steel has its centre of area at 280 mm from top of beam. If fcu = 40 N/mm2

and fpu = 1600 N/mm2, determine the following details based on IS – 1343 – 1980

code provision. a) the minimum area of steel to avoid failure by fracture of steel b) the maximum area of steel which would ensure a ductile failure (under reinforced beam) c) flexural strength of section corresponding to case (b) d) the ultimate flexural strength of the section. 5. a) Explain the modes of failure due to shear.

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b) A PS.C. beam of rectangular section of size. 250 × 600 mm is prestressed with a straight cable with constant eccentricity of 100 mm. The beam spans 10 m and carries a load of 25 KN/m and the prestressing force in the cable is 1200 KN. Concrete has a density of 24 KN/m3. Calculate the maximum principal stresses at a cross-section 300 mm away from support.

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6. A PS.C. beam element has a symmetrical T-S/C with maximum depth of 320 mm (top and bottom flange of 160 mm width and 70 mm thickness. The wed is 50 mm thick). The properties of section are A = 31400 mm2, I = 3700 × 105mm4, Zb = Z t = 230 × 104mm3, self wt = 0.76 KN/m. It is prestressed with a force 185 KN at an eccentricity 110 mm. Assume Es/Ec = 6, Ec = 3.0 × 104 N/mm2, fcr = 4N/mm2. Evaluate the maximum deflection at the following stages a) Prestress + Self wt of the beam b) Prestress + Self wt + line load of 6 KN/m on a span of 6m c) Cracking load d) 15 times the working load.

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7. A precast pretensioned beam of rectangular section has a breadth of 100 mm and depth of 200 mm. The beam with an effective span of 5m, is prestressed by tendons with their centroids coinciding with the bottom kern. The initial force in the tendons is 240 KN. The loss of prestress may be assumed to be 15 %. The beam is incorporated in a composite T-beam by casting a top flange of breadth 400 mm and thickness 40 mm. On top of the precast unit the composite beam supports a line load of 4.0 KN/m. Calculate the resultant stresses developed in the precast and cast-in-situ concrete assuming the pretensioned unit as (i) unpropped and (ii) propped during the casting of the slab. Assume the same modulus of elasticity for concrete in pre-cast beam and in situ cast slab. 8. Explain briefly :

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i) Advantages and disadvantages of statically indeterminate structure ii) Need for composite construction iii) Analysis of prestressed concrete by force concept iv) Mechanism of sheer resistance in uncracked beam of prestressed concrete member.