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I Semester M.E. (Civil) Degree Examination, July 2016 Major : (Prestressed Concrete/Structural Engineering) 2K8PC101 : PRESTRESSED CONCRETE STRUCTURES Time : 3 Hours
Max. Marks : 100
Instructions : 1) Answer any five full questions. 2) Use of IS-1343 and IS-456 is permitted. 3) Assume missing data suitably. 1. A simply supported prestressed concrete beam of cross section 400 mm × 600 mm, spans over 10 m. It is subjected to an UDL of 30 kN/m and a Prestressing force of 1740 kN, with a Prestressing cable of parabolic profile. The cable is anchored at the C.G of the cross section at the supports and has a dip of 160 mm at Centre span. Analyse the beam for the effect of prestress by Stress Concept and verify the results by Load Balancing Concept. Draw Stress diagram. 20 2. A Prestressed concrete beam 250 mm × 360 mm has a span of 12 m. The beam is prestressed by steel wires of area 350 mm2, provided at an uniform eccentricity of 60 mm, with an initial prestress of 1250 N/mm2. Determine the percentage loss of stress in the wires if the beam is a) Pre-tensioned and b) Post-tensioned, for the following data Creep strain = 45 × 10–6 for pre-tensioned and 22 × 10–6 for post-tensioned, Shrinkage strain = 300 × 10 –6 for pre-tensioned and 215 × 10 –6 for post-tensioned, Relaxation of steel stress = 5% of initial stress, Friction coefficient for wave effect = 0.0015 m’ Anchorage slip = 1.25 mm, Modulus of elasticity of steel = 210 kN/mm2 Modulus of elasticity of concrete = 35 kN/mm2.
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3. A simply supported prestressed concrete beam having a rectangular cross section 150 × 300 mm, span over 6 m. It carries a live load of 15.5 kN/m. The beam is prestressed by a trapezoidal cable consisting of 6 wires of 7 mm diameter, the cable eccentricity being 56 mm within the central middle third of the span and varies linearly to zero at the supports and stressed at 1200 N/mm2. If the modulus of Elasticity of concrete is 3.5 × 104 N/mm2, calculate the maximum deflection of the beam at the following stages; a) Self weight + Prestress b) Self weight + Prestress + Live load c) Cracking Load (modulus of rupture = 4 N/mm2) and d) 1.6 times the working load. 4. a) Explain the different types of failure of PSC beams.
b) A post tensioned beam with unbounded tendons is of rectangular section 500 mm × 1000 mm. the cross sectional area of Prestressing steel is 2000 mm2, the effective prestress after considering all losses is 1000 N/mm 2 (fpu = 1600 N/mm2). The effective span of the beam is 15 m, estimate the ultimate moment of resistance of the Section as per IS code. Assume M40 grade concrete. 14 5. A simply supported beam of effective span 10 m is subjected to a super imposed dead and live loads 6 kN/m and 10 kN/m. Design a post tensioned rectangular section Type-II beam by Limit state method. Take fck = 35 N/mm2, fp = 1400 N/mm2 and fci = 30 N/mm2, (Zone – II). 20 6. a) State and explain, Guyon’s Theorem of Linear Transformation.
b) A two span continuous beam ABC (AB = BC = 8m) is simply supported at (A) and (C) and continuous over (B). The beam is 240 mm × 800 mm in section and is prestressed with a straight cable at a constant eccentricity of 150 mm towards the soffit. The effective prestress in the cable is 400 kN. The beam carries an UDL of 4.8 kN/m along with two point loads of 5 kN at mid span of each span in addition to its own weight. Sketch the pressure line due to prestress + loads. Also determine the extreme fiber stress in concrete across a section at (B). 14
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7. A rectangular pre tensioned concrete beam 100 mm × 230 mm and the prestress after all losses have occurred is 12 N/mm2. The beam is incorporated in a composite T-beam by casting a top flange of breadth 300 mm and a depth of 50 mm. Calculate the maximum UDL that can be supported on a simply supported span of 4.5 m without any tensile stresses occurring, for propped and un-propped condition. 20 8. Explain briefly any four of the following : a) Prestressed concrete simply supported beams and continuous beams. b) Minimum Section Modulus. c) Concordant cable profile. d) Efficiency of the section. e) Thrust line and pressure. —————————