SPSC 2011 Assistant Engineer / Assistant Executive Engineer (Civil) BPS-17, Engineers Cadre CCE (2011) — Theory of Structures & Strength of Materials Paper

Assistant Engineer / Assistant Executive Engineer (Civil) BPS-17, Engineers Cadre CCE (2011) — Theory of Structures & Strength of Materials. Combined Competitive Examination for Engineers Cadre · Thursday 24 March 2011, 2:00 pm to 5:00 pm · Max marks 100. Attempt any 05 questions. Figures in the paper are described in words.

1. 1(a) Define the terms Shear force and Bending moment. Discuss the utility of Shear force and Bending moment Diagrams. (09) (b) Draw Shear force and Bending moment Diagram for the beam shown in the figure. (11) Figure: a beam pinned at the left end A and resting on a roller support 5.0 m from A, with a 1.0 m overhang beyond the roller. Loads: a 6 t point load 1.5 m from A; a uniformly distributed load of 2 t/m over the 2.0 m length from 3.0 m to 5.0 m; a 3 t point load at the free end of the overhang (6.0 m from A).

2. 2(a) What are flat plates? Give the classification of flat plates and discuss the methods of determining the elastic stresses in flat plates. (09) (b) The cylinder of the steam engine is 18 in. diameter and the maximum steam pressure is 125 psi. Find the thickness of the plate cylinder head of steel if the working stress is 15000 psi and the edges are simply supported. (11)

3. 3(a) What do you understand by oblique planes? Which planes are called principal planes? (09) (b) Derive an expression for stresses on oblique section of body subjected to direct tensile stress σ along x-axis and 3σ along y-axis. (11)

4. 4An unknown weight falls through 1 cm on a collar rigidly attached to the lower end of a vertical bar 3 m long and 6 cm² in section. If the maximum instantaneous extension is known to be 2 mm, what is the corresponding stress and value of the unknown weight? Take Young's modulus of elasticity as 2.0 × 10⁶ kg/cm². (20)

5. 5A steel rod of cross sectional area 800 mm² and two brass rods each of cross sectional area 500 mm² together support a load of 25 kN as shown in the figure. Calculate the stresses in the rods. Take E for steel as 200 GPa and E for brass as 100 GPa. (20) Figure: a rigid plate carrying 25 kN rests on the three rods. The two brass rods are 200 mm long; the central steel rod stands in a recess in the base and is 250 mm long, with its top level with the brass rods.

6. 6(a) Derive relationship between slope, deflection and radius of curvature. (10) (b) A cantilever beam 15 cm wide, 10 cm deep and 2 m span carries a uniformly varying load of 5 T/m at the free end and 15 T/m at the fixed end. Find the slope and deflection of the cantilever at the free end. Use E = 1.0 × 10⁶ kg/cm². (10)

7. 7A continuous beam (see figure) 10 m long is resting on supports at same level at A, B and C. Determine the moments over the beam using three moment theorem and draw the bending moment diagram. Also compute support reactions and draw shear force diagram. (20) Figure: span AB = 6 m with a 5 t point load 2 m from A; span BC = 4 m with a uniformly distributed load of 1 t/m.

8. 8(a) What is lateral strain? What is relationship between lateral strain and Poisson's ratio? (07) (b) A steel bar of length 3 ft and diameter 0.75 inch when tested for tensile strength observed 2 in increase in length and 0.1 in reduction in diameter. Compute strain, lateral strain and Poisson's ratio. (13)