B.Tech II Year I Semester Examinations, November/December - 2023

STRENGTH OF MATERIALS-I

(Civil Engineering)

Time: 3 hours

Max. Marks: 70

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Note: 1. Question paper consists of Two parts (Part-A and Part-B)

2. Answer ALL the questions in Part-A

3. Answer any FOUR Questions from Part-B

PART-A (14 Marks)

1. a) Define the terms: Elasticity, plasticity, ductility and brittleness. (2M)

b) Define Poisson's ratio and write the relation between E, G and K. (2M)

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c) Define shear force and bending moment. (2M)

d) What are the assumptions made in the theory of simple bending? (2M)

e) Define torsional rigidity and polar modulus. (2M)

f) Define Principal stresses and Principal planes. (3M)

g) Write the expression for maximum deflection of a cantilever beam with a point load at the free end. (1M)

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PART-B (56 Marks)

2. a) A steel rod of 3 cm diameter is enclosed centrally in a hollow copper tube of external diameter 5 cm and internal diameter 4 cm. The composite bar is then subjected to an axial pull of 45000 N. If the length of each bar is equal to 15 cm, determine (i) The stress in the rod and tube, and (ii) Load carried by each bar. Take E for steel = 2.1 x 10⁵ N/mm² and for copper = 1.1 x 10⁵ N/mm². (7M)

b) A circular bar rigidly fixed at both ends is 2m long. A load of 20kN is applied at a distance of 1.5m from the left end. Determine the reactions at the supports. (7M)

3. Draw the shear force and bending moment diagrams for the beam given in Fig.1. (14M)

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4. A timber beam of rectangular section is to support a load of 20 kN uniformly distributed over a span of 3.6 m when simply supported. If the depth of the section is to be twice the breadth, and the stress in the timber is not to exceed 7 N/mm², find the dimensions of the cross-section. (14M)

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5. A solid shaft transmits 250 kW at 100 r.p.m. If the shear stress is not to exceed 75 N/mm², what should be the diameter of the shaft? If this shaft is replaced by a hollow one whose internal diameter is 0.6 times the external diameter, what should be the external diameter to transmit the same power at the same speed if the maximum shear stress is the same? (14M)

6. At a point in a strained material, the principal stresses are 100 N/mm² (tensile) and 60 N/mm² (compressive). Determine the normal stress, shear stress and resultant stress on a plane inclined at 50° to the axis of the major principal stress. Also determine the maximum shear stress at the point. (14M)

7. A cantilever beam of length 3 m is carrying a uniformly distributed load of 2.5 kN/m over a length of 2 m from the fixed end. Determine the slope and deflection at the free end. Take E = 2 x 10⁵ N/mm² and I = 8 x 10⁴ mm⁴. (14M)

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