B.Tech II Year I Semester Examinations, December - 2018

STRENGTH OF MATERIALS-I

(Common to CE, CEE)

Time: 3 hours Max. Marks: 75

Note: This question paper contains two parts A and B.

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Part A is compulsory which carries 25 marks. Answer all questions in Part A.

Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks.

PART- A (25 Marks)

1. a) Define Lateral strain and Poisson’s ratio. [2M]

b) Define Bulk modulus and write the relationship between Young’s modulus and Bulk modulus. [3M]

c) Define Shear force and Bending Moment. [2M]

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d) Write the assumptions made in the theory of simple bending. [3M]

e) Define Torsion and Torsional rigidity. [2M]

f) Write the equation for deflection of a simply supported beam with point load at centre. [3M]

g) What are the limitations of Euler’s formula? [2M]

h) Define principal stresses and principal planes. [3M]

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i) Define thin and thick cylinders. [2M]

j) What are the applications of strain rosettes? [3M]

PART- B (50 Marks)

2. a) A steel bar 25 mm diameter is loaded as shown in Figure. Determine the stress in each part, total elongation. Take E = 2x10⁵ N/mm². [5M]

b) Define thermal stresses. Derive the expression for thermal stresses when a bar is fixed at both the ends. [5M]

OR

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3. a) A steel rod of 3 cm diameter is enclosed centrally in a hollow copper tube of external diameter 5 cm and internal diameter of 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 stresses in the rod and tube, and ii) Load carried by each bar. Take E for steel = 2.1 x 10⁵ N/mm² and E for copper = 1.1 x 10⁵ N/mm². [5M]

b) Define i) Elasticity ii) Plasticity iii) Ductility iv) Malleability. [5M]

4. Draw SFD and BMD for the beam shown in Figure. [10M]

OR

5. A simply supported beam of length 5 m carries a uniformly distributed load of 1 kN/m run over the entire length. In addition to this it also carries a point load of 2.5 kN at a distance of 1 m from the left support. Draw the S.F and B.M diagrams. [10M]

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6. A timber beam 100 mm wide and 150 mm deep supports a U.D.L over a span of 4 m. If the safe stresses are not to exceed 28 N/mm² in bending and 2 N/mm² in shear, calculate the maximum load which the beam can carry. [10M]

OR

7. a) Derive bending equation from first principle. [5M]

b) A rectangular beam 100 mm wide and 250 mm deep is subjected to a maximum shear force of 50 kN. Determine: i) Average shear stress, ii) Maximum shear stress, and iii) Shear stress at a distance of 25 mm above the neutral axis. [5M]

8. A cantilever of length 2 m carries a point load of 2 kN at the free end and another load of 1 kN at a distance of 1 m from the free end. Find the deflection at the free end. Take E = 2x10⁵ N/mm² and I = 10⁸ mm⁴. [10M]

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OR

9. A beam of length 6 m is simply supported at its ends and carries two point loads of 48 kN and 40 kN at a distance of 1 m and 3 m respectively from the left support. Find: i) Deflection under each load ii) Maximum deflection, and iii) The point at which maximum deflection occurs. Take E = 2x10⁵ N/mm² and I = 85 x 10⁶ mm⁴. [10M]

10. A cylindrical vessel, whose ends are closed by flat plates is subjected to an internal pressure of 1.5 N/mm². The internal diameter of the vessel is 500 mm and length is 1.8 m. Determine the thickness of the shell if stress is limited to 90 N/mm² and the longitudinal stress is limited to 60 N/mm². Find also the permissible intensities of internal pressure if the thickness of the shell is 15 mm. [10M]

OR

11. 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^o to the axis of major principal stress. Also determine the maximum shear stress at the point. [10M]

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