Strength of Material - B.Tech 3rd Semester Exam., 2017

2017•Semester 2•Civil-CA•End Semester
Bihar Engineering University, Patna
B.Tech 3rd Semester Exam., 2017

Strength of Material

Time: 03 HoursCode: 021306Full Marks: 70

Instructions:

  1. The marks are indicated in the right-hand margin.
  2. There are NINE questions in this paper.
  3. Attempt FIVE questions in all.
  4. Question No. 1 is compulsory.
Q.1 Choose the correct answer of the following (any seven):[14]

  1. The ratio of lateral strain to linear strain is known as

    1. modulus of elasticity
    2. modulus of rigidity
    3. Poisson's ratio
    4. elastic limit

  2. The temperature strain in a bar is ___ proportional to the change in temperature.

    1. directly
    2. indirectly
    3. Either (i) or (ii)
    4. None of the above

  3. Moment of inertia of a semi-circle about its XX-axis is given by

    1. \( 0.22r^3 \)
    2. \( 0.11r^4 \)
    3. \( 0.14r^4 \)
    4. \( 0.2r^4 \)

  4. The strength of the beam mainly depends on

    1. bending moment
    2. c.g. of the section
    3. section modulus
    4. its weight

  5. A cantilever beam AB of length \( l \) has moment \( M \) applied at free end. The deflection at the free end B is given as

    1. \( M^2l/EI \)
    2. \( Ml^2/2EI \)
    3. \( Ml/2EI \)
    4. \( Ml^3/2EI \)

  6. A beam of length \( 6 \text{ m} \) carries a point load \( 120 \text{ kN} \) at its centre. The beam is fixed at both ends. The fixing moment at the ends is

    1. \( 40 \text{ kNm} \)
    2. \( 90 \text{ kNm} \)
    3. \( 120 \text{ kNm} \)
    4. \( 150 \text{ kNm} \)

  7. Which of the following are usually considered as thin cylinders?

    1. Boilers
    2. Tanks
    3. Water pipes
    4. All of the above

  8. Thin cylinders are frequently required to operate under pressure up to

    1. \( 5 \text{ MN/m}^2 \)
    2. \( 15 \text{ MN/m}^2 \)
    3. \( 30 \text{ MN/m}^2 \)
    4. \( 250 \text{ MN/m}^2 \)

  9. In thick cylinders, the radial stress in the wall thickness

    1. is zero
    2. is negligibly small
    3. varies from the inner surface to the outer surface
    4. Any of the above

  10. The stress due to suddenly applied load is ___ times that of gradually applied load.

    1. two
    2. three
    3. four
    4. five
Q.2 Solve both questions :[14]

  1. A steel bar is \( 900 \text{ mm} \) long, its two ends are \( 40 \text{ mm} \) and \( 30 \text{ mm} \) in diameter and the length of each rod is \( 200 \text{ mm} \). The middle portion of the bar is \( 15 \text{ mm} \) in diameter and \( 500 \text{ mm} \) long. If the bar is subjected to an axial tensile load of \( 15 \text{ kN} \), find its total extension, assuming \( E = 200 \text{ GN/m}^2 \).

  2. The following data relate to a bar subjected to a tensile test: Diameter of bar \( = 30 \text{ mm} \), Tensile load \( = 54 \text{ kN} \), Gauge length \( = 300 \text{ mm} \), Extension of the bar \( = 0.112 \text{ mm} \), Change in diameter \( = 0.00366 \text{ mm} \). Calculate the Poisson's ratio and the values of three moduli.

Q.3 Solve this question :[14]

  1. Two mutually perpendicular planes of an element of material are subjected to direct stresses of \( 10.5 \text{ MN/m}^2 \) (tensile) and \( 3.5 \text{ MN/m}^2 \) (compressive) and shear stress of \( 7 \text{ MN/m}^2 \). Using both analytical and graphical methods, find-
    (a) the magnitude and direction of principal stresses;
    (b) the magnitude of the normal and shear stresses on a plane on which the shear stress is maximum.

Q.4 Solve both questions :[14]

  1. With the help of suitable assumptions, deduce torsion equation for a hollow circular shaft.

  2. A hollow circular shaft \( 20 \text{ mm} \) thick transmits \( 294 \text{ kW} \) at \( 200 \text{ r.p.m.} \) Determine the diameters of the shaft if the shear strain due to torsion is not to exceed \( 8.6 \times 10^{-4} \). Assume modulus of rigidity as \( 80 \text{ GN/m}^2 \).

Q.5 Solve both questions :[14]

  1. The following figure shows a loaded beam: (a) Sketch the shear force and bending moment diagrams giving the important numerical values.

    (b) Calculate the maximum bending moment and the point at which it occurs.

    Question Diagram
Q.6 Solve both questions :[14]

  1. A cantilever of length \( l \) carries uniformly distributed load of \( W \) per unit run for a distance \( \frac{3l}{4} \) from the fixed end. Find the slope and deflection at the free end.

  2. A cantilever of length \( l \) carries a point load \( W \) at the end. If the moment of inertia of the section increases uniformly from \( I \) at the free end to \( 2I \) at the fixed end, calculate the deflection at the free end.

Q.7 Solve both questions :[14]

  1. Calculate the change in dimensions of a thin cylindrical shell due to an internal pressure. Also calculate the change in length and diameter of the cylindrical shell.

  2. A cylindrical shell \( 3 \text{ m} \) long which is closed at the ends has an internal diameter of \( 1 \text{ m} \) and a wall thickness of \( 15 \text{ mm} \). Calculate the circumferential and longitudinal stresses induced and also change in dimensions of the shell if it is subjected to an internal pressure of \( 1.5 \text{ MN/m}^2 \). Take \( E = 200 \text{ GN/m}^2 \) and \( 1/m = 0.3 \).

Q.8 Solve both questions :[14]

  1. Discuss and derive Lame's theory for thick shells.

  2. Calculate the thickness of metal necessary for a cylindrical shell of internal diameter \( 160 \text{ mm} \) to withstand a pressure of \( 25 \text{ MN/m}^2 \), if maximum permissible tensile stress is \( 125 \text{ MN/m}^2 \).