MECHANICS OF SOLIDS 2018 Question Paper — Government College of Engin…

Instructions

• Attempt five questions in all, selecting at least two questions from each section.
• Assume any missing data.
• Use of scientific calculator is allowed in the examination hall.

Questions

Section A

• Q1. (a) A bar $2\text{ cm} \times 4\text{ cm}$ in cross-section and $40\text{ cm}$ long is subjected to a radial tensile load of $70\text{ kN}$. It is found that the length increases by $0.176\text{ mm}$ and lateral dimension of $4\text{ cm}$ decreases by $0.0044\text{ mm}$. Find : (i) Young's modulus (ii) Poisson's ratio (iii) Change in volume of the bar (iv) Bulk modulus. [10] (b) Draw stress-strain diagram for mild steel and explain it briefly. [10] [20 marks]
• Q2. A cantilever of length $2\text{ m}$ carries a uniformly distributed load of $2\text{ kN/m}$ length over the whole length and a point load of $3\text{ kN}$ at the free end. Draw the shear force and bending moment diagram for the cantilever. [20] [20 marks]
• Q3. (a) A hollow shaft of diameter ratio $3/8$ is required to transmit $600\text{ kW}$ and $110\text{ rpm}$, the maximum torque being $20\%$ greater than mean. The shear stress is not to exceed $63\text{ N/mm}^2$ and twist in $3\text{ m}$ lenth not to exceed $1.4$ degree. Taking modulus of rigidity of shaft material as $84\text{ kN/mm}^2$, determine the diameter of shaft. [15] (b) What is the relation between shear force and loading function of a beam ? [5] [20 marks]
• Q4. A steel rod of $20\text{ mm}$ diameter passes centrally through a copper tube of $50\text{ mm}$ external diameter and $40\text{ mm}$ internal diameter. The tube is closed at each end rigid plates of negligible thickness. The nuts are tightened lightly home on the projecting parts of the rod. If the temperature of the assembly is raised by $50\text{ }^\circ\text{C}$, calculate the stresses developed in copper and steel, Take E for steel and copper as $200\text{ GN/m}^2$ and $100\text{ GN/m}^2$ and $\alpha$ for steel and copper as $12 \times 10^{-6}\text{ per }^\circ\text{C}$ and $23 \times 10^{-6}\text{ per }^\circ\text{C}$. [20] [20 marks]

Section B

• Q5. A cylindrical vessel, whose ends are closed by means of rigid flange plates, is made of steel plate $3\text{ mm}$ thick. The length and the internal diameter of the vessel are $50\text{ cm}$ and $25\text{ cm}$ respectively. Determine the longitudinal and hoop stresses in the cylindrical shell due to an internal fluid pressure of $3\text{ N/mm}^2$. Also calculate the increase in length, diameter and volume of the vessel. Take E as $2 \times 10^5\text{ N/mm}^2$ and Poisson's ratio $0.3$. [20] [20 marks]
• Q6. A beam of length $8\text{ m}$ is simply supported at its ends and carries two point loads of $36\text{ kN}$ and $46\text{ kN}$ at a distance of $1.5\text{ m}$ and $4\text{ m}$ from the left support. Find : (i) Deflection under each load (ii) Maximum deflection (iii) The point at which maximum deflection occurs, given $\text{E} : 2 \times 10^5\text{ N/mm}^2$ and $\text{I} : 85 \times 10^6\text{ mm}^4$. Use Macaulay's method. [20] [20 marks]
• Q7. (a) Derive an expression for the Euler' crippling load for a long column with one end fixed and other end free. [10] (b) Explain a technique used to develop initial compressive stresses near the inside wall of the cylinder. [10] [20 marks]
• Q8. What do you understand by the term theory of failures ? Explain any two theories of failure. [20] [20 marks]

Related pages

• MECHANICS OF SOLIDS syllabus
• All MECHANICS OF SOLIDS papers from 2018

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• MECHANICS OF SOLIDS 2018 question paper — end-term
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• MECHANICS OF SOLIDS 2018 question paper — end-term