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

Instructions

• Attempt five questions selecting at least one questions from each unit.

Questions

Unit I

• Q1. (a) Explain the stress strain diagram for : (i) ductile materials (ii) brittle materials. (b) Two parallel walls $6\text{ m}$ apart are stayed together by a steel rod of $25\text{ mm}$ diameter passing through metal plates and nuts at each end. The nuts are tightened when the rod is at a temperature of $100\text{ }^\circ\text{C}$. Determine the stress in the rod when the temperature falls down to $60\text{ }^\circ\text{C}$, if (i) the ends do not yield (ii) the ends yield by $1\text{ mm}$. Take $E = 200\text{ GPa}$ and co-efficient of linear expansion $= 12 \times 10^{-6}/^\circ\text{C}$. [20 marks]
• Q2. A steel rod $20\text{ mm}$ diameter passes centrally through a copper tube of $25\text{ mm}$ internal diameter and $35\text{ mm}$ external diameter. Copper tube is $800\text{ mm}$ long and is closed by rigid washers of negligible thickness which are fastened by the nut threaded on the rod. The nuts are tightened till the load on the assembly is $20\text{ KN}$. Calculate initial stresses in the copper tube and steel rod. Calculate the increase in the stresses when one nut is tightened by one quarter of a turn relative to the other. Take pitch of the thread as $1.6\text{ mm}$. Take $E$ for steel and copper as $200\text{ GPa}$ and $100\text{ GPa}$ respectively. [20 marks]

Unit II

• Q3. (a) Calculate the ratio of the torque transmitted by a solid shaft to the torque transmitted by a hollow shaft by comparing their strength. (b) Find the angle of twist per metre length of a hollow shaft of $100\text{ mm}$ external and $60\text{ mm}$ internal diameter, if the shear stress is not to exceed $35\text{ MPa}$. Take $C = 85\text{ GPa}$. [20 marks]
• Q4. Two close coiled helical springs wound from the same wire, but with different core radii having equal number of coils are compressed between rigid plates at their ends. Calculate the maximum shear stress induced in each spring, if the wire diameter is $10\text{ mm}$ and the load applied between the rigid plates is $500\text{ N}$. The core radii of the springs are $100\text{ mm}$ and $75\text{ mm}$ respectively. [20 marks]

Unit III

• Q5. For the beam ABCD shown: A beam ABCD, $4\text{ m}$ long is overhanged by $1\text{ m}$ and carries load as shown. Draw the shear force and bending moment diagrams for the beam and locate the point of contraflexure. [20 marks]
• Q6. (a) A rectangular beam is to be cut from a circular log of wood of diameter D. Find the ration of dimensions for the strongest section in bending. (b) A beam of triangular cross section having base width of $100\text{ mm}$ and height of $150\text{ mm}$ is subjected to a shear force of $13.5\text{ kN}$. Find the value of maximum shear stress and sketch the shear stress distribution along the depth of the beam. [20 marks]

Unit IV

• Q7. A steel girder of uniform section, $14\text{ metres}$ long is simply supported at its ends. It carries concentrated loads of $90\text{ kN}$ and $60\text{ kN}$ at two points $3\text{ metres}$ and $4.5\text{ metres}$ from the two ends respectively. Calculate : (i) the deflection of the girder at the points under the two loads. (ii) the maximum deflection. Take $I = 64 \times 10^{-4}\text{ m}^4$ and $E = 210 \times 10^{-6}\text{ kN/m}^2$. [20 marks]
• Q8. (a) Define slenderness ratio and equivalent length of a column. (b) A 'T' section $150\text{ mm} \times 120\text{ mm} \times 20\text{ mm}$ is used as a strut of $4\text{ m}$ long with hinged at its both ends. Calculate the crippling load, if Young's modulus for the material be $200\text{ GPa}$. [20 marks]

Related pages

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

Other years

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