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

Instructions

• Attempt any five questions selecting atleast one from each unit.
• Assume missing data.
• Each question carry equal marks.

Questions

UNIT - I

• Q1. Direct stresses of $120\text{ MN/m}^2$ in tension and $90\text{ MN/m}^2$ in compression are applied to an elastic material at a certain point on planes at right angles to another. If the maximum principal stress is not to exceed $150\text{ MN/m}^2$ in tension, to what shearing stress can the material be subjected? What is then the maximum resulting shearing stress in the material? Also find the magnitude of the other principal stress and its inclination to $120\text{ MN/m}^2$ stress? Also find the solution graphically?
• Q2. Derive the expression for the direct strain on an oblique plane due to two normal pulls and a shear force.

UNIT - II

• Q3. A compound shaft is made by rigidly securing a sleeve of phosphor bronze on a solid steel shaft 40 mm diameter. If the maximum shear stresses to be attained in the two materials of the shafts are $40\text{ MN/m}^2$ and $64\text{ MN/m}^2$ for bronze and steel respectively, determine: i) Outer diameter of the sleeve ii) Torque transmitted by the compound shaft iii) Power transmitted by the shaft at $200\text{ rpm}$. iv) Angle of twist of the shaft per meter length. Take the $C_{\text{steel}} = 80\text{ GN/m}^2$ and $C_{\text{bronze}} = 40\text{ GN/m}^2$.
• Q4. Two close coiled helical springs wound from the same wire, but different core radii having equal number of turns are compressed between rigid plates at their ends. Calculate the maximum shear stress induced in each spring, if the wire diameter is 10 mm and the load applied between the rigid plates is $500\text{ N}$. The core radii of the spring is $100\text{ mm}$ and $75\text{ mm}$ respectively.

UNIT - III

• Q5. A steel bar 120 mm in diameter is completely encased in an aluminium tube of 180 mm outer diameter and 120 mm inner diameter so as to make a composite beam. The composite beam is subjected to a bending moment of $15\text{ kNm}$. Determine the maximum stress due to bending in each material. Take $E_s = 3E_{\text{al}}$.
• Q6. A beam AB 10 m long carries a uniformly distributed load of $20\text{ kN/m}$ over its entire length together with the concentrated load of $50\text{ kN}$ at the left end A and $80\text{ kN}$ at the end B. The beam is to be supported at two props at the same level, 6 m apart, so that the reaction is same at each. Determine the positions of the supports and draw the shear force and bending moment diagrams. Find the value of the maximum bending moment. Locate the points of contraflexure/inflexion, if any? [Diagram showing beam AB with UDL and point loads]

UNIT - IV

• Q7. A horizontal steel girder having uniform cross section is 14 m long and is simply supported at its ends. It carries two concentrated loads as shown. Calculate the deflections of the beam under the loads C and D. Take $E = 200\text{ GPa}$ and $I = 160 \times 10^6\text{ mm}^4$. [Diagram showing simply supported beam with loads at C and D]
• Q8. A T section $150\text{ mm} \times 120\text{ mm} \times 20\text{ mm}$ is used as a strut of 4 m long with hinged at its both ends. Calculate the crippling load if Young's Modulus for the material is $200\text{ GPa}$.

Related pages

• MECHANICS OF SOLIDS syllabus
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