Amos Qp2.docx

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MES INSTITUTE OF TECHNOLOGY & MANAGEMENT, CHATHANNOOR SECOND SERIES EXAMINATION, APRIL 2019 ME202 ADVANCED MECHANICS OF SOLIDS

Time: 2 Hrs Max Marks: 40

ME-4 Answer any two questions

1. a. Define Euler-Bernoulli hypothesis. What are the conditions for the validity of this assumption? 4marks

b. Define unsymmetrical bending of beams. Discuss the situations in which beams are subjected to unsymmetrical bending. 4marks c. Derive the following equation for flexure stress of an unsymmetrical cross section subjected to an arbitrary bending moment in the y-z plane. 12marks σxx =

MY (Z IZ −Y IYZ )− MZ (YIY −ZIYZ ) IZ IY − I2YZ

2. a. Define shear center. Explain the significance of shear centre in problems of bending of beams. 5marks 5marks

b. Describe the method of finding shear centre of thin walled open sections. c. Prove that flexure stress on a layer at a distance of y from the neutral axis of a curved beam is σxx = -

y r0

MZ

( −y A(ρ

0

)

− r0 )

10marks

3. a. Sketch the circumferential stress distribution for a thick cylinder subjected to internal pressure only. Write the expression for σr, σθ, σθmax. 5marks b. State and prove reciprocal relation in strain energy. And explain its application with an example. 5marks

c. Obtain the stress distribution in a rotating solid disc of radius ‘b’ with no external forces at the outer surface. 10marks 4. a. Write down the general bi-harmonic equation of stress compatibility in polar coordinate system. 4marks 4marks

b. Write down the general equations of radial and tangential stress in a thick cylinder. c. A cantilever beam of angle section is 1m long and is fixed at one end, while it is subjected to a load of 3kN at the free end at 200 to the vertical. Calculate the bending stress at A, B and C and also the position of the neutral axis. 12marks

Scheme of valuation

1. a. Euler-Bernoulli hypothesis,assumption 2+2 marks b. Define unsymmetrical bending of beams. Discuss the situations of unsymmetrical bending. 2+2 marks c. Derive the equation for flexure stress of an unsymmetrical cross section subjected to an arbitrary bending moment in the y-z plane 12 marks 2.

a. Define shear center. Explain the significance of shear centre in beams 3+2 marks

b. Explain method of finding shear centre of thin walled open sections. 5 marks c. Derive expression for flexure stress of a curved beam 10 marks 3.

a. Sketch the circumferential stress distribution for a thick cylinder subjected to internal pressure only. Write the expression for σr, σθ, σθmax. 2+ 3 marks b. State reciprocal theorem and its application 3+2 marks c. Derive stress distribution in a rotating solid disc with no external forces at the outer surface 10 marks

4.

a. Write down bi-harmonic equation of stress compatibility in polar coordinate system 4 marks b. Write down equations of radial and tangential stress in a thick cylinder. 2+2marks c. Calculate the bending stress at A, B and C and also the position of the neutral axis. 4+4+4 marks

Prepared by

Academic Coordinator

HOD