NATIONAL INSTITUTE OF TECHNOLOGY, ROURKELA - 769 008

Mid Semester Examination

B. Tech. 7th Semester (AUTUMN), SEPT - 2012Subject: ADVANCED MECHANICS OF SOLIDS (CE-316)Full Marks: 30

Duration of Exam: 2 HoursAnswer any five questions. All questions carry equal marks .This question paper contains 1 page.

1. The state of stress at a point is characterized by the matrix shown below. Determine the principal stresses and the direction cosines of the maximum principal stress axes. Units are in KPa.

2. A solid shaft of diameter shown below is subjected to an axial tensile force P =10kN and a torque T = 50Nm. At point A on the surface determine the principal stresses, the octahedral shearing stress and the maximum shearing stress. Assume shear stress on the cross-section is given by elementary mechanics of solid formula as where is the shear stress at radial distance .

3. Derive the differential equations of equilibrium for a stressed body in terms of the six rectangular stress components at a point and the body forces per unit volume in the x, y and z directions Bx, By and Bz.4. If the displacement field is given by u = kxy, v = kxy and w = 2k ( x +y )z

where k is a constant small enough to ensure applicability of the small deformation theory,

(a) Write down the strain matrix(b) What is the linear strain in the direction with direction cosines l = m = n = ?5. At the critical point in a member, the three principal stresses are nonzero. The yield point stress for the material is y. If two of the principal stresses are equal, say, 2 = 3, show that the factor of safety based on the maximum shear stress criterion is equal to the factor of safety based on the maximum octahedral shear stress criterion.

6. For a two dimensional state of stress, prove the following condition of compatibility:

7. Write briefly about the (a) Maximum shear stress theory (b) Maximum principal strain theory (c) Maximum principal stress theory and (d) Maximum octahedral shear stress theory.****************P

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