Solid Mechanics (SM) SPPU Endsem Question Paper May 2024

Questions

1. Q1

   1. a)

      A beam of cross section shown in Fig. 1 is bent about horizontal axis. If a bending moment is 12 kN-m determine the stresses at the top fiber and also at 35 mm from top fiber. Draw bending stress distribution diagram.

      [8]
   2. b)

      This part has equations that don’t show as text. Open the PDF to read it.

      [9]
   OR

2. Q2

   1. a)

      Determine the maximum tensile and compressive bending stresses in the beam shown in Fig. 3. Take I = 30×10 6 mm 4

      [8]
   2. b)

      This part has equations that don’t show as text. Open the PDF to read it.

      [9]

3. Q3

   1. a)

      A hollow steel rod 300 mm long is to be used as torsional spring. The ratio of inside to outside diameter is 1:2. The required stiffness of this spring is 200 N-m /degree. Determine the outside diameter of the rod. If value of G is 8×10 4 N/mm 2 .

      [9]
   2. b)

      A rectangular steel bar 40 mm × 50 mm in cross-section, pinned at each end and subjected to axial compression. The bar is 2 m long and E = 200 GPa. Determine the buckling load using Euler’s formula and corresponding stress.

      [9]
   OR

4. Q4

   1. a)

      Determine the diameter of a solid shaft which will transmit 300 kW at 400 rpm. The maximum shear stress should not exceed 40 N/mm 2 and twist should not be more than 10 in a shaft length of 3 m. The modulus of rigidity of the material is 1×10 5 N/mm 2 .

      [9]
   2. b)

      This part has equations that don’t show as text. Open the PDF to read it.

      [9]

5. Q5

   1. a)

      The state of plane stress at a point is represented by the stress element shown in Fig. 5. Determine the stresses acting on an element oriented 30º clockwise with respect to the original element.

      [9]
   2. b)

      A solid shaft is subjected to bending moment of 20 kN-m and twisting moment 10 kN- m. Find the diameter of the shaft according to 1) Maximum distortion energy theory 2) Maximum strain energy theory Take stress at elastic limit = 210 MPa, Poisson’s ratio = 0.3 and Factor of safety = 2.5.

      [9]
   OR

6. Q6

   1. a)

      A point is subjected to a tensile stress of 250 MPa in the horizontal direction and another tensile stress of 150 MPa in the vertical direction. The point is also subjected to a simple shear stress of 30 MPa, such that when it is associated with the major tensile stress, it tends to rotate the element in the clockwise direction. What is the magnitude of the normal and shear stresses inclined on a section at an angle of 20° with the major tensile stress. Use Mohr’s Circle Method.

      [9]
   2. b)

      A bolt is subjected to an axial pull of 10 kN & a transverse shear force of 5 kN. Determine the diameter of the bolt required based on. 1) Maximum distortion energy theory 2) Maximum shear stress theory 3) Maximum principal stress theory Take elastic limit in simple tension = 200 MPa, Poisson’s ratio = 0.2 and Factor of safety = 3. Q. No 5(a), Fig. 5 4

      [9]

7. Q7

   1. a)

      A 100 mm diameter bar with a built in bracket is fixed to the wall and loaded as shown in Fig. 6. Determine the principal stresses at the top extremity of the vertical diameter for the section marked A.

      [8]
   2. b)

      This part has equations that don’t show as text. Open the PDF to read it.

      [9]
   OR

8. Q8

   1. This part has equations that don’t show as text. Open the PDF to read it.

      [17]