CE 236 — STRENGTH OF MATERIALS

PART A — (10 ? 2 = 20 marks)
1. State the principle of virtual work.
2. State the Maxwell reciprocal theorem.
3. Define degree of static indeterminacy of a structure.
4. Write the three moment equation, stating all the variables used.
5. What is the middle third rule?
6. What are the assumptions in Euler's theory of columns?
7. Differentiate between spherical and deviatoric components of stress tensor.
8. What is meant by volumetric strain?
9. Define shear centre.
10. What is meant by fatigue failure?
PART B — (5 ? 16 = 80 marks)
11. Using the theorem of three moments draw the shear force and bending moment diagrams for the following continuous beam.

12. (a) Using unit load method, find the vertical deflection of joint F and horizontal deflection of joint D of the following truss. Axial rigidity AE is constant for all members.

Or
(b) (i) A simply supported beam of length 10 m is subjected to a udl.
10 kN/m over the left half of the span and a concentrated load 4 kN, 2.5 m from the right support. Find bending strain energy. Flexural rigidity is uniform and equal to EI.
(ii) State the Engesser's theorem and Castigliano's theorem.
13. (a) Using Euler's theory, find the buckling load for the columns with following boundary conditions :
(i) Fixed-free (ii) Fixed-hinged.
Or
(b) A column with one end hinged and the other end fixed has a length of
5 m and a hollow circular cross section of outer diameter 100 mm and wall thickness 10 mm. If = 1.60 ? 105 N/mm2 and crushing strength N/mm2, find the load that the column may carry with a factor of safety of 2.5 according to Euler theory and Rankine-Gordon theory. If the column is hinged on both ends, find the safe load according to the two theories.
14. (a) Determine the principal stresses and principal directions for the following 3D-stress field.
MPa.
Or
(b) Discuss the following theories of failure for metals with suitable derivations :
(i) Maximum shear stress theory of failure
(ii) Maximum distortion energy theory of failure.
15. (a) A semicircular bar of circular cross section with radius 20 mm is fixed at one end and loaded at the other end as shown in the figure. Find the stresses at points A and B.

Or
(b) A cylinder of outer diameter 280 mm and inner diameter 240 mm shrunk over another cylinder of outer diameter slightly more than 240 mm and inner diameter 200 mm to form a compound cylinder. The shrink fit pressure is 10 N/mm2. If an internal pressure of 50 N/mm2 is applied to the compound cylinder, find the final stresses across the thickness. Draw sketches showing their variations.