Part - 1

1.a. What do you mean by principle of super position?

1.b. Define different modulii.

1.c. Define Bending Moment and B. M. D.

1.d. Explain with neat sketches different types of beams.

1.e. Define shear stress and write the formulae for calculating this stress.

1.f. Write the assumptions in simple bending theory.

1.g. State "Rankin's theorem of failure".

1.h. Write the limitations of maximum shear stress theory.

1.i. Define moment area theorem II.

1.j. What is Macaulay's method and how this is different from double integration method of calculating slope and deflections in a beam.

Part - B

2.a. Draw stress - strain diagram for mild steel, brittle material and a ductile material and indicate salient points.

2.b. A circular ally bar 3 m log uniformly tapers from 40mm diameter to 25mm diameter. Calculate the elongation of the rod under the axial force of 75kN. Take E=140GPa.

3 Define Resilience and derive the equation of stresses for a body subjected to sudden and impact loading.

4 Draw S.F.D and B.M.D for the cantilever beam shown in figure 1.

5 Draw S.F.D and B.M.D for the Over hanging beam shown in figure 2.

6 A simply supported beam of span 8 m carries a udl of 15 kN/m over the entire span. If the maximum allowable stress due to bending is restricted to 175 $\mathrm{N} / \mathrm{mm}^{2}$, determine the cross sectional dimensions if the section is: a) Rectangular with depth twice the breadth. b) Hollow circular section having a diameter ratio of 0.7.

7.a. Prove that for a rectangular section maximum shear stress is 1.5 times of average stress.

7.b. Prove that for a Circular section maximum shear stress is 1.33 times of average stress.

8 A rectangular block of material is subjected to a tensile stress of 120 $\mathrm{N} / \mathrm{mm}^{2}$ on one plane and a tensile of 45 $\mathrm{N} / \mathrm{mm}^{2}$ on a plane at right angles to the former. Each of the above stresss is accompanies by shear stress of 60 $\mathrm{N} / \mathrm{mm}^{2}$. Determine the principal stresses, principal planes and the maximum shear stresses.

9 A Solid shaft is subjected to torque of 30 kN m and bending moment of 15 kN m. If the allowable stress is 164 Mpa, find the diameter of the shaft using: a) Maximum stress thory b) Maximum shear stress theory, Poisson's ratio is 0.3.

10.a. Derive the formulae used to find the slope and deflection of a beam by Moment Area method.

10.b. Using Moment area theorems find the values of slope and deflection for a cantilever beam of length 'L' subjected to Moment 'M' at the free end?

11 A cantilever of length '4a' is carrying a load of W at the free end, and another load of W at its center. Calculate the slope and deflection of the cantilever at the free end, using conjugated beam method.