1. (b) Draw SFD and MID for a simply supported beam given in figure 2 with a given set of loads. Mark the point of maximum bending moment points

2. (a) Derive the equation of theory of simple bending M/I = f/y = E/R.

Or

(b) (i) What is section Modulus? How it is related to the flexural strength of a section?

     (ii) Prove that in case of rectangular section, maximum shear is 1.5times the average shear stress.

3. (a) Using double Integration method, solve for slope and deflection of a cantilever with a concentrated load at free end.

Or

(b) A cantilever of uniform section 6m long carries a load of 2kN at the free end and 3kN at 3m from the fixed end. Determine the maximum deflection of the cantilever at the free end by Macaulay's method. Take σ_E = 200 GN/m² and I = 300 x10⁵ mm⁴.

4. (a) Deduce and expression for the crippling load for a column by Euler's theory.

Or

(b) Determine the section of a cast iron hollow cylindrical column 5m long with ends firmly built-in if it carries an axial load of 30 kN.The ratio of internal diameter to external diameter is 3/4,Use factor of safety of 3. Take σ_E = 550 and a = 1/1600.

5. (a) (i) How will you determine the degree of indeterminacy for various beams. Explain with proper examples. Also refer the methods to solve the problems.

(ii) Explain the concept of analysis of a portal frames with number of indeterminacy.

Or

(b) A load of 150N produced a deflection of 15mm when placed at the center of the bar of length 3m. Determine the Euler's buckling load that the same bar can support if used as a column with both ends restrained in position but not in direction.