1.a. Draw stress versus strain curve for mild steel specimen subjected to axial tension indicating the salient points

1.b. Derive the expression for elongation of tapering circular bar due an axial load P. Use standard notation.

1.c. A circular bar of uniform cross sectional area of 1000 mm² is subjected to forces as shown in the figure. If Young's Module for the material is 200 GPa, determine the total deformation

2.a. Define the four Elastic constants.

2.b. A compound bar consists of a steel rod of 20 mm diameter rigidly fitted into a copper tube of 20 mm internal diameter and 5 mm thickness. Determine the stresses induced in the different materials wen the compound bar is subjected to an axial tensile load of 50 kN. Take Es = 200 GPa and Ec = 120 GPa.

2.c. A steel bar is 20 m long at a temperature of 20$^\circ$C . Find the free expansion of the rod , if the temperature is raised to 65$^\circ$ C . Take E = 200GPa, $\alpha$ = 12X 10^-6/$^\circ$C. FInd the thermal stress produced when

i) free expansion of the rod is conpletely prevented

ii)the rod is permitted to expand by 5.8mm only

3.a. Show that the shear stress on the principal plane is zero

3.b. At a point in a strained material the stresses acting are as shown in the figure. Determine the

i)Principal stresses and their planes

ii) maximum shear stresses and their planes

iii) Normal and shear stresses on the inclined plane AB

4.a. Derive Lame's equations for radial and hoop stresses for thick cylinder subjected to internal and external fluid pressures.

4.b. A closed cylindrical steel vessel of 4 mm plate thickness with plane ends carries fluid under a pressure of 3 MPa. The diameter of cylinder is 25 cm and length is 75 cm. Calculate the longitudinal and hoop stresses in the cylinder wall. Also determine the change in diameter, length and volume of cylinder. Take E = 210GPa , $\micro$ = 0.286

5.a. Derive the relationships between load intensity, shear force and bending moment.

5.b. For a simply supported beam subjected to a UDL of intensity W/unit length throughout plot the SFD and BMD and prove that maximum Bending moment is $\frac{Wt^2}{8}$

6.a. For the cantilever beam shown in figure, plot the SFD and BMD

6.b. For the overhanging beam shown in figure , plot the SFD and BMD. Locate points of contra flexure if any.

7.a. List the assumptions in theory of Simple bending.

7.b. Define

i) Section modulus.

ii) Modulus of rupture.

iii) Moment in resistance

7.c. A T-beam with a flange of 100 mm X 20 mm and with a web of 200 mm x 100 mm is used as a simply supported beam over a span of 8 m. It carries a UDL of 1.5 kN/m throughout. Determine the maximum compressive and maximum tensile stresses and plot the variation across the depth of the beam.

8.a. Derive the Euler's equation for buckling load on an elastic column with both ends pinned or hinged.

8.b. A hollow rectangular cast iron column has external dimensions of 150 mm x 200 mm and all round metal thickness of 25 mm . the column is 5 m long with both ends fixed. if E for column material is 120 GPA , compute the critical value of load on this column by Euler's formula. Compare the value of load obtained by Rankine's formula . Take f_e = 500 MPa and $\alpha$ = $\frac{1}{1600}$ /div> (10 marks) 00