1.a. Determine the maximum weight W that can be supported by two wires as show in fig. if the stress in each wire is not to exceed 120 $\mathrm{N} / \mathrm{mm}^{2}$

1.b. A cantilever beam of solid circular section and 3 m long carries a concentrated load of 25kN an its free end. If the max bending stress in tension and compression are not to exceed 100 $\mathrm{N} / \mathrm{mm}^{2}$ and 60 $\mathrm{N} / \mathrm{mm}^{2}$. calculate the diameter of the beam required.

1.c. A 230 mm x 350 mm simply supported beam carries a UDL of 20 kN/M over a span of 8 M. Determine the maximum shear stress at a section 2 m from the support.

1.d. A rectangular column of 230 mm x 350 mm and and 4 M lomg used as a column. If one end is hinged and other is fixed , find the safe load the column can carry FOS-2.5. use Euler's formula.

1.e. Derive the expression for strain energy due to gradually applied axis load.

2.a. An unknown weight falls through 15 mm on a collar rigidly attached at the lower end of the bar 4 m long and 800 $ m^{2} $ in area. If the maximum instantaneous elongation is 3 mm, find the corresponding stress and the value of unknown weight. Take E = 210k$\mathrm{N} / \mathrm{mm}^{2}$.

2.b. A circular rod ABC is subjected to axial compressive load of 50 kN. The part AB is hollow circular. With outer diameter of 25 mm and inner diameter of 10 mm and length of 200 mm. The part BC is solid circular with diameter of 25 mm and length of 300 mm. Calculate total decrease in length of the bar. Take E= 210k$\mathrm{N} / \mathrm{mm}^{2}$.

2.c. Draw the shear force and bending moment diagram for the beam loaded as shown in fig.

3.a. Explain with the help of neat sketch concept of equivalent section use in flitched beam.

3.b. A hollow circular column of 2.8 m long is fixed at one end and free at the other end, has to support a load of 500 kN. The internal diameter is 0.8 times external diameter . Calculate the external diameter with FOS =4. Take $\sigma c=330 \mathrm{N} / \mathrm{mm}^{2} \quad \mathrm{a'}=1 / 7500$

3.c. A inverted T beam having web 20 mm x 100 mm and flange 120 mm x 20 mm, has a span of 5m and is simply supported at ends. Find the maximum load the beam can carry if the compressive and tensile stress not to exceed 60k$\mathrm{N} / \mathrm{mm}^{2}$ and 75k$\mathrm{N} / \mathrm{mm}^{2}$.

4.a. A flitched beam consist of wooden joist 150 mm wide and 300 mm deep strengthen by steel plate of 10 mm thick at bottom. Find the moment of resistance by using transformed area concept . permissible stress in wooden joist is 8 $\mathrm{N} / \mathrm{mm}^{2}$. Take Es = 15Ew

4.b. A beam of square section of size 200 mm x 200 mm is placed with one of it's diagonal horizontal and it carries a shear force of 80 kN. Draw the shear stress distribution diagram.

4.c. Derive the relation between SF, BM and rate of loading W

5.a. A cylindrical shell is 3 m long and 1.2 m in diameter and 12 mm thick is subjected to internal pressure of 1.8k$\mathrm{N} / \mathrm{mm}^{2}$ calculate change in dimension of shell. Take E = 210k$\mathrm{N} / \mathrm{mm}^{2}$ 1/m = 0.3

5.b. At a point in strained material the stresses on two mutually perpendicular plane are 120k$\mathrm{N} / \mathrm{mm}^{2}$ and 80k$\mathrm{N} / \mathrm{mm}^{2}$ both are tensile. Find the normal, tangential and resultant stress at a plane inclined to the major principle plane.

5.c. Determine the area of core section for rectangular section of size 230 mm x 350 mm.

6.a. A hollow circular steel shaft of 5 m length has to transmit 150 KW power at 120 rpm. If internal diameter is 0.6 times external diameter , total angle of twist not to exceed and shear stress is limited to 50 $\mathrm{N} / \mathrm{mm}^{2}$. Determine the diameter of shaft. Take G = 84k$\mathrm{N} / \mathrm{mm}^{2}$.

6.b. In the rectangular section 400 mm wide and 300 mm deep is subjected to compressive load of 80 kN at an eccentricity of 40 mm and 75 mm from centroidal xx and yy axis. Find stress at each corner.

6.c. A rod of 300 mm long and 20 mm in diameter is heated through $100^{\circ} \mathrm{C}$ and at the same time pulled by force P. If the total elongation is 0.4 mm. What is the magnitude of P take E = 210k$\mathrm{N} / \mathrm{mm}^{2}$ and $\alpha=12 \times 10^{-6}$