What is point of counterculture? In which beam will it occur? 4. Derive the relation teens the intensity of load and shear force, in bending theory. 5. Draw the shear stress distribution diagram for an ‘section. 6. Derive an expression for the power transmitted by a circular shaft in S. I. Units, which is subjected to a torque T in N m. 7. Distinguish between close coil and open coil helical springs. 8. Derive an expression for the longitudinal stress in a thin cylinder subjected to an uniform internal fluid pressure. 9.
What is the normal stress on an inclined plane in a block when it is subjected to two mutually perpendicular normal stresses and shear stress? 10. State the condition for the use of Macaulay’s method. Art-B (5 X 16 = 80 Marks) 1 1 . (a) A bar of mm diameter and mm long is subjected to an axial pull of ink . The extension of the bar is found to be 0. 1 mm, while decrease in the diameter is found to be 0. Mm. Find the Young modulus, Poisons ratio, (OR) (b) An aluminum rod of 22 mm diameter passes through a steel tube of 25 mm internal diameter and mm thick.
The rod and tube are fixed together at the ends at a temperature of 300 C. Find the stresses in the rod and tube when the temperature is raised to 1500 C. SEES = skewering , Al = INK,t-NRC as = 12 x 10-610 C. 12. (a) Draw the SF and BMW diagram for the beam shown in Fig 1. Find the values at important points and indicate in the diagram. (b) Draw the SF and BMW diagrams for the beam shown in Fig. 2. Find the maximum values and their position. Give the values at important points in the diagram. Figure 2: 13. A) A simply supported beam of uniform flexural rigidity El and span l, carries two symmetrically placed loads P at nonwhite of the span from each end. Find the slope at the supports and the deflection at midshipman. Use moment area theorems. (OR) (b) A simply supported beam of span l, carries an LID of w/unit length from the left hand support Upton the centre of the beam. Find the midshipman deflection by strain energy method. 14. (a) A helical spring of circular cross section wire 18 mm in diameter is loaded by a force of NON .
The mean coil diameter of the spring is mm. The modulus of rigidity is INK/mm . Determine the maximum shear stress in the material of the spring. What number of coils must the spring have for its deflection to be mm? (OR) (b) A hollow shaft is to transmit skew at RPM. The internal diameter is 0. 6 of the external diameter. The maximum torque is 40% more than the mean torque. If the shear stress is not to exceed NON/mm , find the external and internal diameters of he shaft. 15. (a) A thin cylinder 1. M internal diameter and mm long is subjected to an internal pressure of AN/mm . If the maximum stress is limited to NON/mm , find the thickness of the cylinder. E = knee/mm and Poison’s ratio = 0. 3. Also find the changes in diameter, length and volume of the cylinder. (b) At a point in a strained material the horizontal tensile stress is NON/mm and the vertical compressive stress is NON/mm . The shear stress is NON/mm . Find the principal stresses and the principal planes. Find also the maximum shear stress and its planes. 2