POKHARA UNIVERSITY Level: Bachelor Programme: BE Semester - Spring Year 2010 Full Marks : 100 Pass Mark : 45 : 3 hrs Time Course: Strength of Materials Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marh. Attempt all the questions. l. a. Find total, external and internal indeterminacy of the following structure. 2 Internal Hinge 2. b. A spherical vessel of 1.5m internal diameter and 5rrun thick is filled with a fluid under pressure until its volume is increased by 250cm3. Calculate the pressure exerted by the fluid on the vessel. Take E = 210KN/mm2, µ = 0.3. c. Derive Euler's formula for critical load for a column with one end fixed and other end free. Also mention the assumption made while deriving Euler's fonnula. Calculate principal centroidal moment of inertia and its direction for the given section. l--1m--l I l T Im l.. 3m T Im l.. 3m 6 7 15 3. a. Draw shear force diagram, axial force diagram and bending moment diagram of the following plane frame. 9 ·K 2m + 2m I-- 3m •I• 3m -+2m-, b. Draw shear force diagram, axial force diagram and bending moment diagram of the following frame. 6 8kN A j.-2m •+• 4. 20 2m •I• 4m "I a. Find change in length of the given bar (circular) after the application of load as shown in figure. Take E = 220KN/mm2. 7 T lOKN . 10mm 20mm ,_I---'----- 20KN l b. Find stress in each of the given composite bar of length 100mm and hence calculate the final length of the composite section if temperature is decreased by100°1 1-C-. c_;-:-e:-le_r Copper Steel 2 A= 60mm A=40mm2 6 a =ISx10- !°C a =12x10-61°c ---lOOmtn ---------- < E=l 80KN/mm2 E=220KN/mm2 5. a. An infinitely small element consists of forces in two mutually perpendicular plane as shown in figure. Determine the normal and 8 1 2 12 shearing stress on the inclined plane at an angle 30° with the vertical. Also calculate principal stresses their directions and maximum shear stress. 30MPa 30MPa 50MPa ----- i,-+i .---50MPa 30 1Pa b. Verify the above result by constructing Mohr's Circle. 6. a. A simply supponed T - beam having cross section as shown in the figure is 3.5m long. If it carries bending moment of25kN-m, calculate maximum bending stresses intension and in compression. 7. j-2ocm-J b. A hollow circular shaft 10m long is required to transmit 130kW power when running at a speed of 300rpm. If the maximum shearing stress allowed in the shaft is 100N/mm2 and the ratio of inner to the outer diameter is 0.5, find the dimensions of the shaft and also the angle of twist of one end of the shaft relative to the other end. Take G = 80kN/mm2. Write shon notes on any two: a. Relation between elastic constants b. Flexure equation c. Relation between load shear force and bending moment 3 3 8 7