## Mid Examination Essay

Leading University, Sylhet Dept. of Civil Engineering Midterm Examination-2011 2nd year 2nd semester, Course No: CE 213; Course Title: Solid Mechanics II Total marks: 30, Time: 1 hours and 30 minutes Answer any three from the following questions Q1. (a) Define crippling load. Derive the formula of crippling load for one end fixed and other end hinged column. 5 (b) A compound shaft consisting of a steel segment and an aluminum segment is acted upon by two torques as shown in figure 1.

What is the total angle of twist at the free end, if maximum shear stress in the shaft is limited to 83 Mpa for steel and 55 Mpa for aluminum? Assume the modulus of rigidity to be 83×1000 N/mm2 for steel and 28×1000 N/mm2 for aluminum. 5 Q2. (a) What is effective length of a column and slenderness ratio? What are the differences between strut and column? 4 (b) A 50mm by 100mm timber is used as a column with fixed ends. Determine the minimum length at which Euler’s formula can be used if E = 10 Gpa and the proportional limit is 30 Mpa.

What central load can be carried with a factor of safety of 2 if the length is 2. 5 m? 6 Q3. (a) What are the limitation of Euler’s formula. Prove that hoop stress is twice time greater than longitudinal stress for cylinder. 5 (b) A pipe of internal diameter 150mm & 4mm thickness made of mild steel loading a tensile yield stress at 380 N/mm2. Determine the maximum permissible internal pressure if factor of safety is 4. 5 Q4. (a) A closely coiled helical spring has absorbed 50 N-m of energy when compressed 40mm. The coil diameter is eight times the wire dia.

If there are ten coils and modulus of rigidity is 0. 86x105N/mm2, determine i)Diameter of coil ii)Diameter of wire iii)Maximum shear. 5 (b) What is stiffness of spring? Derive the equation of stiffness of spring. 5 Q5. (a) Define shaft. Show that the hollow circular shaft whose inner diameter is half the outer diameter has a torsional strength equal to 15/16 of that of a solid of the same outside diameter. 5 (b) A solid steel shaft 5m long is stressed at 80Mpa when twisted through 40. Using C = 83 Gpa, compute the shaft diameter. What power can be transmitted by the shaft at 20 Hz? 5