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VTU Civil Engineering (Semester 3)
Strength of Materials
December 2016
Total marks: --
Total time: --
INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary

Solve any one questions Q.1(a,b) and Q,2(a,b)
1(a) Name and define the four elastic constants.
6 M
1(b) Deternine the value of "P" and the total deformation of the stepped bar. Take E =2.1×105N/mm2. Refer fig.Q1(b).
!mage
10 M

2(a) Derive the relationship between Young's modulus and bulk modulus.
6 M
2(b) A steel bar is placed between two copper bars, each having same area and length as the steel bar. These are rigidly connected together at a temperature of 25°C. When the temperature is raised to 325°C, the length of the bar is increased by 1.5mm. Compute the original length and final stresses in each bar. Take Esteel=210GPa and Ecopper=100GPa; αsteel = 12×10-6/°C and αcopper=17.5×10-6/°C.
10 M

Solve any one questions Q.3(a,b) and Q,4(a,b)
3(a) Explain the procedure to construct Mohr's circle and to find principal stresses and their planes.
4 M
3(b) The stresses acting at a point in a two dimensional stress system is as shown in fig.Q3(b). Determine: i) Principal stresses
ii) Normal and tangential stress on the plane AB
iii) Maximum shear stress.
!mage
12 M

4(a) Derive an expression for hoop stress in thin cylinder.
4 M
4(b) Find the thickness of the metal necessary for a steel cylindrical shell of internal dia 150 mm to with stand an internal pressure of 50N/mm2. The maximum hoop stress in the section not to exceed 150N/mm2. If the thickness is found using the cylinder analysis, what is the percentage error?
12 M

Solve any one questions Q.5(a,b) and Q,6(a,b)
5(a) Derive the relationship betweeen intensity of load, shear force and bending moment.
6 M
5(b) Draw shear force and bending moment diagrams for the beam shown in figQ5(b).
!mage
10 M

6(a) Define i) Shear force
ii) Bending momment and iii) Point of contra flexure.
3 M
6(b) For the beam AC shown in fig.Q6(b) determine the magnitude of the load 'P' acting at C. Such that the reaction at supports A and B are equal. Also draw SF and BM diagrams, locate the point of contra flexure if any.
!mage
13 M

Solve any one questions Q.7(a,b) and Q,8(a,b,c)
7(a) What are the assumptions is bending theory?
4 M
7(b) A beam simply supported at end having cross section as shown in fig.Q7(b) is loaded with a udl over a spn of 8mm. The allowable bending stress in tension is 30N/mm2 and that in compression is 45N/mm2. Determine the maximum value of udl, the beam can carry.
!mage
12 M

8(a) Differentiate between short and long columns.
4 M
8(b) What are the limitations of Euler's theory?
4 M
8(c) A column 6m long has both of its ends fixed and has a timber section of 150mm×200mm. Determine the crippling load on the column. Take E = 17.5×103N/mm2.
8 M

9(a) Derive the torsion equation with usual notations.
8 M
9(b) A hollow shaff of external dia 120mm transmits 300KW power at 200rpm. Determine the maximum internal dia. If the maximum shear stress in the shaft is not to exceed 60N/mm2.
8 M

10(a) Explain Maximum Principal Stress theory.
4 M
10(b) A solid circular shaft is subjected to bending moment 0f 9000N-m and a twisting moment of 12000N-m. In a simple uniaxial tensile test of the same material, it gave the following particulars: Stress at yield point= 300N/mm2; E = 200GN/mm2. Estimate the least dia required using i) Maximum principal stress theory
ii) Maximum shear stress theory. Take FOS=3 and μ =0.25.
12 M

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