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 =2.1×10

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^{5}N/mm^{2}. 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 E

_{steel}=210GPa and E_{copper}=100GPa; α_{steel}= 12×10^{-6}/°C and α_{copper}=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.

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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/mm

^{2}. The maximum hoop stress in the section not to exceed 150N/mm^{2}. 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).

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10 M

6(a)
Define i) Shear force

ii) Bending momment and iii) Point of contra flexure.

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.

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!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/mm

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^{2}and that in compression is 45N/mm^{2}. 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 = 17.5×10

^{3}N/mm^{2}.
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/mm

^{2}.
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/mm

ii) Maximum shear stress theory. Take FOS=3 and μ =0.25.

^{2}; E = 200GN/mm^{2}. Estimate the least dia required using i) Maximum principal stress theoryii) Maximum shear stress theory. Take FOS=3 and μ =0.25.

12 M

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