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SPPU 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 question fromQ.1(a,b) and Q.2(a,b)
1(a) A steel bar of variable section is subjected to forces as shown Fig.1. Taking EI= 205 kPa, determine the total elongation:
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6 M
1(b) A laminated wooden beam 120 mm wide and 180 mm deep is made of three 120mm× 60mm planks guled together to resist longitudinal shear. The beam is simply supported over a span of 2.5 m. If the allowable shearing stress in the glued joint is 0.5 MPa, find the safe udl the beam can carry.
6 M

2(a) Determine the values of stresses in portion AB and BC of the steel bar shown in figure 2, at the temperature -45°C of the bar, knowing that a close fit exists at both the rigid supports, when the temperature is +24&de;C Take E = 200 GPa and α =11.7×10-6/°C for steel.
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6 M
2(b)(i) What are the assumptions in the theory of pure bending?
4 M
2(b)(ii) A steel wire of 10 mm diameter is bent into a circular arc of 20 m eadius. Determine the maximum stress induced in it. Take Young's modulus for steel 200 Gpa.
2 M

Solve any one question fromQ3(a,b) and Q.4(a,b)
3(a) A hollow circular shaft of 6m length and inner and other diameters of 75 mm and 100 mm respectively is subjected to torque of 10kN-m. If G = 80 GPa, determine the maximum shear produced and the total angle of twist.
6 M
3(b) A plane element in a body is subjected toa tensile stress of 100 MPa accompanied by shear stress of 25 Mpa. Find:
i) Normal and shear stress on a plane inclined at 20° with tensile stress.
ii) The maximum shear stress on the plane.
6 M

4(a) A steel, rod 40 mm diameter and 5m in length is suddenly subjected on an axial pull 50 kN. Determine:
i) Take work done and
ii) Maximum and instantaneous elongation. Take E = 200 Gpa.
6 M
4(b) A solid shaft 100 mm indiameter is subjected simutaneously to an axial compressive force of 600 kN and to the torque the twist the shaft through an angle of 1.5° in a length of 8m. If modulus of rigidity G =80 Gpa, determine the principal stress and maximum shear in the shaft.
6 M

Solve any one question fromQ5(a,b) and Q.6(a,b)
5(a) A simply supported beam loaded and supported as shown in figure.3. Plot SFD and BMD for the beam.
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6 M
5(b) The BMD of a beam of span 12m is as shown in figure 4. Construct loading diagram from BMD.
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6 M

6(a) Draw SFD and BMD for a beam shown in figure 5.
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6 M
6(b) A simply supported beam 8 m long carries three point loads at 100 kN, 150kN, and 200kN at 2m, 5m and 7m from left roller support. The self weight of thebeam is 25kN/m. The right end support is hinged. Draw S.F. and B.M. diagram for the beam.
7 M

Solve any one question fromQ.7(a,b) and Q.8(a,b)
7(a) If the limit of proportionally of steel is 250 MPa and modulus of elasticity 200 Gpa. Determine the slenderness ratio at which the Euler's formula fora fixed ended column can be used.
6 M
7(b) A rectangular strut 150mm × 120 mm thick. It carries a load of 180 kN at an eccentricity of 10 mm in a plane bisecting the thickness. Find the maximum and minimum intensity of stress in the section. Also find permissible eccentricity for no tension condition.
7 M

8(a) Calculate the critical load for a strut which is made up of a bar circular in section, 1.2 long and which is hinged at one end and fixed at the other end. The same bar when freely supported at its ends gives the central deflecion of 3 mm, when a load of 100 N is placed at its centre. Also find the safe load taking factor of safety equal to 3.
7 M
8(b) Explain core of a section. Hence obtain core of section for reactangular column of size 120 mm × 120 mm.
6 M

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