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Strength of Materials Question Paper - Jun 18 - Civil Engineering (Semester 3) - Visveswaraya Technological University (VTU)
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Strength of Materials - Jun 18
Civil Engineering (Semester 3)
Total marks: 80
Total time: 3 Hours
INSTRUCTIONS
(1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Draw neat diagrams wherever necessary.
1.a.
For a bar of uniform section derive an expression for elongation due to self weight
(6 marks)
00
1.b.
Evaluate the deformation of the bar given E1 = E2 = 20 GPa. refer figure given below
(10 marks)
00
OR
2.a.
Derive and expression between Young's modulus , Modulus of rigidity and Poison's ratio.
(10 marks)
00
2.b.
A circular rod of diameter 200 mm and 500 mm long is subjected to a tensile force of 45 kN modulus of elasticity = 200 kN / mm2 . Find stress , strain and elongation of bar due to applied load
(6 marks)
00
3.a.
At a certain point in a stressed body, the principal stresses are $\sigma_{x}=80$ MPa and $\sigma_{y}=-40$ MPa . Determine $\sigma \operatorname{and} \tau$ on the planes whose normal's are +30$^\circ$ and +120$^\circ$ with x- axis
(16 marks)
00
OR
4.a.
Derive an expression of tangential stress and longitudinal stress of thin walled pressure vessels.
(8 marks)
00
4.b.
A rectangular block of material is subjected to tensile stress of 100 N/mm2 on one plane and a tensile stress of 50N/mm2 on a plane at right angles together with shear stress of 60N/mm2 on same planes, find:
(8 marks)
00
i) direction of the principal plane
ii)magnitude of the principal plane
iii)magnitude of greatest shear stress.
5.a.
Define
(8 marks)
00
i) bending moment
ii) shear force
iii)shear force diagram
iv) bending moment diagram.
5.b.
Draw SFD an BMD for the cantilever beam shown in figure.
(8 marks)
00
OR
6.a.
Derive the relation between load intensity , bending moment and shear force.
(6 marks)
00
6.b.
A beam ABC, 8 m long has supplied at A and B , it is long between A and B. the beam carries an UDL of 10kN/m between A and B . At th free point C , a point load of 15kN acts. Draw BMD and locate point of contra flexure , if any.
(10 marks)
00
7.a.
Explain pure bending with an suitable example and mention the assumptions of pure bending.
(6 marks)
00
7.b.
A cast iron beam section shown in figure is freely supported on a span of 5 m . If the tensile stress is not to exceed 20N/mm2 . Find the safe UDL, which the beam can carry. Find also the maximum compressive stress
(10 marks)
00
OR
8.a.
Derive an Euler's crippling load when both of the columns are pinned
(8 marks)
00
8.b.
A hollow cylindrical cost iron column is 4m long both ends being fixed. Design the column to carry a axial load of 250 kN. Use Rankine's formula and factor of safety = 5 . the internal diameter may be taken as 0.80 time the external diameter. Take EC = 550 N/mm2 and $\alpha$ = $\frac{1}{1600}$
(8 marks)
00
9.a.
Derive torsional equation for circular shaft.
(8 marks)
00
9.b.
A steel shaft transmits 105 KN at 160 rpm. If the shaft is 100 mm in diameter . Find the torque on the shaft and the maximum sharing stress induced
(8 marks)
00
OR
10.a.
Define pure torsion , polar modulus and torsional rigidity
(6 marks)
00
10.b.
A solid shaft is subjected to a torque of 15 kN-m. Find the necessary diameter of the shaft if the allowable shearing stress is 60 N/mm2 and the allowable twist is 1 degree in a length of 20 diameters of the shaft. take C = 8 x 104 N/mm2
(10 marks)
00
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