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Strength of Materials Question Paper - Jun 17 - Civil Engineering (Semester 3) - Visveswaraya Technological University (VTU)
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Strength of Materials - Jun 17
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.
Define
(6 marks)
00
i) Poison's ratio
ii) volumetric strain
iii) Temperature stresses
1.b.
A steel bar of 20 mm diameter is subjected to tensile load test. Determine stress, strain, Young's modulus, % elongation from the following data:
(10 marks)
00
Gauge length = 200mm, Extension at a load of 100 kN = 0.147 mm, Total elongation 50 mm. Also determine the % decrease in cross sectional area of the specimen if the diameter of the rod at failure is 16 mm.
OR
2.a.
Derive the relationship between Young's modulus and shear modulus with usual notation.
(6 marks)
00
2.b.
A steel tube 45 mm external diameter and 3 mm thick encloses centrally at a solid copper bar 30 mm diameter. The bar and the tube are rigidly connected together at their ends at a temperature of 30$^\circ$ . Find the stresses developed in each material when heated to 180$^\circ$ .
(10 marks)
00
Take ES = 200 GPa, as = 10.8 X 10-6/$^\circ$C ; EC = 110GPa, ac = 17 X10-6/$^\circ$C
3.a.
Derive Lami's equation for thick cylinders
(6 marks)
00
3.b.
The state of stress at a point in a strained material is as shown in the Fig Q3(b)
(10 marks)
00
Determine :
i) Principal stresses and principal planes
ii)Max shear stress and its plane
iii)Sketch the stress diagram showing stresses and planes
OR
4.a.
Derive expressions for normal stress and tangential stress for a number subject to uni axial loading
(6 marks)
00
4.b.
A shell 3.25 m long, 1 m diameter is subjected to internal fluid pressure of 1 MPa. If the thickness of the shelf is 10 mm . ind Hoop stress, longitudinal stress , max shear stress and change in diameter and length. Take E = 2X 105 MPa, $\frac{1}{m}$ =0.3.
(10 marks)
00
5.a.
Derive the relationship between load intensity, shear force and bending moment.
(6 marks)
00
5.b.
A simply supported beam is subject to a point load of 15 kN together with udl of 15kN/m applied as shown in fig Q5(b). Draw SFD and BMD. Find also point of zero and its corresponding BM
(10 marks)
00
OR
6.a.
Show that max BM for a simple supported beam of length l carrying udl of intensity W/unit length is $\frac{Wl \ltsup\gt2\lt/sup\gt}{8}$
(6 marks)
00
6.b.
Draw SFD and BMD for the load diagram, shown in Fig Q6(b). . Mark the values of salient points.
(10 marks)
00
7.a.
Derive the bending equation , $\frac{M}{l}$ = $\frac{f}{y}$ = $\frac{E}{R}$ with usual notation
(6 marks)
00
7.b.
A hallow tube of 6 m length with external diameter 6o mm and thickness 10 mm is subject to minimum crippling load. Find Euler's critical load for this column :
(10 marks)
00
i) When both ends are fixed
ii) When one end fixed other end hinged. Assume E = 200GPa.
OR
8.a.
Derive expression for crippling load for a long column when both ends are hinged
(6 marks)
00
8.b.
A circular pipe of external diameter 70 mm and thickness 8 mm is used as a simply supported beam over an effective span of 2.5 m.Find the max concentrated load that can be applied at the centre of the span if permissible stress in the tube is 150 N/mm2
(10 marks)
00
9.a.
Derive the torque equation $\frac{T}{l}$ = $\frac{f}{R}$ = $\frac{C}{l}$ with usual notation
(6 marks)
00
9.b.
State the theories of failures . Explain briefly any two of the theories.
(10 marks)
00
OR
10.a.
State the assumption made in the theory of pure tension.
(6 marks)
00
10.b.
A hallow tube shaft has to transmit 600kW power at 80 rpm. The maximum torque developed may exceed the mean torque by 40%. Design a suitable section if the working stress is 90 MPa. Take diameter ratio as 0.8. What will be the angular twist measured over a length of 2m if C = 84 GPa?
(10 marks)
00
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