Envlmnt No.
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER- III EXAMINATION - SUMMER 2020
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Subject Code: 3130608 Date:04/11/2020
Subject Name: Mechanics of Solids
Time: 02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
- Attempt all questions.
- Make suitable assumptions wherever necessary.
- Figures to the right indicate full marks.
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| Marks | |
| Q.1 (a) State’s Law of Parallelogram of forces. | 03 |
| (b) Define force and writes its characteristics. | 04 |
| (c) Find the magnitude and direction of resultant of force system shown in fig. 01. | 07 |
| Q.2 (a) What is meant by free body diagram? Draw free body diagram for box place on a table. | 03 |
| (b) Define : (1) Isotropic material (2) Anisotropic material (3) Homogeneous material (4) Orthotropic material. | 04 |
| (c) Find the minimum (least) value of force P to keep the sphere in the position shown in fig. 02. The radius of sphere 1 is 5cm and sphere 2 is 10cm. The weight of sphere 1 is 100N and sphere 2 is 200N. | 07 |
| OR | |
| (c) Draw shear force diagram and bending moment diagram for a beam shown in fig. 03. | 07 |
| Q.3 (a) What is difference between deficient truss and redundant truss. | 03 |
| (b) Explain types of supports with usual notations. | 04 |
| (c) Find the CG of plane lamina shown in fig 4. | 07 |
| OR | |
| Q.3 (a) Explain : (1) Poisson’s ratio (2) Hook’s law (3) Bulk modulus. | 03 |
| (b) A bar of 3m long and 20mm diameter is rigidly fixed in two supports at certain temperature. If temperature is raised by 60° C, find the thermal stress and strain of the bar. Also find thermal stress and strain if support yields by 2 mm. Take a=12x10-6/°C and E = 2x105 N/mm². | 04 |
| (c) State and explain with figure Pappu’s —Guildinus theorem of surface area of Revolution. | 07 |
| Q.4 (a) Enlist the assumptions made in theory of torsion. | 03 |
| (b) A beam simple supported and carries an U.D.L. of 50 kN/m over whole span. The size of beam is 150mm x 400mm. If maximum stress in the material of beam is 100N/mm² find the span of beam. | 04 |
| (c) Determine the centroid of the section shown in fig. 05. | 07 |
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| Q.5 (a) A tensile load of 40 kN is acting on a rod of 30mm diameter and a pull of 80 kN is transmitted through a steel wire. Find the minimum diameter of the wire, if the stress is not to be exceed 80 N/mm². | 04 |
| (b) Explain types of beams with notations. | 07 |
| (c) Determine moments of inertia of a section shown in fig. 06 about horizontal centroidal axis. | 03 |
| Q.5 (a) Define: (1) Shear Force (2) Bending Moment (3) Points of contraflexure | 04 |
| (b) Derive the relation between : (1) Young’s Modulus (2) Modulus of Rigidity (3) Possion’s Ratio | 07 |
| (c) A hollow steel shaft, 3m of length must transmit a torque of 25 kNm. The total angle of twist in this length is not to exceed 2.5° and the allowable shearing stress in the material is 90 MPa. Calculate the inside diameter of the shaft and thickness of the metal. G = 85 GN/m². | 03 |
| OR | |
| (a) Draw shear stress distribution diagram for : (1) I section (2) Circular section (3) Triangular section | 04 |
| (b) Explain assumptions made in theory of pure bending. | 07 |
| (c) A square prism of metal 60mm x 60mm in cross section and 300mm long is subjected to a tensile stress of 450 MPa along its longitudinal axis, lateral compression of 240 MPa and lateral tension of 120 MPa along the pair of sides. If E = 150 GPa, calculate the changes in dimensions, change in volume of metal. µ=0.36. | 07 |
100N
130N
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Smooth surface
Fig. o1 Fig. 02
50 kN 50kN
50 kN[ T L
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A B ¢
Fl's . 03 p
20cm 20cm™m
200mm —__——_1 Iu(m
Cixculay Hole Z 5
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25mm wadius 0T e I
430m.
| 20m
b zoomm——,tc ' e ep
20
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Fiq. 05 Fig. 06
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