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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
BE/PDDC- SEMESTER- 1st 2nd • EXAMINATION WINTER 2018
Subject Code:2910601 Date: 07/01/2019
Subject Name: Mechanics of Solids
Time:10:30 AM to 01:00 PM Total Marks: 70
Instructions:
1. Attempt any five questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1

Define the following terms (Any Seven):
(1)Volumetric strain (2)Perfect Truss (3)Radius of Gyration (4)Factor of safety (5)Moment of Inertia (6)Principal plane (7)Point of Contraflexure (8)Coplanar Concurrent forces (9)Torsion
07

A steel rod 20 mm in diameter is inserted inside a brass tube of 20 mm internal diameter and 40 mm external diameter, the ends are rigidly connected together. The whole assembly of 1.2m is heated by 60°. Find value and nature of stress developed in both the materials.
Es 200 GPa and Eb 100 GPa, αs 11.6 x 10-6 and αb 18.7 x 10-6/°C.
07
Q.2

Determine the M.I. of the I-section about its centroidal xx and yy axis. The particulars are: Top flange 300 mm x 50 mm ,Web 50 mm x 300 mm and Bottom flange 150 mm x 50 mm. The body is symmetrical about yy axis.
07

A 2.0 m long steel bar is having uniform diameter of 40 mm for a length of 1.5 m and in the next 0.5 m its diameter gradually reduces from 40 mm to 20 mm as shown in Fig.1. Determine the elongation of this bar when subjected to an axial tensile load of 200 kN. Given E 200 GN/m2.
07
Q.3

Find the centroid with respect to point O for given fig. 2.
03
Determine reaction at support A and B as shown in fig.3.
04

Determine reaction at supports and draw shear force and bending moment diagrams for cantilever beam as shown in fig.4.
07
Q.4

The direct stresses at a point in the strained material are 120 N/mm2 compressive and 80 N/mm2 tensile as shown in Fig.5. There is no shear stress. Find the normal and tangential stresses on the plane AC. Also find the resultant stress on AC.
07

A simply supported beam of span 3.0 m has a cross-section 120 mm × 180 mm. If the permissible stress in the material of the beam is 10 N/mm2, determine
maximum udl it can carry
maximum concentrated load at a point 1 m from support it can carry.
Neglect moment due to self weight.
07
Q.5

The following forces act at a point:
20 N inclined at 30° towards North of East,
25 N towards North,
30 N towards North West,
35 N inclined at 40° towards south of West.
Find the magnitude and direction of the resultant force.
03
Explain the following laws of mechanics with sketch:
i. Parallelogram law of forces
ii. Law of Transmissibility
04
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Determine the forces in all the members of the truss shown in Fig.6 and indicate
the magnitude and nature of forces on the diagram of the truss. All inclined
members are at 60° to horizontal and length of each member is 2 m.
07
Q.6 A system of connected flexible cables shown in Fig.7 is supporting two vertical
forces 200 N and 250 N at points B and D. Determine the forces in various
segments of the cable.
07
Write assumption made in theory of pure bending and derive,
Relationship between bending stresses and radius of curvature.
Relationship between applied bending moment and radius of curvature.
07
Q.7 Derive relationship between modulus of elasticity and bulk modulus 07
A hollow shaft is to transmit 200kW at 80 r.p.m. If the shear stress is not to
exceed 60 MPa and internal diameter is 0.6 of external diameter, find the
diameters of the shaft.
07

Fig.2
Fig.1
Fig.3 Fig.4
Fig.5 Fig.6
Fig.7
Dimensions are in mm