This document appears to be an exam for an engineering mechanics course, consisting of multiple choice and numerical problems. It covers topics like units, forces, equilibrium, centroids, moments of inertia, beam loading, stresses, strains, and material properties. The problems calculate values like reaction forces, centroid locations, moments of inertia, stresses, strains, temperatures changes and deformations based on given engineering structures and materials under certain loads or conditions.

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C14–CE–105
4019
BOARD DIPLOMA EXAMINATION, (C–14)
OCT/NOV—2016
DCE—FIRST YEAR EXAMINATION
ENGINEERING MECHANICS
Time : 3 hours ] [ Total Marks : 80
PART—A 4×10=40
Instructions : (1) Answer all questions.
(2) Each question carries four marks.
1. Define the terms (a) base units and (b) derived units. 2+2
2. Define the terms (a) equilibrium and (b) equilibriant. 2+2
3. State the following laws : 2+2
(a) Triangle law of forces
(b) Parallelogram law of forces
4. Define the terms (a) centre of mass and (b) centre of gravity. 2+2
5. State the coordinates of centroids for the following areas : 2+2
(a) Triangle
(b) Semi-circle
6. Define the terms (a) moment of inertia and (b) radius of
gyration. 2+2
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7. (a) State parallel axis theorem.
(b) The moment of inertia of an isosceles triangle about its
base is 1250 104 4
´ mm and its base is 150 mm. Find the
height of the triangle. 2+2
8. Define the terms (a) bulk modulus and (b) modulus of rigidity. 2+2
9. Define the terms (a) proof resilience and (b) modulus of
resilience. 2+2
10. A tube has external diameter 30 mm and length 720 mm. It is
subjected to an axial force of 18 kN. If the stress in the tube is
not to exceed 92 MPa—
(a) determine the internal diameter of tube;
(b) calculate the change in length of the tube.
(Take E = ´2 105 2
N mm/ ) 2+2
PART—B 10×4=40
Instructions : (1) Answer any four questions.
(2) Each question carries ten marks.
11. (a) State polygon law of forces. 3
(b) A body of weight 1000 N is suspended by two strings of 4 m
and 3 m lengths, attached at the same horizontal level 5 m
apart. Calculate the forces in the strings. 7
12. (a) Mention the types of loadings on beams with diagrams. 4
(b) A beam of span 8 m is simply supported at its ends and
carries two concentrated loads of 30 kN and 40 kN at a
distance of 2 m and 4 m from left supports. It also carries
an u.d.l. of 20 kN/m for a length of 3 m from A. Determine
the reactions at supports. 6
13. (a) Show the position of centroid in semi-circle and rectangle. 2
(b) A trapezoidal lamina has uniform batter on both sides. Its
top width is 200 mm, bottom width is 300 mm and height
is 600 mm. Determine the position of the centroid from
base. 8
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14. (a) Define polar moment of inertia. 2
(b) Find the moment of inertia about horizontal and vertical
axes passing through centroid for a rolled steel T-section,
whose size of flange is 250 mm×50 mm and size of web is
200 mm×50 mm. 8
15. (a) State perpendicular axis theorem. 2
(b) Find the moment of inertia of an I-section about its
centroidal x-x axis, with top flange 60 mm×100 mm, bottom
flange 120 mm×10 mm and web 80 mm×10 mm. It has a
top cover plate of size 100 mm×10 mm. 8
16. (a) Define yield stress and ultimate stress. 3
(b) A mild steel tube of outer diameter 114·3 mm and 4·5 mm
thickness is subjected to an axial compression of 125 kN.
Determine whether the tube is safe, if the permissible
stress in the material is 110 MPa. What maximum load can
be supported by the tube? Taking an FS of 4, find the
crushing load. 7
17. Steel rod AB of diameter 30 mm and length 680 mm is held
between two grips at ends A and B. Temperature of the rod is
uniformly raised from 26 °C to 64 °C. Assuming the rod to be
stress free at 26 °C, find—
(a) temperature strain and temperature stress in the rod, if the
end grips do not yield;
(b) temperature strain and the axial force developed in the rod,
if the end grips yield by 0·2 mm. Assume E = 210GPa and
a = × ´ -
12 5 10 6
per °C. 5+5
18. The modulus of rigidity of a material is 40 GPa. A 10 mm
diameter rod of that material is subjected to an axial tensile
force of 6 kN and the change in its diameter is observed to be
0·002 mm. Calculate—
(a) Poisson’s ratio;
(b) modulus of elasticity of the material. 6+4
H H H
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