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Reg.
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
THIRD SEMESTER B.TECH DEGREE EXAMINATION JANUARY 2017
ME 201: MECHANICS OF SOLIDS
MA, ME, MP, MT, PE, SF)
Maximum Marks: 100 Time 3 Hours
PART A
Answer any three questions.
1. Explain the stress-strain curve of a mild steel bar in tension test.
A straight bar 450 mmlong is 40 mm in diameter for the first 250 mm length and 20
mm diameter for the remaining length. If the bar is subjected to an axial pull of 15 kN find
the maximum and minimum stresses produced in it and the total extension of the bar. Take E
2 × 105 N/mm2.
2. A bar made of brass and steel as shown in Fig.1 is held between two rigid supports A
and C.Find the stresses in each material if the temperature rises by 40°C. Take Eb 1×
105 N/mm2 ;αb 19 × 10-6 °C Es 2 × 105 N/mm2 αs 12 × 10-6 °C
Fig 1
3. What is a stress tensor? Explain different ranks of a tensor.
A cylindrical bar is 20 mm diameter and 800 mm long. During a tensile test it is
found that the longitudinal strain is 4 times the lateral strain. Calculate the modulus of
rigidity and the bulk modulus, if its elastic modulus is 1× 105 N/mm2. Find the change in
volume, when the bar is subjected to a hydrostatic pressure of 100 N/mm2.
4. A solid shaft of 6m length is securely fixed at each end. A torque of 80 Nm is applied to
the shaft at a section 2 m from one end.
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Find the fixing torques set up at the ends of the shaft.
If the shaft is of 50 mm diameter, find the maximum shear stresses in the two
portions.
Find the angle of twist for the section where the torque is applied.
Take C 105 N/mm2.
PART B
Answer any three questions
5. Draw SFD and BMD for the overhanging beam shown in Fig. 2. Locate the points of
contraflexure. Also determine the maximum bending moment.
Fig. 2
6. Derive the relation between intensity of loading, shear force and bending moment at a
section of a uniformly loaded beam.
A simply supported beam of length 4m carries a uniformly distributed load of 3kN/m
over the central 2m length and two point loads 2kN and 3kN at distances 0.5m and 3.5m
from the left support. Draw SFD and BMD. Locate the point of maximum bending
moment and find out the maximum bending moment.
7. What is pure bending? Explain with example.
A wooden beam 3m long is simply supported at its ends and has a cross section
200mm x 400mm. It carries a uniformly distributed load of 40kN/m over the entire
span. Calculate the bending stress at a point 100mm above the bottom and 1m from the
left support.
8. Explain how beams of uniform section can be designed in practice
At the critical section of a I-beam, the value of vertical shear force is 40kN and the
sectional dimensions Flange width 200mm, flange thickness 30mm, web
thickness 40 mm and total depth 300mm. Draw the shear stress distribution across
the depth of the section.
5kN/m
10kN 20kN 9kN
2m 3m 4m 2m 2m
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PART C
Answer any four full questions.
9. A beam of length 6m is simply supported at its ends and carries two point loads of 48kN
and 40kN at a distance of 1m and 3m respectively from the left support. Find the
deflection under each load and the maximum deflection by Macaulay's method. Given
2x105 N/mm2 and 85x106 mm4.
10. State of stress at a point in a material is 100N/mm2 (tensile) upon a horizontal plane and
50N/mm2 (compressive) upon a vertical plane. These planes also carry a shear stress of
75N/mm2 as shown in fig. Determine principal stresses, maximum shear stress, plane of
maximum shear stress and the resultant stress on the plane of maximum shear stress.

i. 100 N/mm2
75 N/mm2
50 /mm250 N/mm2
100 N/mm2
11. Explain double integration method to find the deflection of a cantilever beam with a
point load at the free end
12. Derive Euler's buckling load for slender columns with ends hinged
13. A 1.5m long column has a circular cross section of 5cm diameter. One of the ends of the
column is fixed in direction and position and other end is free. Taking factor of safety as
calculate the safe load using Rankin's formula, take yield stress as 560 N/mm2 and α
1/1600 for pinned ends
14. Explain the terms:
a. Principal planes and principal stresses
b. Mohr's circle of stresses
c. Strain rosettes