Simple stresses and Principal Stresses

1. STRENGTH OF MATERIAL (SOM)
Instructor: Suryakant Kumar
Copyright © Gaya College of Engineering, Gaya
GAYA COLLEGE OF ENGINEERING
MECHANICAL ENGINEERING – SEM IVTH
Assignment – 1
Due Date: 10.04.2020
Max. Marks: 50
Instructions:
1. Attempt all the questions.
2. Marks to each Question is shown on the right hand side of each question.
3. Draw diagrams with pencils and use only A4 Plain paper.
4. Question are based on Course Outcome 1 (CO-1)
Q.1. Derive formula for calculating Axial Elongation in case of a tapered bar with larger diameter as
d1 and smaller diameter as d2. Assume length of the tapered bar to be L and loaded with a force P as shown
below.
10-Marks
Q.2 If a test bar is found to taper uniformly from (D-a) mm diameter to (D+a) diameter, prove that
the error involved in using mean diameter as D to calculate the young’s modulus E is (
𝟏𝟎𝐚
𝐃
)
𝟐
percent.
10-Marks
Q.3 Calculate the normal and shear stresses on a plane making angle  with the Y axis under biaxial
state of stress shown below. Also calculate the principal stresses, principal planes, and plane of
maximum shear.
10-Marks

2. Q.4 The intensity of resultant stress on a plane AB is shown below at a Point in a material under
stress is 80 N/mm2
and inclined at an angle of 30° to the normal to that plane. The normal component
of stress on another plane BC, at right angles to the plane AB is 60 N/mm2
.Determine:
a. The resultant stress on the plane BC.
b. Principal stresses and their directions.
c. Maximum shear stresses and their planes.
10-Marks
Q.5 (a) A bar 30mm×30mm×250mm long is subjected to a pull of 90 kN in the direction of its length. The
extension of the bar was found to be 0.125 mm, while the decrease in each lateral dimension is found to be
0.00375 mm. Find the Young’s Modulus, Poisson’s ratio, Modulus of rigidity, and Bulk modulus for the
material of the bar.
05-Marks
(b) A cube of material is under the action of a compressive stress on its faces. If the volume of the cube
decreases by 0.1%, Find the uniform stress in the cube. Also find the percentage reduction in the length of a
side of the cube. Take E = 2×105
N/mm2
and µ=0.3.
05-Marks