e g k problems.ppt strength of msterials problems

diploma candiates scjs

1. Recap
In the last class, we have learnt about
• Relationship between ‘E’ and ‘C’
• Relationship between ‘E’ and ‘K’
• Relationship between ‘E’, ‘C’, and ‘K’
1

2. Objective
On completion of this class, you
would be able to understand
• Solving problems on the relationship
between different elastic constants
2

3. A bar of 30 mm dia is subjected to a
pull of 60KN. The measured extension over
a gauge length of 200 mm is 0.09 mm and
change in dia is 0.0039 mm. Find the
Poisson's ratio and the values of the three
moduli.
Problem 1
3

4. Given data:
Diameter of bar, d = 30 mm
Load, P = 60x1000 KN
Gauge length, L = 200 mm
Extension, δl = 0.09 mm
Change in dia δd = 0.0039 mm
Problem 1 (Contd..)
4

5. To Calculate:
• Poisson’s ratio
• Young’s modulus
• Shear modulus
• Bulk modulus
Problem 1 (Contd..)
5

6. Solution:
Poisson’s ratio = (lateral strain) / (linear
strain)

Lateral strain = change in diameter /
original diameter
= 0.0039 / 30
= 1.3x10
-4

Problem 1 (Contd..)
6

7. Linear strain = change in length / original
length
= 0.09 / 200 = 4.5 X 10
-4
Poisson’s ratio(1/m) = (lateral strain) / (linear
strain)
= 1.3x10
-4
/ 4.5 X 10
-4

= 0.289
Problem 1 (Contd..)
7

8. Young’s modulus = stress / strain

Stress = load / area
= 60 x 1000/ (∏/4x30
2
)
= 84.88 N/mm
2
Strain = change in length / original
length
= 0.09 / 200
= 4.5 X 10
-4
Problem 1 (Contd..)
8

9. Young’s modulus = stress / strain
= 84.88 / 4.5 X 10
-4

= 1.89 X 10
5
N/mm
2
Shear modulus, G = ?
E = 2G(1+1/m)
1.89 X 10
5
= 2G( 1+ 0.289)
= G (2x1.289)
G = 1.89 X 10
5
/ (2x1.289)
= 0.73 X 10
5
N/mm
2

Problem 1 (Contd..)
9

10. Bulk modulus, K = ?
E = 3K(1- 2/m)
1.89 X 10
5
= 3K( 1-2x 0.289)
K = 1.89 X 10
5
/ (1-2x 0.289)
= 1.49 X 10
5
N/mm
2
Problem 1 (Contd..)
10

11. A cylindrical bar is 20 mm in dia
and 1m long. During a tensile test it was
found that longitudinal strain is 4 times
the lateral strain. Calculate the three
moduli and Poisson's ratio. Take Elastic
modulus is 1 X 10
5
N/mm
2.
Find the
change in volume ,when the bar is
subjected to a hydrostatic pressure of
100 N/mm
2

Exercise
11

12. Summary
In this class we have learnt about solving
• Problems determining various elastic constants
12