PHY11 Lesson 7

ELASTICITY

ELASTICITY
The ability of a strained body to recover its size and shape after deformation. stress – characterizes the strength of forces causing the deformation.

F stress 
A

in

2

or pascal (Pa)

strain – the resulting deformation.

Hooke’s Law:

stress elastic mod ulus  strain 3 Types of Stress tensile or compressive stress – changes the length of a strained body. tensile stress

bulk stress – changes the volume of a strained body. bulk stress

shear stress – opposite forces act at different points in the body. shear stress

Tensile and Compressive Stress
Consider a body of initial length lo acted upon by a tensile or compressive force of F.

F stress 
A

l strain  lo Young’s Modulus (Y)

 F 
  stress  A 
Y
 strain  l 
 
l 
 o 

Flo
Y
Al

Example 1

Bulk Stress
When uniform pressure p acts on a body, the volume of the body decreases.

F pressure 
 stress
A
V strain 
Vo
 F 
  stress  A 
B
 strain  V 

V 

 o 

Bulk Modulus (B)

p
B
 V

V
 o

B






p
V
Vo

Example 2

Shear Stress and Strain
When equal and opposite forces act tangent to the opposite sides of a body, a shear strain is produced.

F// stress 
A

x strain  h x

h

x tan   h Shear Modulus (S)

F// h
S
Ax

F//
S

A

tan 

Example 3

F// = 9.0 x 105 N

A = 5.0 x 1-4 m2

F

Ssteel = 7.5 x 1010 Pa

a ) s. strain 

s. stress F//

 2.4 x10  2
S
AS

F

b) x  (h)( s.strain)  2.4 x10 3 m

F
F

Example 4

Example 5