Stress and Strain

Question 1

Tension

Reaction force sign and description

Answer 1

Is being stretched and pinned in place.
Reaction force has a positive sign.

Question 2

Compression

Reaction force sign and description

Answer 2

Is being squeezed and pinned in place.
Reaction force has a negative sign.

Question 3

Calculating Direct Stress

Equation and what the symbols mean

Answer 3

σ=F/A_0
Where:
σ is stress in N/m^2 or pa
F is force in N
A_0 is crossectional area in m^2

Assumes forces are evenly distributed

Question 4

Calculating Direct Strain

Equation and what the symbols mean

Answer 4

ε=∆L/L_0
Where:
ε is strain (no units)
∆L is the change in length (m)
L_0 is the original length (m)

• When the bar increases in length, this is called direct tensile strain
• When the bar decreases in length, this is called direct compressive strain

Question 5

Hooke’s law

Equation and explanation

Answer 5

F∝x
(Force is directly proportional to extension (x))
* This is generally true for all materials when deformations are small relative to the length.

Question 6

Young’s Modulus

Explanation and equation (and what the symbols mean)

Answer 6

• The constant of proportionality between stress and strain is known as the elastic modulus, or Young’s modulus
• σ=Eε
  Where:
  σ is stress in Pa or N/m^2
  E is Young’s modulus in Pa or N/m^2
  ε is strain (no units)

Question 7

Stress-strain Curves (for a metal)

Description of curve and different stages

Answer 7

1. Linear elastic region where stress and strain are directly proportional
2. The yield point where the curve is no longer linear
3. Ultimate tensile strength where the material will be permanently deformed
4. Necking failure wher the material necks and then snaps.

Question 8

Features of a Stress-strain curve

Answer 8

• The gradient of the curve is the Young’s modulus
• Other materials behave differently (i.e. will have differnent curves)
• Linear elastic region is typically small (<1% strain)