Question

A fatigue test was conducted in which the mean stress was 46.2 MPa and the stress amplitude was 219 MPa.

(a) Calculate the maximum stress level (in MPa).

(b) Calculate the minimum stress level (in MPa).

(c) Calculate the stress ratio.

(d) Calculate the magnitude of the stress range (in MPa).

Answer 1

a)σ₁ = 265.2 MPa

b)σ₂ = -172.8 MPa

c)
`Stress\ ratio =-0.65`

d)Range = 438 MPa

Step-by-step explanation:

Given that

Mean stress ,σm= 46.2 MPa

Stress amplitude ,σa= 219 MPa

Lets take

Maximum stress level = σ₁

Minimum stress level =σ₂

The mean stress given as

`\sigma_m=(\sigma_1+\sigma_2)/(2)`

`2\sigma_m={\sigma_1+\sigma_2}`

2 x 46.2 = σ₁ + σ₂

σ₁ + σ₂ = 92.4 MPa --------1

The amplitude stress given as

`\sigma_a=(\sigma_1-\sigma_2)/(2)`

`2\sigma_a={\sigma_1-\sigma_2}`

2 x 219 = σ₁ - σ₂

σ₁ - σ₂ = 438 MPa --------2

By adding the above equation

2 σ₁ = 530.4

σ₁ = 265.2 MPa

-σ₂ = 438 -265.2 MPa

σ₂ = -172.8 MPa

Stress ratio

`Stress\ ratio =(\sigma_(min))/(\sigma_(max))`

`Stress\ ratio =(-172.8)/(265.2)`

`Stress\ ratio =-0.65`

Range = 265.2 MPa - ( -172.8 MPa)

Range = 438 MPa