Goodman and Soderberg Failure Criteria Soderberg

m b

m b S

m S b

b S

mS

S

S

SS

SS

m a

f

y

f

f

y

f

ym f a

fm

ya

σ σ

σ σ

σσ

+ =+ =

+ =

=

= −

− + =

−

=

( )

( )

0

0

1

Goodman

m b

m b S

m S b

b S

mS

S

S

SS

SS

m a

f

ut

f

f

ut

f

utm f a

fm

uta

σ σ

σ σ

σσ

+ =+ =

+ ==

= −

− + =

−

=

( )

( )

0

0

1

Sf

Sy Sut

Sy

Goodman Failure Line

Yield Line

Soderberg Failure Line σσm

σσa

What happens if the alternating stress is low and constant, but the mean stress continues to increase ? The ratio of to is the factor of safety − + =

= − +

=

σ σ

σ σ

σσ

m y a

m a y

m

m

S

equation of yield line

S

n

'

( )

'

'

σσm Sut σσm’

Sf

Sy

Sy

Goodman Failure Line

Load Line

σσa’ Failure

Vary alternating stress and hold mean stress constant

SS

n

fm

uta

a

a

1 −

=

=

σσ

σσ

'

'

ratio of to is the factor of safety

σσm

σσa

Sf

Sy Sut

Sy

Goodman Failure Line

Yield Line

σσm’

σσa’

maintain load line ratio, increase alternating and mean stresses σσ

σσ

σσσ

σσσ

σσ

'

'

'

'

'

'

'

a

mm f

m

ut

ma

m

f

utf

mf

a

m

f

ut

m

m

SS

S

SS

S

S

S

n

= −

+

=

=+

=

1

Sf

Sy Sut

Sy

Goodman Failure Line

Yield Line

σσm

σσa

Given the following information, construct a Goodman Failure Diagram and determine factors of safety considering constant alternating stress and increasing mean stress, constant mean stress and increasing alternating stress, and increasing mean and alternating stress with a constant load line slope. σσa’ = 8.72 ksi σσm’ = 10.5 ksi Sut = 80 ksi Sy = 60 ksi Sf = 21.8 ksi