[Machine Design] - Theories of failure under static load

@shrinkdworld-WWdBBc • Oct 22, 2024

Oct 22, 2024

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Theories of failure under static load

Need of these theories

The strength of machine member depends on material used. And these properties are usually calculated from simple tension or compression tests. There for predicting the failure stresses for member subjected to bi-axial or tri- axial stress is more complicated.

The principal theories of failure for machine member subjected to bi-axial stress are as follows.

1] Maximum Principal (or normal) Stress theory (Also known as Rankine Theory)
2] Maximum Shear Stress theory (also known as Guest’s or Tresca’s theory )
3] Maximum principal (or normal) Strain theory (Also known as Saint Venant Theory)
4] Maximum Strain energy theory (also known as Haigh’s theory)
5] Maximum distortion energy theory (also known as Hencky & Von Mises theory)

For brittle materials, the limiting strength is the ultimate stress tension or compression
For ductile materials, the limiting stress is the stress at yield point.

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ShrinkDWorld

@shrinkdworld-WWdBBc • Jul 23, 2011

1] Maximum Principal or normal Stress theory ( Rankine Theory) -->

According to this theory, the members fails when maximum principal or normal stress in system reaches to limiting value.
Limiting stresses
For ductile material is yield stress
For brittle material (do not have well definite yield point) is ultimate stress.
According to above theory, taking factor of safety (F.S.) in account , the principal or normal stress (δt1 ) in a bi-axial stress system is given by

δt1= δyt/F.S. For ductile materials
δt1= δut/ F.S. For brittle materials

Where,
δyt =Yield stress in tensile test
δut = Ultimate stress

This theory is generally used for brittle materials.[FONT=&quot]

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ShrinkDWorld

@shrinkdworld-WWdBBc • Jul 23, 2011

2] Maximum Shear Stress theory (Guest’s or Tresca’s theory ) -->
According to this theory, the failure is occurs at a point in member when maximum shear stress reaches to the value equal to shear stress at yield point in simple tension test.
Mathematically
τmax = τyt/F.S.
where,
τmax = Maximum shear stress in system
F.S.= factor of sefty
τyt = Shear stress at yield point determined from simple tension test.
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ShrinkDWorld

@shrinkdworld-WWdBBc • Jul 23, 2011

3] Maximum principal (or normal) Strain theory (Also known as Saint Venant's Theory)
According to this theory the failure/ yielding occurs at a point when maximum principal strain reaches to limiting value of strain.
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#-Link-Snipped-#
where
Î´[SUB]t1[/SUB]& Î´[SUB]t2[/SUB] = Maximum & minimum principal stresses.
Îµ= strain at yield point.
1/m = Passions ratio
E= Youngâ€™s Modulus.
F.S.= Factor of safety

This theory is rarely used due to unreliable results in many cases.

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ShrinkDWorld

@shrinkdworld-WWdBBc • Jul 23, 2011

{Reserved For 4] Maximum Strain energy theory (also known as Haigh’s theory)}
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ShrinkDWorld

@shrinkdworld-WWdBBc • Jul 23, 2011

{Reserved For 5] Maximum distortion energy theory (also known as Hencky & Von Mises theory)}

Now below we can discuss above topic.
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scot davidson

@scot-davidson-TiiYvi • Jan 9, 2016

Am really sorry to disturb you but would you mind having a look at this question for me as I don't know what approach to take with this question thank you
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Jah Knows

@jah-eckCwF • Nov 17, 2018

How to find factor of safety using (MSST) without given yield stress

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