[Machine Design] - Theories of failure under static load

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.

Replies

  • ShrinkDWorld
    ShrinkDWorld
    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="]

    [/FONT][FONT="]

    [/FONT]
  • ShrinkDWorld
    ShrinkDWorld
    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.
  • ShrinkDWorld
    ShrinkDWorld
    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.
    #-Link-Snipped-#
    #-Link-Snipped-#
    where
    δ[SUB]t1[/SUB]& δ[SUB]t2[/SUB] = Maximum & minimum principal stresses.
    ε= strain at yield point.
    1/m = Passions ratio
    E= Young’s Modulus.
    F.S.= Factor of safety

    This theory is rarely used due to unreliable results in many cases.
  • ShrinkDWorld
    ShrinkDWorld
    {Reserved For 4] Maximum Strain energy theory (also known as Haigh’s theory)}
  • ShrinkDWorld
    ShrinkDWorld
    {Reserved For 5] Maximum distortion energy theory (also known as Hencky & Von Mises theory)}

    Now below we can discuss above topic.
  • scot davidson
    scot davidson
    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
  • Jah Knows
    Jah Knows

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

You are reading an archived discussion.

Related Posts

me

I want to say hello to my fellow engineers. 'm very happy to be on CE😁 ​
Let's face it- typing on Apple keyboard brings peace to mind. Once you use Apple's keyboard, you don't want to go back to the standard keyboard that you use with...
CAT 2011, the entrance exam conducted by the IIMs for the management programmes of its 13 B schools, is expected to be held from Saturday, 22 October 2011 to Friday,...
I have always been fascinated by how people make create cartoon characters? I have been trying to do the same but with little luck.Can anyone guide me as to which...
heya! Peter here.