Maximum Principal Stress Theory – Theories of Elastic Failure – Strength of Materials


Hello friends here in this video we are going to see what is meant by Maximum Principle Stress Theory now maximum principle stress theory here it means that when we are talking about principle stress principle stresses are tensile stress and compressive stress so it means this theory basically deals with tensile or compressive stress and it states that here I write the statement of that now here I have written the statement for maximum principle stress theory it states that the failure of a material or a component will take place when the maximum value of stress exceeds the limiting value of stress now let us try to understand what is the meaning of this by drawing a diagram now here I draw two stress-strain graphs first the first one now here I have two different graphs the first graph which I have drawn it is for ductile materials and the second one which I have drawn it is for brittle materials now as we can see in the first graph that is for ductile materials when we are increasing the stress strain also increases and there is a point in this graph that is point D where we are having maximum value of stress now from this graph it is clear that after the maximum stress has been reached then there is a region from D to e in which even if the stress goes on decreasing the strain value increases and finally at Point E the material breaks so if in any material the value reaches the maximum value of stress then after that maximum value has been reached that material can break anywhere so the chances should be to avoid the material to operate in the maximum stress condition we have to reduce the working stress so that the material does not reach maximum stress so this is for brittle or ductile material next check it for brittle material brittle material as we know it fails without giving any prior warning so when we are increasing the stress value the strain increases and finally there is a point where the material breaks and at that point the stress is called as Sigma ultimate that is ultimate stress so as per the definition or the statement of maximum principle stress theory here we have written that it states that the failure of a material or a component will take place when the maximum value of stress exceeds the limiting value of stress the limiting value of stress is here the maximum stress and then if we are increasing the stress from this value that is point D has been reached then the material can fail anywhere similarly for brittle materials as we can see if the material has reached ultimate stress value then it can break anywhere so as per the maximum principle stress theory as per the maximum principle stress theory working stress or permissible stress for ductile materials is given by we need to reduce the value of working stress so that it does not go into the maximum stress condition and for that we have to use factor of safety that is the permissible stress I’ll write down Sigma permissible will be equal to since we are writing for ductile materials in case of ductile materials the maximum stress it is also called as yield stress Sigma suffix Y so it is yield stress upon factor of safety so therefore the permissible stress will become Sigma Y upon fos so it means if we can use this relation we can reduce the value of stress which is the working stress and the material will be it we can avoid the failure of that material next similarly working stress or permissible stress for brittle materials is given by the permissible stress for brittle materials the maximum stress at which the material breaks it is called as Sigma ultimate that is ultimate stress upon factor of safety which is Sigma ultimate upon fos and as we have seen in case of the maximum principle stress theory we are only using tensile and compressive stresses here we are not considering shear stresses and hence this theory it is used for brittle muddy mostly because they are stronger in shear as compared to the ductile materials

38 Replies to “Maximum Principal Stress Theory – Theories of Elastic Failure – Strength of Materials”

  1. yield stress is taken as failure criteria for ductile materials..and max stress and yield stress are along different points in stress strain diagram

  2. Nice video but i think max value of stress to be considered for ductile material is the UTS not the yield point(in the video it seems UTS is confused with yield point.Yield point comes below the UTS in stress-strain curve.) and the max value of stress to be considered for brittle material is the yield point.(as it breaks soon after the yield point.)

  3. Little confusing, Point A is the proportional limit, just above Point A before Point B is the yield stress, and point D is the ultimate stress or more commonly known as ultimate tensile stress. However, in this video he keeps calling the ultimate tensile stress the yield stress and it is wrong. My machine Design book by Norton, even states that it is Sut which stands for Sigma Ultimate Tensile. This guy needs to stop calling it yield as he does in all his videos

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  5. is it so simple? why i didnt see mohr circle with ur analysis? is it enough to just consider the stress in one dimension?

  6. sir,why we taked about shear at the end of the lecture and in this thory case is only about compression and tension.then why we used shear for applicability of material ahich is ductile and brittle?

  7. In simple testing machine permanent deformation consider as failure of material so yield point consider as maximum stress
    So you are wrong Sr

  8. i think u are confused with the yield stress .u said for ductile material failure point is ultimate stress .

  9. Nice information sir ty…but maximum stress should be ultimate stress not yield stress I think so. ..btw because u of interest in som is generated inside me

  10. More importantly this theory can not be used for a Ductile Material, because for a Ductile material the failure criteria is Yielding not UTS and in ductile materials failure can also occur due to shear, but this theory does not say anything about the Shear stress, so It CAN NOT be used for Ductile material

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  12. Bakwaaas , you are pointing max stress as yield stress at the end 😂, you are very good example for students how to score marks and make disasters when it comes to real environment, please do delete the Video

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