Maximum Shear Stress Theory – Theories of Elastic Failure – Strength of Materials
Hello friends here in this video we are going to see Maximum Shear Stress theory I write the statement for that first maximum shear stress theory it states that so here this is a statement of maximum shear stress theory it states that the failure or yielding yielding means permanent deformation so the failure of permanent deformation of a component occurs when the working stress value reaches the limiting strength value in a material so if the working stress reaches the limiting strength limiting strength is nothing but maximum stress in the material then we can say that the material is going to fail and here I can explain this in a manner by drawing a graph here we have a stress-strain graph in which first there is proportional limit then permanent deformation then upper and lower real point after that it reaches maximum stress value here this is Sigma Max and finally it will be failing at the breaking point so now here as we are talking about the maximum shear stress so the failure of yielding yell failure of yielding means at Point D the material is subjected to maximum stress and this graph which I have drawn it is for ductile materials so the maximum stress and since here I have written the failure of a or yielding of a component occurs when the working stress value reaches the limiting strength which is the stress here I have written in this case it is shear stress so we have to avoid we have to avoid the material to reach up to maximum stress that is if we can decrease the value of stress then the material won't be going up to point D it will remain below point D and if it is remaining below point D then the failure chances are very rare or very less because the material won't cross the maximum stress value so we should try to bring the material below point D and that we can do it by using the condition in which we use factor of safety so therefore we can say that permissible or working shear stress it will be given by tau permissible is equal to tau max that is the maximum shear stress divided by fos that is factor of safety next this same shear stress relation can also be written as therefore the permissible shear stress is also written as ultimate stress upon to into factor of safety because the value of shear stress is half of the value of yield stress so here I have replaced the maximum shear stress with the yield stress because yield stress is the maximum value of stress in case of ductile materials and hence here I can write down that maximum shear stress theory is used for ductile materials so here in this video we have seen what is meant by maximum shear stress theory