Has the Material Yielded Under Combined Bending and Torsion?

[R.C]

Im currently writing a lab report on combined bending and torsion and comparing yield points to theory. I'm not quite sure I know what is going on though. I understnad what Tresca and Von Mises is but I'm not sure how they apply. If I were to use the equations and obtain a value over 1 for each criteria, does this mean that the material has yielded and is now in plastic deformation? Has anyone got any simple explanations and applications of this theory, I'd really appreciate it.

 

[PhanthomJay]

I

Im currently writing a lab report on combined bending and torsion and comparing yield points to theory. I'm not quite sure I know what is going on though. I understnad what Tresca and Von Mises is but I'm not sure how they apply. If I were to use the equations and obtain a value over 1 for each criteria, does this mean that the material has yielded and is now in plastic deformation? Has anyone got any simple explanations and applications of this theory, I'd really appreciate it.

I don't know much about Tresca, but I've used Von Mises on a few occasions. Von Mises is just a combined shear and bending stress and axial stress equation that uses the 'square root of the sum of the squares' combined stresses, with shear stress adjusted by a factor of root 3 so that the combined stress resultant can be compared to the yield stress of the metal(shear ultimate stress is approximately the tensile yield stress dived by root 3). So what I do is determine the design load bending and axial stress, and multiply it by an overload factor, then determine the shear load stress, multiply it by a load factor and the sq rt of 3, then take the sq rt of the sum of the squares of those values and be sure that the result is less than the yield stress. As an example using USA A36 steel which has a tensile yield stress of 36 Ksi, if the bending stress with overload factor is 30 ksi and the shear stress with overload factor is 5 ksi, then the sq rt of [(30)^2 + 3(5)^2)] is 31.2 ksi less than 36 ksi...OK! Now you can go to Wiki and read all about plasticity and principal stress etc but just keep combined stresses per formula less than yield and you are fine (and using a healthy overload factor saves the day)

 

[timthereaper]

Von Mises and Tresca are just theories of when yielding begins. Von Mises is based on distortion energy and Tresca is based on maximum shear stress. Depending on which one you want to use, you plug in your principal stresses and see if the value is below your material tension allowable. If it is, you can say it won't yield. However, usually von Mises is for ductile materials and Tresca is used for brittle materials, but that's not a hard and fast rule.

 

[R.C]

Thank you both. Excellent help.