# Stress/Strain Transformation Question !

• posted

I have a simple hollow shaft that is subjected to axial load and torque Fy and a torque My respectively. | Fy=-25000 lbs v My=48000 in*lb --------- | | | | | | | | | | | | | | | | | | | | | | | | | | | |

------Fixed-------->X

I am forgetting something about the principal (max/min) stresses and strains and how to convert between them. My calculations for the shaft shown above are given below. Area, A=2.3 in^2 Polar Moment, J=1.754 in^4 Modulus, E=29e6 psi Shear Modulus, G=11.4e6

1. Calc for Axial Load Stress, Sy=-10870 psi Strain, ey=Sy/E=-374e-6

1. Calc for Torque Shear Stress, Tau=29070 psi Shear Strain, exy=Tau/G=2550e-6

2. Calc Max and Min STRAIN using Mohr's Circle, ex=0 emax=-374/2 + sqrt( (374/2)^2 + (2550/2)^2 )=1102e-6 emin=-374/2 - sqrt( (374/2)^2 + (2550/2)^2 )=-1476e-6

1. Calc Max and Min STRESS using Mohr's Circle Smax=24100 psi Smin=-35000 psi.

Finally, my question (if you've read this far). Why, or how can I convert between the principal stresses to get the principal strains?

We are doing a strain gage application and I am saying we will read emax and emain(1102 and -1476). Another guy is using the principal stresses, dividing them by the elastic modulus and saying we will read those strains (831 and -1207).

Who is correct?

Thank You for your help...and patience.

• posted

-- And the transverse strain = -nu*ey

-- I think you need to consider the transverse strains as well.

This isn't so easy. Draw a stress element. Smax is Sx' and Smin is Sy'. Sz' = Txy = 0. The principal stress axes are x' and y' here.

ex' = [Sx' - nu(Sy' + Sz')]/E = [Sx' - nu(Sy' + 0)]/E for this problem ey' = [Sy' - nu(Sx' + Sz')]/E = [Sy' - nu(Sx' + 0)]/E for this problem ez' = [Sz' - nu(Sx' + Sy')]/E = [0 - nu(Sx' + 0)]/E for this problem

The shear stresses and resulting shear strains are all zero.

Then solve for the principal strains. Not that easy.

The gages need to be oriented with the principal strain axes to directly read emax and emin.

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