Modulus of [Elasticity|Rigidity] and Shear Modulus

If you apply 1.5x10^3Nm to some material; that force is called the stress and how the material deforms is called the strain.

If you are applying some force or stress to a material; is there standard deformation calculations to see just how much they'll deform?

Shear stress and shear modulus are not the same. They're related (for torsion in a shaft etc) by the equation you gave, T/J = Fs/R, where J = modulus of rigidity, R = radius. You know how to calculate J from previous thread!

That equation and T/J = G*theta/L are not either/or, they both apply. theta is the angle of twist over length L.

G and E are not the same, though they have same units, GPa. They are related by the formula G = E/2/(1 + ν) where ν (nu) is Poisson's ratio, usually taken as 0.26 in my recollection, though between that and 0.29 doesn't make a deal of difference.

thank you; this is what I was trying to refer to in my question #4.

Now I should be able to calculate the needed values and then use those in my formulas to try and sort this issue out.

p.s.

I apologize for the delay, real life calls sometimes!

Is the shear modulus is actually the modulus of rigidity as denoted by G?

Is the shear stress is denoted by Fs?

That material sheet that I posted in the original post doesn't use modulus of rigidity but uses modulus of elasticity. Looking at this website it seems that modulus of elasticity is another name for Young's modulus or denoted by E.

Although the way modulus of elasticity is described in the link, why would the same behavior be described in so many different ways with different names and symbols?

If that's the case I can get the modulus of rigidity by solving the problem G = E/2(1+v) in this case v [Poisson's ratio] is provided by the material sheet above as 0.29

Is the shear modulus is actually the modulus of rigidity as denoted by G? Yes

Is the shear stress is denoted by Fs? Yes

That material sheet that I posted in the original post doesn't use modulus of rigidity but uses modulus of elasticity. As far as I can see it doesn't use either of them, but it defines them both, and also bulk modulus. I don't see your problem,

Looking at this website it seems that modulus of elasticity is another name for Young's modulus or denoted by E. That's correct.

Although the way modulus of elasticity is described in the link, why would the same behavior be described in so many different ways with different names and symbols? It's not the same behaviour, the various moduli relate to material being stressed in different ways.

If that's the case I can get the modulus of rigidity by solving the problem G = E/2(1+v) in this case v [Poisson's ratio] is provided by the material sheet above as 0.29. That's right. The table didn't need to list all 3 of E, G and ν as they're related by the formula, but it did and you can check the figures agree near enough (I haven't checked, maybe exact in ksi, a bit out in GPa but near enough in practice).

The formula you gave for angle of twist theta doesn't immediately drop out of the relation between shear stress and shear strain, given in various posts and links. To derive it would need a calculation involving integration. But I'm sure it's correct as it agrees with one in my (old) copy of Roark, and other sources.

Also note that J in the formulas for Fs and theta is only the same for both in the case of a cylindrical shaft. For other shapes it's different and if you get involved in that you need to study the literature.

thank you, this was very helpful clarifying those questions.

Also thanks for the heads up about the tips about those calculations apply to solid shafts!

No problem!

Looking at it again, the formula for angular twist does come out readily from the definitions, I was over-thinking it in my comment.

A year or 2 back I wanted to calculate figures for a helical spring with rectangular "wire". I made the mistake of assuming the torsional J-value could be got from the perpendicular axes theorem (adding the 2 J-values at right angles to each other and to the plane of twisting). This only works for circular sections. Other forum members put me right, we can all help each other!