Shear Stiffness of a rod

[Brian6700]

Hi everyone,

I know this is a very basic question, but I'm having trouble finding it online. I know the axial stiffness of a circular solid member such as a rod is AE/L but what is the formula for the shear stiffness of a rod? Is it GA/L (where G is shear modulus)?

Thanks alot!

 

[rb1957]

? a rod carries axial load, only. it has no shear stiffness ... if it carries shear (=transverse) load, it'd be a beam ('cause it'd need moment capability)

 

[moon161]

Do you mean a rod in torsion? Gamma (twist angle, radians)=TL/JG

 

[Brian6700]

No I was looking for the formula giving the stiffness associated with the lateral direction as opposed to the axial direction.

 

[rb1957]

still, you're talking about beams (taking lateral load requires bending).

you might work back from axial stiffness ... stress = P/A, strain = P/(AE), deflection = (PL)/(AE), so stiffness = (AE)/L (P = kx).

your problem is the deflection of a beam is less straight-forward to calc.

 

[BrianE22]

It's usually quite a bit smaller than the deflection due to bending. Blodgett talks about it a bit (see enclosed).

 

[BrianE22]

Let me clarify the above: I should have said the deflection due to shear is quite a bit less than the deflection due to bending (in most cases). The exception would be for short beams. The Blodgett blurb gives deflection, not stiffness.

 

[rb1957]

actually he does (give the equation for stiffness) ...

it would have helped if you'd posted this originally, cause the words are the same but the meaning is different ... i was about to write he's talking about the deflection due to shear of a beam, i think trying to point out that the shear deflections dominate for short beams and "normally" we consider only deflection due to bending.

but i'd caution you in applying this (not sure where you're going with this) ... you can't separate the two deflections in the real world. for "typical" beam applications i think we can reaonably ignore the deflections due to shear, 'cause they are much smaller than bending deflections. however, short beams require special attention.