## How to calculate J and Cw for non-standard shapes?

## How to calculate J and Cw for non-standard shapes?

(OP)

I have an inverted "T" shape and I need to calculate the J and Cw values. I donot have quick access to the Roark Book, as I understand it is in there. Does anyone know how to do this?

## RE: How to calculate J and Cw for non-standard shapes?

b = width of the flange

tf = thickness of the flange

h = height from the tip of the stem to the mid-height of the flange (d - tf/2)

tw = thickness of the stem

J = 1/3 x ((b x tf^3) + (h x tw^3))

Cw = 1/36 x ((b^3 x tf^3)/4 + (h^3 x tw^3))

So a verification -

Let b = 4

tf = .5

h = 6.25

tw = .3

Then I get J = 0.2229

Cw = 0.2387

Cw = 0 for small thicknesses

## RE: How to calculate J and Cw for non-standard shapes?

Is a "T" value valid for an inverted T?

Also, I thought the values depended on a "mesh", or matrix...?

Guess I really don't understand how these values are derived.

## RE: How to calculate J and Cw for non-standard shapes?

## RE: How to calculate J and Cw for non-standard shapes?

## RE: How to calculate J and Cw for non-standard shapes?

Now if you try the same thing with a T-section, there is no opposite flange to create the couple that can carry the torsion. Even with your beefy section, the warping will be a small effect.

## RE: How to calculate J and Cw for non-standard shapes?

## RE: How to calculate J and Cw for non-standard shapes?

## RE: How to calculate J and Cw for non-standard shapes?

## RE: How to calculate J and Cw for non-standard shapes?

I find all the given formulae for various shapes fine and dandy, however I would like somthing more along the lines of a derivation.