## Unequal Leg Angle Bending - Symmetry Parameter Bw (CSA S16-19)

## Unequal Leg Angle Bending - Symmetry Parameter Bw (CSA S16-19)

(OP)

Hi Everyone,

I am trying to evaluate the bending capacity of an unequal length angle (L 127x89x9.5.

The CSA design equation requires you to calculate the symmetry parameter of the section and that involves the evaluation of an area integral. Please see the attached screenshot.

Does anyone know of a solved example or reference for the evaluation of this variable?

Thank you

I am trying to evaluate the bending capacity of an unequal length angle (L 127x89x9.5.

The CSA design equation requires you to calculate the symmetry parameter of the section and that involves the evaluation of an area integral. Please see the attached screenshot.

Does anyone know of a solved example or reference for the evaluation of this variable?

Thank you

## RE: Unequal Leg Angle Bending - Symmetry Parameter Bw (CSA S16-19)

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

## RE: Unequal Leg Angle Bending - Symmetry Parameter Bw (CSA S16-19)

Green's Theorem for line integrals

you'll need to find functions for P and Q such that the difference of the partial derivates = z(w^2+z^2)

z and w can the be written in parametric form for each edge vertices as, each (z,w) pair is a transformation of the (x,y) coordinates to the principal axis angle:

w(t) = w1+t(w2-w1)

z(t) = z1+t(z2-z1)

and then back substituted into P and Q so the integral is from 0 to 1 dt instead of dz or dw.

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

## RE: Unequal Leg Angle Bending - Symmetry Parameter Bw (CSA S16-19)

dw/dt = (w2-w1) => dw = (w2-w1)dt

dz/dt = (z2-z1) => dz = (z2-z1)dt

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

## RE: Unequal Leg Angle Bending - Symmetry Parameter Bw (CSA S16-19)

## RE: Unequal Leg Angle Bending - Symmetry Parameter Bw (CSA S16-19)

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer

## RE: Unequal Leg Angle Bending - Symmetry Parameter Bw (CSA S16-19)

-Laurent

www.ClearCalcs.com

## RE: Unequal Leg Angle Bending - Symmetry Parameter Bw (CSA S16-19)

I will have to find time and go through the calculations in the references shown!

Much appreciated :)

## RE: Unequal Leg Angle Bending - Symmetry Parameter Bw (CSA S16-19)

L8x4:

L4x3 1/2:

L2 1/2 x 1 1/2: (This one is actually sensitive to the thickness)

Equal Leg: (Numerical precision -- 1.33 E -15 is pretty much 0)

Formula for Each linear edge of the angle defined by start point (w1,z1) and end point (w2,z2):

For Green's Theorem assume P=0, so need to integrate the function with respect to w. Then perform the parametric substitutions and change of variable to dt.

The sheet models the fillets with several straight line segments.

My Personal Open Source Structural Applications:

https://github.com/buddyd16/Structural-Engineering

Open Source Structural GitHub Group:

https://github.com/open-struct-engineer