Unequal leg single angle bending AISC F10-6

[SEwannaB]

I have an unequal leg, single angle to analyze by AISC equation F10-6 and have to figure the BETAw per the commentary. Does anyone know what are the values z and w in the BETAw equation in Tbl C-F10.1 (AISC 13th, p.16.1-284)? Must have something to do with the z and w axes, but what? Do you happen to have a better equation than that friggin' integral?

The problem is determining allowable bending for a 5/16" bent plate angle shape with 3" leg top and variable depth (vertical) leg. The beam is cantilever and depth is from 6" at free end to 18" at fixed. There is no lateral restraint (there is lateral support at the bottom of the long leg, but not at centroid).

thx

 

[iponom]

Sorry kind of a late reply but just found your post.

ok so obviously the problem here is that you are not sure how to solve and integral. z and w are variables for the dimensions of an angle.

so here is a hint, 1/Iw * Integral(from -z to +z) of [f(w)*(z*(w^2 + z^2))]dz

where z is the location of the coordinates of angle from bottom to top of an the angle leg with respect to W axis; and f(w) is a function of angle leg with respect to W axis.

for angle geometry refer to p. 17-42 - very helpful in figuring out stuff like the location of shear center...

for more info about the bent plate refer to

AISC pp.10 - 149-152

 

[iponom]

you could split the integral into two to make your life easier in figuring out f(w)... Good luck!
and btw, if I am correct, f(w) will be equation of (2) lines, one short one and one long one

try deriving one of the values from the table above to make sure you got the right answer