Deflection of flanges in angle and C shapes?

[777gne]

Forgive me if this is the wrong forum to post this query, as it's not exactly a structural problem. For a given AISC "C" shape or angle, if the member is supported at its web or bottom leg respectively by bolting or welding to another rigid member, how can the deflection of either flange be analyised given a situation where there are multiple point loads on the flange in question?

Example:

Take a C3x4.1 orient both flanges pointing up then lag through the web into a concrete slab so that deflection of the member itself is neglegible. Now start loading up either of the flanges with 2 equal point loads, say equally spaced along the length of the flange.

How can one determine the deflection at a given load and/or where the stress will exceed the yield strength?

 

[777gne]

the above last sentence should read:

How can one determine the deflection OF THE FLANGE at a given load and/or where the stress will exceed the yield strength?

sorry...

GNE

 

[dbuzz]

Do you mean a point load at the flange tip, P, causing the flange to bend about its root at the web? If so, that's just cantilever bending. There will be an "effective width" of flange that resists the bending. Assume a load distribution of 1:1 through the flange. The effective width of the flange at the root, B, will then be equal to 2*L.

P
--------x------- - flange tip
/ \ |
/ \ L
/ \ |
---------------- - flange root at web

|---B---|

 

[tincan]

treat the leg as a plate fixed at one edge with a vertical load, if the two point loads are far apart, they should have little effect on the other since the channel legs are not that great of a length.