Equivalent area of Z-shape beam

[kotawsu]

Hello everyone, I am doin a structural analysis of a Z-shape beam bolted to a flat panel. I want to find the equivalent area of the Z-shape beam. I have constrained one end of the aluminum beam in the x-direction and i am pulling the other end of the composite beam in the x-direction. So now i have displacement of the aluminum beam at the unconstrained end and the reaction force and hence i can calculate the area. But there is local deformation in the bottom flange of the aluminum due to the presence of the fasteners. So how do i calculate the equivalent area of the aluminum beam? any ideas. Thanks.
Kota

 

[JStephen]

I'm not sure I understand the question entirely. If you have a structural section continuously attached to a flat plate or panel, there are a couple of different approaches. I'm not sure this is what you're asking, though.

One approach is to take an arbitrary width of the flat panel and assume it acts with the structural section. Typically, I'll use 16t on either side.

Another approach is shown in the appendices of AISC-ASD, where they give an equivalent width to use for an analysis. But as I recall, you calculate the stress, use it to calculate the width, then recalculate the width, etc. In my cases, these widths always come up greater than the 16t mentioned above. AISC ASD mentions the source of this method- von Karman, if I remember it right.

I have seen, but do not have current copies of, aluminum design manuals published by the aluminum associate. These seem fairly exhaustive, and may cover this case. And it occurs to me that aluminum sheets riveted to a stiffener describes a lot of airplane construction, so I would expect the question has been studied exhaustively by someone.

 

[kotawsu]

why exactly do people go for equivalent area in the analyticala models but not the actual cross sectional area?

 

[JStephen]

If the flat plate is thin, and the stiffener itself is a section that yields before buckling, then the portion of the plate near the stiffener will also yield before buckling, while farther out, it will buckle before yielding. So one way to handle this is somehow calculate the width that will yield, and just work with that width.

Additionally, if the thin plate is wide enough, it will not all deflect two-dimensionally like a beam- parts near the beam will deflect with the beam, while parts farther out will not. IE, it will not maintain the theoretical cross section in bending.

With a stiffener welded to a cylindrical shell, you can use shell theory to figure the effective parts of the cylinder.

 

[kotawsu]

since there is local deformatrion in the bottom flange of stiffner because of the fastener which point do i select from the entire Z shape aluminum beam to calculate the width frm fem and hence caluclate the equivalent area. Any idea??