Cantilever Plate bending with UDL

[SALTRAM4567777]

I have a cantilever plate rigidly clamped on one side and free on the other sides, with the plate being very long in the direction perpendicular to the cantilever span. For a point load applied near the free edge, I usually determine the required plate thickness considering load spread at 45 degrees. My question is, for a uniformly distributed load (UDL) along the length of the plate, how should the required thickness be calculated? Do we still apply the 45-degree load spread assumption, or is there a different approach for UDL in this case? Any guidance or references would be helpful.

 

[SE2607]

I find it remarkable so many people in this thread have spent the significant time discussing a 45degree shear lag when we have a UDL line load. I've been very confused by most of this.

The case of the 45 degree distribution width for a concentrated load was brought up by the OP which, in my opinion, has less credence than a distribution with equal to the unit length of the applied UDL.

 

[SE2607]

The sketch below is the case where a concentrated load P is applied at the free edge, causing a deflection 'd' at the point of application. Using Yield Line theory, the value of m, which is the plate moment per unit length turns out to be P/8.

For the case of a UDL running perpendicular to the long edges, a similar calculation could be performed along the lines suggested by Greg Locock.

View attachment 14959

This would suggest a 45 degree distribution width is conservative.

 

[SE2607]

I find it remarkable so many people in this thread have spent the significant time discussing a 45degree shear lag when we have a UDL line load. I've been very confused by most of this.

You lack creativity in your wordsmithing.

 

[EngDM]

If the UDL is perpendicular to the fixed edge, and the plate is much longer than the UDL extending away from support, I don't see why you'd use a unit width. If the UDL was running parallel to the fixed edge, then the bending would be uniform about the support, but in the case illustrated by BA's sketch it seems yield line would be more appropriate.