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.

 

[jhnblgr]

Post a sketch

 

[Lomarandil]

If the load is uniform in the direction parallel to the fixed edge, you'd typically design that on a unit length basis.

 

[SALTRAM4567777]

The load is perpendicular to cantilever plate as a UDL.

 

[HTURKAK]

The load is perpendicular to cantilever plate as a UDL.

Is this UDL line load or area load? Post a sketch.

 

[SALTRAM4567777]

I am trying but I am not able to attach a sketch. Some issue on my side. It's a UDL Line load acting perpendicular .

 

[BAretired]

Line load perpendicular to fixed edge. 45 degrees looks okay to me.

 

[human909]

Treat the plate as a simple cantilever beam. You have a long line load so it is just a simple cantilever calculation with a point load of a unit length x UDL. for a beam that is a unit length wide.

 

[SALTRAM4567777]

Thanks @BAretired for posting the sketch.

I understand simplifying it to a unit-width cantilever beam with UDL. My only doubt is about the effective width. For a point load on a plate, we often assume 45-degree load spread to calculate bending resistance. In the case of a continuous line load along the length, do we still consider same effective 45 degree effective width, or is treating it as a unit-width beam sufficient for plate thickness design?

 

[SE2607]

Thanks @BAretired for posting the sketch.

I understand simplifying it to a unit-width cantilever beam with UDL. My only doubt is about the effective width. For a point load on a plate, we often assume 45-degree load spread to calculate bending resistance. In the case of a continuous line load along the length, do we still consider same effective width or beyond unit width, or is treating it as a unit-width beam sufficient for plate thickness design?

I can't understand how it can be anything other than having a unit length to resist a uniformly distributed concentrated load at the end of the cantilever. Please enlighten me. I'm new at this stuff. I only started doing structural engineering 48 years ago.

 

[SALTRAM4567777]

If this case was as simple as you suggest, it would be covered in Roark’s — but it’s not. The closest case is a plate clamped on one edge with the others simply supported. Using a 45-degree effective width from that logic gives a plate thickness far higher than FEA results, making it overly conservative. My question is purely how to determine realistic effective width, so we avoid unnecessary overdesign — not to oversimplify a complex plate bending problem. Years of experience don’t always translate to understanding.