Plate bending and effective section
Plate bending and effective section
(OP)
A simple plate bending problem. A 1/4" plate (say 8" x 4") is bolted by one bolt and has about 400# load at the edge.
What will be the effective area to calculate the section modulus? I believe I can not use the full anle length. And what is the reference for this? I have in past taken effective width as 4 x t. Thanks.
What will be the effective area to calculate the section modulus? I believe I can not use the full anle length. And what is the reference for this? I have in past taken effective width as 4 x t. Thanks.






RE: Plate bending and effective section
The book "Formulas for Stress and Strain", by Roark, discusses the subject under the section "Beams of Relative Great Width". The effective width depends on the type of supports (free or fixed), the manner of loading (concentrated or uniform, and the ratio of width to span.
For a cantilever plate with a concentrated load on the edges, as is the case of hoist wheels hung from the bottom flange of monorail beams, I have used an effective width of 2 times the distance from the edge of the flange to the web of the beam.
For plates spanning between two continuous supports, I believe the effective width is close to 16 times the plate thickness.
RE: Plate bending and effective section
I also assume your bolt has a nominal diameter of about 5 mm and a hardened, thick washer with OD of about 11 mm. I assume overlap of your plate with the bolted interface is 20 mm, which makes your cantilever length about 80 mm. I also assume your plate is bolted to a relatively very stiff interface.
For this specific problem (which should be assumed nonscalable to other thicknesses, plate aspect ratios, and load values unless proven otherwise), and under all the above assumptions, the effective width of your cantilever beam w.r.t. plate deflection appears to be about 11.0*t, whereas the effective width w.r.t. plate stress appears to be about 9.3*t.
Why the effective width is different w.r.t. deflection versus stress I can only attribute to the unusual boundary conditions (BCs), stress concentrations, etc.; i.e., the BCs are not the same as a plain cantilever beam. And note that the above answer is different from dlew's 16*t, because you have different BCs (as he qualified).
Given your applied load and an effective width 9.3*t, your plate appears highly overstressed (assuming steel A36). It appears you would need to increase material tensile yield strength to something like 600 MPa (87 ksi), or increase your A36 plate thickness to, say, 8.5 mm. Also check the bolt stress. The above assumes the bolt holds, but I didn't check it. Another possible option, though I didn't check it, might be to add another bolt, to reduce a detrimental stress concentration you're getting near your one bolt (caused by having only one bolt).