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Two Point Loads on Stair Treads

Two Point Loads on Stair Treads

Two Point Loads on Stair Treads


I need to determine the max deflection of a FRP (fiberglass-reinforced plastic) stair tread subjected to two point loads. Here below a picture which illustrates loads and dimensions:

Does anyone know any formula to calculate the deflection (assumed to be at the center of tread)? Since FRP is anysotropic, to simplify the problem we can assume it as 2 point loads exerced on a simply supported beam.

Any advice is welcome


RE: Two Point Loads on Stair Treads

You want to use superposition for two cases, one for each point load. Or a quick Google search gives this:

Depending on the material properties, shear deflections might also be important

just call me Lo.

RE: Two Point Loads on Stair Treads

Hi Lo,

thanks for your quick reply. I came across the same calculator on structx.com. Unlike steel, shear deflections shall be calculated for this material. Do you have any formula that takes into account both bending and shear moments for this particular load?


RE: Two Point Loads on Stair Treads

I wouldn't expect on a span of this amount that we'd be getting into significant shear deflections. Especially considering that FYP is elastic essentially until rupture. If it works for overall strength, then the stresses should be low enough that shear deformations don't play a huge role.

I assume this is a short term loading check? Otherwise there is the potential for creep in FRP structures.

RE: Two Point Loads on Stair Treads

This thread provides classic solution to deflection due to shear deformation. Link

RE: Two Point Loads on Stair Treads


RE: Two Point Loads on Stair Treads

I have found this online:

The question the arises: why is the bending component different from the one shown on Structx.com?

RE: Two Point Loads on Stair Treads

Sorry I found the answer by myself:

They considered half the load for the equation.

This thread can be closed.


RE: Two Point Loads on Stair Treads

The real question is how much of the tread width do you consider effective?

I would ignore the shear deflection effects and use 150mm of the 275mm as effective resisting the load at the nosing.

RE: Two Point Loads on Stair Treads

I once worked for an FRP manufacturer and designed structures with FRP shapes. It is customary to include shear effects in deflection calcs. In the steel joist business, I've seen people calculate the Ix of the chords, use that as an equivalent beam, and then add about 20% to the deflection to account for the shear effect in the web members. I suppose for a shortcut you might consider that method. Anyway, you don't always have to be exact, but you shouldn't ignore shear in FRP.

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