Shear problem

[hemis]

I am trying to work out the possible failure of a stair tread. I attach a drawing.

If the spindle is pushed to its extreme, how would the stair tread fail? (assume the steel bits are strong enough).

Do I apply the force P as a shear stress concentrated on the top of the dowel or as a force uniform across the bearing. Which shear area do I consider? A cut through the timber or the bearing area of the timber - both seem logical to me.

Timber is European Beech D35 grade, Steel Stainless.

 

[hemis]

Thank you for your comments.

For what its worth, and I do love a peer review, I attach the work that I sent to the local authority. I was checking an existing stair.

Feel free to criticise the content; It's the only way I learn.

Regards

 

[trainguy]

In response to your original question, the tread will fail in bending - no doubt about it. A chunk of stair that includes part of the bolt hole will rupture.

It really does look like it was designed by an architect...

"Having said that" (reference to comedians Larry David and Jerry Seinfeld), I'd be curious to hear the results of your test.

tg

 

[Ron]

hemis...the actual distribution is a bit more complicated than would first appear, but I would consider your bearing area after initial mobilization to be about 1/2 the projected diameter of the spindle. It would act on a dual surface from the top of the tread to the spindle counterbore depth, from the counterbore to the edge.

That's a little conservative since the actual shear area will extend in a triangular distribution from the bottom of the counterbore to near the bottom outside edge of the tread.

Also, you will have a notch effect at the bottom of the counterbore.

 

[BAretired]

If the spindle is too close to the end of the tread, you could have a splitting of the tread starting at the top of tread and extending down as the spindle is pushed out.

BA

 

[cntw1953]

The question is why the holes dislocated that much.

 

[BAretired]

The spindle has a diameter of one inch. It will be prying against the top of the wood tread when an outward force is exerted on the handrail. The end distance (center of spindle to end of tread) appears from the photograph, to be about one inch.

The minimum permitted end distance for a one inch bolt by CSA 086 (Canadian code) is 7", so the spindle appears to be too close to the end of the tread.

BA

 

[cntw1953]

My claim was on the first step from right, the inner edge of holes looked like fell right on the wood seam. The bore holes on the next (middle) step seems centered. It may not have any significance, just point out what was observed from the photo.

 

[hemis]

Chaps

You are frightening me. This stair is not going to move. A herd of elephants are not going to hurt this stair. When I was putting together my "modes of failure" list, I considered the handrail falling off, or the weld failing, and the bar being pushed or pulled in its socket. BAretired kindly offered the advice about the moment, compression on the bolt and strain compatibility and that is where I am going to look.

I will take on board all the advice on centre-ing and edge space-ing and if I ever have to design a stair I will remember.

Many thanks

 

[woodman88]

hemis, Wood changes over time, so what it is today will not be what it will be like ten years from now. This is something many people do not understand. The edge distances, design values, formulas, etc. for wood design account for this. I just hope that when the handrail becomes loose that they replace the wood and not just keep trying to tighten (and thus crush the wood) the bolts.

Garth Dreger PE
AZ Phoenix area