Shear problem
Shear problem
(OP)
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.
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.






RE: Shear problem
RE: Shear problem
Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask
RE: Shear problem
RE: Shear problem
The horizontal resisting force works on the remaining area below the noth, thus the remaing area suffers tension and shear, I think shear will control though.
RE: Shear problem
How might the stair tread fail? Probably by a shear failure each side of the spindle. A chunk of the tread would simply pop out.
BA
RE: Shear problem
The spindle is a tight fit and probably is dowelled deeper than shown. The bolt and washer are a tight fit.
I thought that the washer would act as a lever and dig into the underside of the tread. The bottom edge would then be a fulcrum putting all the pressure on the top lip (I am looking for the worst case scenario). The top fibres would crush - localised bearing pressure (shear perpendicular to grain) - until a surface area would be achieved that could resist further deformation or the timber would shear or split along the grain. I am trying to picture the surface area resisting the shear. As the surface area increases, the angle of the bearing-area rotates and the resultant force moves down. Its a non-linear problem but I am trying to put math to it.
RE: Shear problem
RE: Shear problem
I am not sure what you mean by the truncated cone. Do you have a reference that I may read to get an understanding.
I submitted my calculation by treating the problem as single-shear on the bearing-area of the dowel. The timber is very under-stressed so should be ok. Doesn't detract from my inability to analyse the problem (in time) though.
RE: Shear problem
RE: Shear problem
How does the system behave? If you place a dowel in a tight fitting hole with no bolt, it can carry moment by bearing against the sides of the recess (a bow tie stress distribution as stated above).
If you omit the recess but use a bolt, the spindle can carry moment by compressing the wood on one side and tensioning the bolt. Shear can be carried by a combination of bolt shear and friction from the compression between steel and wood.
If you provide both recess and bolt, the problem becomes one of strain compatibility. It could be solved using FEM if you know the properties of the wood with any degree of confidence.
BA
RE: Shear problem
RE: Shear problem
If the top rail is stiff enough to take the load, then the detail is not so bad. In that case, you would just need galvanized or stainless screws to tie the spindles down vertically. These wouldn't need to be at every spindle.
RE: Shear problem
BA
RE: Shear problem
I was checking the tread and part of the check involved the failure of the bolted connection, or, how it would fail. In the end, I checked the connection against shear using the logic used in the Timber Designer's Manual. I only have a limited number of timber books so I could not find an example on leverage. I have split many pieces of timber using a crow-bar (never on beech) so I have a fair idea how the step may fail. To be fair, if the handrail fell off and all the load were placed on one of these spindles, the spindle would bend before the beech would break.
However, after this discussion, I think I am able to solve the problem for myself. Your comments on the bow-tie effect and strain compatibility and the pre-stress applied by the bolt have made the problem much simpler to envisage. May even test it out in the workshop.
Still not sure what the "truncated cone" theory is though? I have an idea but I am thinking of punching-shear.
Cheers. Good forum
RE: Shear problem
Personally, I would not do or approve this type of connection for a handrail in wood.
Garth Dreger PE
AZ Phoenix area
RE: Shear problem
RE: Shear problem
RE: Shear problem
RE: Shear problem
BA
RE: Shear problem
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
RE: Shear problem
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
RE: Shear problem
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.
RE: Shear problem
BA
RE: Shear problem
RE: Shear problem
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
RE: Shear problem
RE: Shear problem
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
RE: Shear problem
Garth Dreger PE
AZ Phoenix area