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.

 

[JAE]

I think you would have a stress varying vertically - You show a triangular stress, I wonder if it would be positive on top and negative on the bottom of the tread (i.e. a bow-tie shear diagram shape)

 

[msquared48]

I think it could be more like a pole footing type of distribution.

Mike McCann
MMC Engineering
Motto: KISS
Motivation: Don't ask

 

[ishvaaag]

In the thread, for vertical support for almost any washer a truncated cone in shear about 2 mm wide ring below and say 45 deg aperture above can develop, then calculate shear for a cylinder amidst that truncated surface cone. For lateral support a fixity scheme for a cantilever may work.

 

[cntw1953]

I tend to agree with placing a concentrate load on top of the u notch as indicated by your question "pressure concentrated here?". There is also a concentrate load at inner bottom corner of the notch to form a couple and a horizontal resisting force.

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.

 

[BAretired]

It is not a clearcut question. The answer relies on workmanship. Does the spindle bear tightly against the timber? Is the bolt extending through the wood tread tightened to a snug fit?

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

 

[hemis]

Thanks for the response.

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.

 

[ishvaaag]

If you are trying to treat the truncated cone shear surface mathematically then you may find usefull Mathcad. You set mathematically the equilibrium, then instruct the program to search for the solution (if there's a single one) or optimize for the safest value that gives the lesser resultant available from the setup as portraited in your model.

 

[hemis]

Dear ishvaaag

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.

 

[hemis]

If I modelled the spindle connection using an FEM program, would I get an accurate result? I have only used FEM once or twice (never trusted computers).

 

[BAretired]

The thickness of tread and depth of recess are important variables. The size of bolt is also an important variable as it will effectively act as an extension of the spindle.

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

 

[hemis]

I would model the tread using the tables provided in EN338 for D35 timber. The bolt would add a pre-tension equal to the load/area of the spindle-bearing in the dowel (area = 1475mm2, stress perp. to grain = 2.8 N/mm2, F = 2.8/1475 = 4 kN). I suppose reinforced concrete behaves similarly but timber instead of concrete.

 

[hokie66]

I don't really have anything to suggest about the detail, except to say it is a poor detail if the balustrade spindles are cantilevering. It will be very flexible, especially after shrinkage takes place.

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.

 

[BAretired]

In conclusion, your detail is not very good. Try to come up with a better one.

BA

 

[hemis]

The stair exists, the handrail is firm, it looks good and the architect that designed the stair is very happy. For some reason, I always get the job of checking the work after its built!

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

 

[woodman88]

Base on the NDS (National Design Specification from the American Wood Council) Appendix I "Yield Limit Equations for Connections" assuming the bolt will not bend. Failure due to moment would most typically be a Mode Type II (divided by two as you have only a single wood member). But the NDS assumes that the bolt is 1" or less in diameter with a standard size washer each side of the connection. See the attached file.
Personally, I would not do or approve this type of connection for a handrail in wood.

Garth Dreger PE
AZ Phoenix area

 

[ishvaaag]

Well, I certainly referred to some kind of extension of the theory used in reinforced concrete. With a washer of minimum strength, it needs be to be sheared through the wood to make the joint fail in shaft tension. And anytime you use a washer in tension the compressive forces concentrate mainly in a ring mainly near the shaft. So a truncated cone may not turn an exorbitant proposal. Just for learning next days will look about someone thinking (in written) along these lines.

 

[hemis]

I have managed to obtain a picture of the stair under construction.

 

[JLNJ]

Maybe you can significantly decrease the spacing on your anchoring posts and share the load better.

 

[BAretired]

The holes in the photo appear to be too close to the end of the tread.

BA