Notched timber beam capacity 1

[cobadger]

I am checking the design of a simply-supported, notched timber purlin and need some advice. Based on the NDS section 3.4.3.2, I have calculated the shear capacity of the notch, which is on the tension side on each end of the beam. This calculation yields of capacity of 1402 pounds. If I determine the max. beam length allowed based on shear, and excluding the load a distance "d" from the ends, the max length is 12.24 ft.

When I calcalculate the max. moment capacity of the beam, I have end/support reactions of 1567 pounds and a max length of 9.50 ft.

Am I correct in thinking that moment controls even though the reaction exceeds that of the allowable shear?

Thanks for your advice, Alex



Section 3.4.3.1 of the NDS says I do not have to include the load

 

[UcfSE]

Does the 1567 lbs represent the reaction due to the full load across the beam to calculate moment or the reduced load for calulating shear?

If you can discount load for calculating shear, do so. I think you still have to use the full load for moment. I would check the full loading for bearing at the reactions as well as deflection. I would then check the appropriate Vr' in 3.4.3.2 for shear. The important thing is to be consistent and not apply reductions where they don't make sense, such as using the reduced design shear load to check the end bearing.

 

[cobadger]

UcfSE thank for your help.

The 1567 includes the full load across the beam, as do the bearing calcs. The only place I have taken a reduction is according to 3.4.3 for the shear loading. It all seems correct, but it just seems odd to have a reaction load higher than the shear capacity. When you do a shear and moment diagram, the load covers the entire beam...as there isn't any reduction for shear. I know I could be conservative and assume the shear load goes to the beam ends, but I would like to know if my initial approach was correct.

Thanks again.

 

[UcfSE]

You're taking the load across the full length of the beam for the reaction and across a reduced length of the beam for shear, so the shear design value should logically be less than the reaction when you do this. The reason you can take a reduced load for shear is because the load within a distance "d" of the support is assumed to travel to the support directly through compression across the cross section rather than through bending and shear. I would make the shear force diagram for the entire length of beam and then come in a distance "d" from each end and find the shear at that location. I would then use this shear to compare with the Vr' you found in 3.4.3.2. That way you are comparing shear load to shear capacity instead of getting hung up on comparing shear capacity to bearing load. Alternatively you could not bother with reducing the shear load. This procedure by the way is similar for what is done with concrete beams as far as disregardign load close to the support for shear.

 

[RARWOOD]

My first advice is to base your design on the 2001 NDS. The provisions regarding tension side notches is much more restrictive than what was in the 97 N.D.S. In the 2001 NDS. the multiplier of the un-notched depth divided by the notched depth is squared. Also if you are dealing with glulams the puplished shear values must be reduce 20% when dealing with notched members ( see the NDS Suplement foot notes).

With an un-notched beam when dealing with uniform shear loads you are check the shear capacity at a distance d from the face of the support. The reaction is higher than the shear load because you are not checking the shear at the support. I always found it easier to check the stress so what I would do is calculate the shear a distance d from the support and then determine the shear stress at that point.

Neglecting the load a distance d from the face of the support is similar to the way stirrups were design for concrete when I was designing concrete beams 10 years ago. At that time you were allowed to base the strirrup spacing from the face of the support out to a distance of d on the shear at distance d.

To be quiet honest I am not sure that I ever understood why. I was always told that the load between d and the support face was tranmitted to the support by diagonal tension.

Returning to the 2001 NDS, there now are restrictions regarding the neglect of concentrated load between the face of the support.

One final item it is my understanding that when checking the shear in a notched beam you are not allowed to neglect loads a distance d from the support. The NDS indicates for notched beams the shear should be calculated based on engineering mechanics.

You could consult the NDS commentary or AFPA for more information.

 

[miecz]

If you are checking an existing beam, then use the length of that beam. Find the load that gives the limiting shear and the load that gives the limiting moment. The minimum of the two is your governing load for that beam.