shear forces acting on two unconnected timber beams

[mats12]

Lets say we have 2 timber beams - cross section of a single beam is 180/180 mm

We put one beam on top of the other but we do not connect them at all.

Max shear force above second support is 32,50 kN
What happens to shear stresses in beams? Does shear force distribute based on stiffnes of cross section - in this case half on each beam: 32,50/2 = 16,25 kN?
Or does the bottom beam take over whole force of 32,50 kN?

 

[jayrod12]

I think you may get a number of answers that go either way.

Personally if it was a new design, I would be designing a single beam for the entire shear force. If I was checking an existing condition, I may check the stiffness distribution if required to make it work.

 

[gravityandinertia]

My personal thoughts would be it depends on whether they are connected in a way to carry a moment with composite behavior. If they don't, then you can't think they work together for shear. Basically, one will transfer the shear to the other, and each needs to resist the full shear amount.

I'm speculating this entirely off the fact that shear is the derivative of moment. So if you're moment isn't composite behavior, then your shear won't be either.

 

[EngineeringEric]

To me, if each one is of equal stiffness, each one takes half the load based on stiffness. if we have half the load, half the moment, half the deflection, i would argue half the shear. I will say that you may run into variations due to bearing conditions changing so maybe the lower one take more.

But, this is if analyzing existing. If i was doing my own design, i would design the lower one for all the shear. Rarely does shear ever govern in my experience.

Your example of a cantilever seems to be governed by deflection at tip or possibly negative moment.

 

[SLTA]

In the proverbial vacuum, each would take half. In the real world, there's friction from the load acting between the two which would transfer some of the shear.

Is this a real world problem, or a homework problem?

Please remember: we're not all guys!

 

[MotorCity]

If the two beams remained in full, perfect contact as they deflected, then I would say each shares 1/2 of the load. In reality, full contact will not occur because the deflected shapes will not be exactly the same since one beam is "stretched" more than the other. Think of a simple span beam. The beams would be in full contact at midspan, and the gap between the beams would slightly increase as you go from midspan toward one of the supports. In other words, one beam will slip on the other (which is the reason to connect them if you want each to share 1/2 of the load).

 

[JGard1985]

Agree with Motror City & EngineeringEric. Just make sure you don't have a load case that puts the left hand support into tension!

Jeff
Pipe Stress Analysis
Finite Element Analysis

http://www.xceed-eng.com

 

[straus12]

Not my field, but I have to ask since its somewhat right topic to ask:
why do you guys design beam (at 2nd support)for shear based on force 32,50 kN and not on 32,50 + 30 kN = 62,50 kN (reaction of support). What is the science behind that?

 

[jayrod12]

The beam itself never sees the entire reaction force as shear. Once the load has gotten to the support, it only sees that load in bearing. For wood and concrete, the shear demand is based on shear at the beam depth away from the support, therefore it would never see the shear load from the adjacent span.

 

[dik]

If the timbers are the same, then the shear stress at the interfaxe is 1.5*V/A (A is the total area of the two pieces) and you have to connect the two pieces for this shear stress. Use glue, or a whole bunch of nails or bolts or whatever...

Dik

 

[mats12]

Thanks for answers.

I got another question about bending stresses.

If we connect both beams properly we have a composite cross section that acts as one element.

But if we dont connect them at all, how do you control bending stresses?

are equations bellow alright?

Im wondering can you add up section modulus (sum W1 + W2) of cross sections when beams are not connected?

 

[KootK]

In my opinion, for the non-conposite case, both beams will share moment and shear about equally. Ultimately, local effects will require some of the shear in the upper beam to pass through the lower beam en route to the support. I'm comfortable saying that likely occcurs within "d" of the supports, however, and therefore does not materially affect the low beam shear. The low beam does need to take 100% of the bearing stress of course.

In practice, I'd be inclined to design each beam for 60% of the load.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JLNJ]

The moments are distributed by the relative stiffness (moment of inertia), not just by the section modulus. For beams of uniform materials and width, this is the cube of the relative depths.

I.e. if one beam is twice the depth of the other, it will be eight times as stiff and suck up 8/(8+1) or 88.9% of the moment.

So, yes, you can simply add the section moduli, but only if they are equal. The moments of inertia can be added directly regardless of the relative depths.

 

[IDS]

We have discussed this at very great length before:

http://www.eng-tips.com/viewthread.cfm?qid=379229

But for full length beams of equal cross section the answer is simple: both beams have the same curvature along the full length, so they have the same bending moment, so they must have the same shear force at any section, so they both have 50% of the total shear, assuming plane sections remain plane etc.

Of course in the real beams the shear force doesn't transfer to the support at a vertical plane at a point support, but the end shear transfer mechanisms are just the same as for a single simply supported beam, so on that basis taking 50% of the shear on each beam can be justified. On the other hand, it's an unusual situation, so KootK's 60% rule also seems reasonable to me.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/