Bending Section Modulus Changing

[Jalbno]

Hi everyone, I have a scenario where a plate is bearing on a 2x12 lumber.

I am analyzing the bending in the bottom timber as a cantilever from the edge of the plate.
The bending resistance of the timber is Mr = Material Factor * S * Fy

My question is what I should use for the section modulus. I assumed bd^2/3, with the neutral axis being in the middle of the beam.
A colleague of mine is confident that the section modulus should be bd^2/6, with the section modulus being at the edge of the beam because it is bending around the plate.

any ideas or clarifications?

 

[BridgeSmith]

Last time I checked, the section modulus for a rectangular section with the neutral axis through the center (which I believe is correct for the case shown) is bd^2/6.

Also, "Fy" is generally the yield stress for steel, which is not applicable for wood design.

I'm also not sure about your assumptions for the loading. Is the 2x12 on a soft surface? Have you verified the critical section is at the edge of the plate, and not at the center where the load is applied? Moment at the point of load application checked against the capacity of the plate summed with the 2x12 lumber may be more critical, based on the proportions shown.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[MegaStructures]

Is the steel mechanically attached to the wood? If so this is a composite section and should be analyzed as such, not a cantilever?

If not, then I don’t see why the bearing force isn’t just a distributed load on the simply supported beam?



“The most successful people in life are the ones who ask questions. They’re always learning. They’re always growing. They’re always pushing.” Robert Kiyosaki

 

[Jalbno]

Hi BridgeSmith,

Thanks for your information regarding this. You're correct about Fy for steel, I should have written Fb for timber.

The 2x12 is on a soft surface, the ground with a bearing capacity of 150kpa.

 

[BridgeSmith]

Ok, so the cantilever check with the load uniformly distributed should be somewhat conservative. You should still consider the case of bending of the plate and lumber about the point of application of the load.

Rod Smith, P.E., The artist formerly known as HotRod10

 

[Jalbno]

Thanks BridgeSmith, and MegaStructures for your insight!

Considering the bending of the plate and lumber about the point of application of the load would mean treating it as if it were simply supported?

Thanks,
NJ

 

[ProgrammingPE]

If the neutral axis was at the top of the wood, the stress in the wood would vary from 0 at the top to fb at the bottom. This would mean that the entire section is in tension. Since there is no external tension force, the section would not be in equilibrium. The neutral axis should be located at the centroid where it will be in equilibrium. S = bd^2/6 (BridgeSmith's formula is correct.)

The maximum moment will also be at the center of the steel plate. Even if the applied load was uniform over the steel plate, this would still be true. The moment increases until you reach the point of zero shear which is at the center of the plate due to symmetry.

I wouldn't be considering the wood and plate as a composite section unless I was really trying to get something to work. (The wood would obviously still have to work on its own for the moment up until the edge of the plate and also up until you have enough fasteners between the plate and wood for the section to be composite.)

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[BridgeSmith]

Considering the bending of the plate and lumber about the point of application of the load would mean treating it as if it were simply supported?

Same as what you were doing, except the cantilever length is from the end of the 2x12 to the point load location (center of the plate & 2x12).

Rod Smith, P.E., The artist formerly known as HotRod10

 

[BAretired]

Hi everyone, I have a scenario where a plate is bearing on a 2x12 lumber.

I am analyzing the bending in the bottom timber as a cantilever from the edge of the plate.
The bending resistance of the timber is Mr = Material Factor * S * Fy

My question is what I should use for the section modulus. I assumed bd^2/3, with the neutral axis being in the middle of the beam.
A colleague of mine is confident that the section modulus should be bd^2/6, with the section modulus being at the edge of the beam because it is bending around the plate.

any ideas or clarifications?

Your colleague is correct. S = bd^2/6.

Further clarification: maximum moment in the timber beam will occur near the end of the steel plate provided the steel plate can span its length carrying full uniform load, with a deflection less than that of the timber beam. Otherwise, steel and timber will share the load in proportion to their respective stiffness, EI.

But even if the plate is infinitely stiff, the length of cantilever should be increased slightly to account for length of bearing at the end of the plate.

BA

 

[dik]

for plate I always use Z = b*d^2 / 4... I had a problem yesterday with a lag screw connection that was failing and realised that I had included for prying action; the program was usually used for steel. I realised that with wood, prying action would not likely occur.

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[BAretired]

dik,

I think the question is about stress in the timber beam, not the steel plate.

BA

 

[dik]

My mistake, I thought it was the steel plate... the lag screw problem was real...

Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?

-Dik

 

[BridgeSmith]

I think the question is about stress in the timber beam, not the steel plate.

It was, but checking the moment at the point of the load, also, is prudent, unless there's stiffening for the plate that's not shown.

Rod Smith, P.E., The artist formerly known as HotRod10