T-Beam with a combination of shear + moment 2

[Logan82]

Hi!

I have to evaluate a Beam in a T form receiving Shear + Moment at a moment connection.

The CSA S16-09 does not give a combination criteria in the form of Vf/Vr + Mf/Mr.

It there a combination criteria in a structural standard that would verify this? Or do I have to check this using mechanics of deformable solids theory?

 

[BAretired]

Shear and moment can be checked separately. The I-Beam takes all of the shear. The combined moment of inertia is needed to check moment.

For a cantilever, lateral torsional buckling must be checked.

BA

 

[Enable]

Well, we do have clause 14.6.a which discusses a combination of moment / shear in the context of longitudinally stiffened girders (it's the only clause I know of dealing with it explicitly)

0.727 Mf / Mr + 0.455 * Vf / Vr <= 1.0

However, our Euro brethren do have such a clause (6.2.8.2 of Eurocode 3). In their case, if shear demand is less than 50% of the capacity at the point you are checking, no capacity reduction is required. However, if Vf / Vr > 50% you do have a reduction and they give an equation for it.

 

[Logan82]

@BAretired:
Thank you for your answer!
Note that this is not a cantilever, but a beam with 1 support at each extremity of the member. Both ends are fixed (moment connection).

Also there is no I beam, it is a custom T-Beam built of a cut S-Beam and a channel, so there is no bottom flange.

@Enable:
Concerning clause 14.6, I do not have stiffened girders.

Thank you for the Eurocode 3 reference! In which part of the Eurocode 3 is the section 6.2.8.2?

 

[Enable]

I know you don't have a girder of that vintage, I was just saying that's the only clause I know that deals with it at all in S16!

The clause you are looking for can be found on page 55 / 93 of this PDF (EN 1993-1-1 (2005))

 

[Agent666]

NZ stele code also has a shear/moment interaction formula for what it is worth. Similar to Eurocode there is no interaction if V* is less than 60 percent of the shear capacity, nor moment greater than 75% of the moment capacity (refer to interaction diagram plot below):-

Keep in mind for a tee as well that the shear stress distribution is not uniform/symmetrical like the web of a doubly symmetric I section member, so you'd need to apply whatever provisions are in your code for assessment of that. In the worst case there would usually be a further max reduction to the shear capacity of 0.83 which corresponds to a rectangular section where the ratio of max shear to average shear is typically 1.5. This 0.83 can be used conservatively in your situation for a tee.

The leg of the tee if in compression may be slender as well and subject to local buckling/slenderness effects, so you'd need to consider that as well in working out the plastic moment capacity and the effective section.

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