Design of two story x-braces.

[IngDod]

Greetings,

I would like to ask if anyone can share an example on how to design a two story x brace connection... I am specifically confused as to how to find the shear and moments at different parts of the gusset plates in order to check its limit states. My initial approach (with chevron braces) was to cut the connections at different planes and draw free body diagrams to get the internal forces at the gusset... however after reading the AISC 14th design example I cant seem to reproduce the results for the chevron brace connection and the statics part of the example is not very detailed so I cannot find my error.

What I was doing (for chevron braces.. I have not even tried two story x-braces which is what I actually need) is... Since the two braces have a concurrent point (point A) at d/2 of the beam I decomposed the forces in X and Y directions and add them at this point.. the resultant is the reaction to keep the connection in equilibrium.. as expected I am getting no moments only a vertical(when loads in the braces don't have equal magnitude) and horizontal reaction... After this I perform a horizontal cut right where the gusset meets the beam and using the reactions at point A I can find the shear force and moment at the gusset. After this I figure I need to perform a vertical cut on the connection in order to get the vertical shear on the gusset as well as the moment.. But here is where I simply cant reproduce the results; what I was doing is cutting the connection vertically in half... so that the forces acting on this half are the forces at point A and the external forces from one of the braces.

Thanks.

 

[BAretired]

Are you talking about Example II.C-5? If so, where is the discrepancy between your result and the example. If not, what example are you addressing?

BA

 

[IngDod]

Thanks, yes I was referring to that particular example.. More than a discrepancy is that I cant seem to understand how Mu1' and Mu2' are derived. I thought I could just cut the connection horizontally at B and get the moment at this point using only the forces at the workpoint... but the results I get are very different from the example.

I found another example in the seismic manual that is much closer to my actual situation (2 story x brace), here the only critical section on the gusset that they consider is a horizontal cut close to the beam-gusset interface.. they do not check the vertical critical section (a section that cuts the gusset vertically in half). Also they do not check interaction between shear, axial force and moment at the gusset horizontal section.. which is something I would like to do.. I found the steel tips written by Doctor Astaneh and he recommends using the following:

M/Mp + (P/Pn)2 + (V/Vn)4 < 1

Mp, Pn and Vn are the capacities of the gusset plate.. Pn and Vn I completely understand in the context of gusset plates and I am getting the appropriate limit states from the manual.. I am however confused with Mp.. Is this simply 0.9*Fy*Z of the gusset plate?.. Section F11 of the manual has the provisions for rectangular bars.. but I don't think they are meant to be used for gusset plates where the depth is very large.

 

[IngDod]

Sorry for reposting... I am somewhat confused as to how the transfer of forces happens in this connection... I am attaching a sketch of the connection with the forces to see If someone can tell me If I am on the right track or very wrong. Basically I am trying to get the internal forces in the gusset so I can design it... I have read various examples but the statics part is still confusing for me. Thanks.

 

[BAretired]

IngDod,
I started looking at the example and haven't quite figured it out yet, but check thread507-322006 for some additional information.

BA

 

[IngDod]

Thanks for taking the time to help me with this. I will check it.

 

[BAretired]

IngDod,

On your X-brace forces, if you design the beam for an uplift of 5780# at midspan, it will deflect upwards, but it can't deflect upward or downward without loading the bracing members, so I think you have to equalize the forces in the two braces above the second floor and in the two braces below the second floor in order to remove the net uplift at midspan.

If you take the upper brace forces as (8100+6075)/2 = 7090# each and the lower two forces as (25300+35500)/2 = 30400# each you will have a net vertical of 0.

The upper gusset plate is unaffected by the first story shear, so the moment on the intersection of the upper gusset plate and top of beam will be 10,026*d/2, not 32,970*d/2 as you are showing.

Similarly, the moment on the intersection of the lower gusset plate and the underside of beam will be 42,990*d/2, not 32,970*d/2 as you are showing.

This would be consistent with a second story shear of 10,026# and a first story shear of 42,990# carried by this cross brace.

BA

 

[Agent666]

Dont forget there is probably a moment and shear in the beams to add into any equilibium equations especially with uneven brace forces. I fthe brace connections are not 'pinned there is probably a moment and shear int he braces also Without these you won't neccessarily be able to fully satisfy equilibrium of the system.

 

[IngDod]

@BAretired: Thanks, I see it know there's no way the beam can deflect vertically without loading the braces... this is why in the seismic manual the beam in two story x-braces is not required to be designed for an unbalanced load when one of the braces buckles. The axial load will still exist in the beam as it can move horizontally. Also I think my error when determining the shear forces in the gussets is that I resolved the forces in the working point (middel of the beam) and then worked my way to the gusset from there.. Ignoring the forces in the braces... I failed to treat the resultants in the working point as a reaction and I consider them as the external force instead.

@Agent666: Thanks,the braces are hss slotted to the gusset.. so this connection should be purely axial. I am curious.. can the braces generate moment in the beam even though they all act concentrically trough the working point?. I mean.. If this was a chevron brace any unbalance in the brace forces would result in a vertical force that will cause moment in the beam, but as BAretired pointed put that would not happen in this system.

 

[Agent666]

Rethinking it you are correct, I agree moments will be small in the braces given your configuration as depending on the scale of the connections it's probably safe to consider them as pinned. Mostly secondary actions come about from axial shortening and lengthening as the frame can skew a little. There will always be a small amounts of load transfered into the beam depending on the axial stiffness of the members and resulting non linear effects.



If there is an unbalanced loading on the beam from a floor this can also be the transfered into the braces depending on the degree of fixity created.

 

[BAretired]

Getting back to the original question about Chevron bracing, I am attaching a PDF of AISC Example 11.C-5 showing calculations for a Chevron brace. Page 11C-59 presents calculations in both LRFD and ASD for moments at Points A and B, the locations of which are shown on the next page.

It seems to me that the calculations marked "At Point A" are intended for a point between A and B at the connection of the gusset plate to the underside of beam (Section a---a) because the moment at Point A is zero.

The calculations marked "At Point B" are a mystery to me. Can anyone figure out where the expressions for M[sub]u1[/sub]' or M[sub]u2[/sub]' come from?

I also question the basis for the Shear formula on page 11C-61 but in any event, it does not seem critical in the example selected. I wonder how many engineers carry out analysis of gusset plate internal forces at vertical section b---b. I know I never did.

BA

 

[WinelandV]

BA,

This came up in an earlier thread (possibly 10 or months ago), and yes, the forces "at point A" are really the forces on plane a-a, and point B relates to plane b-b. I've never been able to come up with those moments (Mu1, Mu2) myself, either.

I have run the analysis of the plate across section b-b, but have never liked it. You end up checking for combined bending and compression across that section in many cases, resulting in either a really thick gusset, or needing a stiffener to keep the free edge from buckling. For braces that are very shallow in reference to the horizontal (less than 37 degrees or so), I've gone so far as to use (2) individual plates so that I don't have to carry out that check.

As far as why the check, I'm not entirely sure. I started doing them because it's hard to argue with a reviewer who points out that AISC recommends doing them.

 

[BAretired]

winelandv,

I'm pleased to hear that I'm not alone. The earlier thread you mentioned is probably the one I cited in a post near the beginning of this thread, namely: thread507-322006. Unfortunately, I did not find a satisfactory explanation in that thread, so was wondering if anyone else could clear up the mystery for me. Thanks for trying.

BA

 

[IngDod]

That example instead of being helpful is rather confusing... I lost almost two days trying to make heads or tails of it. In other sources I have seen the vertical check is never performed... they only check for the a-a section and the moment and shear are very straight forward.... I don't understand why here they have moments in their shear equations. A side question... what are the usual thicknesses for this gusset plates? In my particular case I am thinking on using a 3/4" plate... I could go as low as 1/2" and it still checks out (using the load combinations with over-strength factor instead of 1.1*Ry*Fy*Ag) but I think this is a part of the structure where is good to have ample capacity.

 

[JenB]

winelandv,

You mentioned that you've run the analysis on the plate across section b-b before. To what did you compare your axial & bending stresses? The V14.1 Design Examples problem II.C-5 didn't have any axial or moment stresses on the section b-b, but it mentions (pg IIC-69) that if N' and M' are greater than zero, the gusset should be checked for buckling under this stress and the procedure in AISC Manual Part 9 for buckling of a coped beam can be used. I'm not sure how the coped beam buckling equations relate to a gusset plate since I don't have a cope depth (dc) or a cope length (c).

Thanks,
Jen

 

[WinelandV]

JenB,

Originally, I looked at the gusset as a plate in compression, that is, a standard compressive member check using Section E3. This led to REALLY conservative designs... So, I ended up using the coped beam check for a beam coped at both flanges because it's the most conservative of the coped beam situations. As a run-down, I used the depth of the plate as h0 (the reduced beam depth) and the horizontal length of the plate as the length of the cope. Then, calc lambda, followed by Q, followed by the critical buckling stress. I do a simple Pu/A + Mu/S to arrive at the ultimate stress, which is then compared to the factored critical buckling stress.

Hopefully this helps some, but feel free to disagree. I think what I do is overly conservative, but really don't have a better way of doing it.