Steel Panel zone force equilibrium

[Sanjeee]

Dear All,

I'm having a difficulty with understanding, how the force equilibrium is construed in the steel panel zone in order to perform the stress checks. Regarding the book that I'm reading (Advanced analysis and design of steel frames, John Wiley & Sons, Guo-Qiang Li and Jin-Jun Li) writer suggests that panel zone will be in a shear state. So the Qh = (Mgl+Mgr)/hg+1/2*(Qct+Qcb) and Qv=(Mct+Mct)/hc+1/2*(Qgl+Qgr) are acting on the column flanges and continuity plates, respectively.

1.As can be seen the technique is pretty straightforwad and simple, but why not normal forces are not included from column and girders in that Qv and Qh forces?

Another issue related with that panel zone is:
If the stress checks fails in the panel zone, it's been recommended to use doubler plates or diagonal strut in the panel zone. If you choose the diagonal strut then equation for shear in panel zone is been written as tau = Qv*cos(alpha)/(t*h2 +2.6*Ad*hg*hc*cos(phi)/(d²*cos(phi)) and normal stresses acting on panel zone is sigma_d= E/G*tau*h1*h2/(d²*cos(alpha)).

2. So how actually those tau and sigma forces are derived by simple statics means?

Looking at it closely can reveal that some kind of relations has been established between torsional and normal stress effect, based on the inclusion of E and G, but actually how? By equating the strain sigma/E = tau/G ???

Your guidance will be appreciated,

Regards,


P.S. What's the way of writing more sophisticated formulas in the editor (e.g. Greek alphabet, special characters etc..)

 

[JoshPlumSE]

Sanjee -

I don't know how to write more sophisticated formulas on this site, but would love it if someone had some tips / tricks. The extent of my knowledge is font issues (subscript, superscript, bold, italics, underline, et cetea).

Regarding your first question: When you say "normal force" I assume that you're talking about axial compression or tension in the column or beam. Is that correct? If so, that force does act on the panel zone. But, it does not create a SHEAR stress in the panel zone. I believe that is why it is ignored.

Personally I never use diagonal struts. My first desire would be to change column size to a column with a larger web. If that's not possible, then I would try the web doubler plate.


Regarding your 2nd question: I'm not sure exactly what you're asking. The use of G is not related to torsion, but rather to shear.

 

[Sanjeee]

Regarding your first question: When you say "normal force" I assume that you're talking about axial compression or tension in the column or beam. Is that correct?

Yes you are correct.

But, it does not create a SHEAR stress in the panel zone. I believe that is why it is ignored.

This is the crucial part, on what basis you assume/judge that it won't create the shear force. Depending on the unknowns of system, general way of solving those kind of problems is simple means of statics. Writing the equilibrium in X and Y direction, taking the moment to any arbitrary point will give us equation to solve those unknowns. By that, I can prove you that shear acting in the panel zone has a term which includes the axial force term on the columns/beams.

My intention, is to understand logic of that load path assumption acting in the panel zones of columns/girders joint. So I can design them correctly. For example, what will be the force relation in the panel zone,
1.if Column has two different size of girders connecting (one smaller one bigger)?
2.If Column has left girder orthogonally connected while right girder is oblique? (each girder with different size)
3.If Column has two girder obliquely connected with different angles?

Personally I never use diagonal struts. My first desire would be to change column size to a column with a larger web. If that's not possible, then I would try the web doubler plate.

Please don't take me offensive here, but IMHO that's the overdesign. Due to the fact that we couldn't overcome the stress check in the panel zone we increase the columns size.

egarding your 2nd question: I'm not sure exactly what you're asking. The use of G is not related to torsion, but rather to shear.

Regarding the book I'm reading panel zone shear stress and axial stress on diagonal struts is written as previously stated. For those who are familiar with calculation of panel zone, I was intending to remind them, if that will make them recall something form the given equations. It's clear that connection is established between the sigma and tau.

Regards,

 

[structSU10]

I would say that the normal force will cause shear on an oblique plane, but without exploring the specific situation, couldn't say for sure how it was derived.

And your reference to overdesign if the column were upsized is somewhat unfounded. In many cases it is cheaper to increase column size versus add doubler plate and stiffeners due to fabrication costs. AISC has a design guide for stiffening columns (#13), which explains that most of the time upsizing is the correct option to avoid extra fabrication.

 

[structSU10]

I would say that the normal force will cause shear on an oblique plane, but without exploring the specific situation, couldn't say for sure how it was derived.

And your reference to overdesign if the column were upsized is somewhat unfounded. In many cases it is cheaper to increase column size versus add doubler plate and stiffeners due to fabrication costs. AISC has a design guide for stiffening columns (#13), which explains that most of the time upsizing is the correct option to avoid extra fabrication.

 

[Sanjeee]

And your reference to overdesign if the column were upsized is somewhat unfounded. In many cases it is cheaper to increase column size versus add doubler plate and stiffeners due to fabrication costs. AISC has a design guide for stiffening columns (#13), which explains that most of the time upsizing is the correct option to avoid extra fabrication.

If adding some diagonal struts is enough to solve the problem IMHO surely it'll overweight the option of upsizing the column, and don't think that it'll add much to the workmanship/fabrication. The think that makes me uneasy is i couldn't understand the stress derivation of diagonal strut, co I can determine which is better.

At the attachment, please look at the figure.
How do you express T₁ and T₂ as function of acting forces?
How do you express force acting on the diagonal if it's located from B to D point or from A to C point?

Thanks for helping,

 

[Sanjeee]

Sorry here is the attachment,

 

[ishvaaag]

Respect that the standing Axial load in the column influences the panel zone design -even for orthogonal beams and columns- there's no the lesser doubt according to AISC 360-10 for it determines the formula to choose (see section J.10.6. Web Panel Zone Shear) and at some value of the axial compression in the column, the axial load takes part the formula itself. This must be no surprise since the interaction of the axial and shearing stresses needs be apparent in one way or other in the strength check.

I hope to find some time to evaluate the panel zone shear for the case in your figure, if no other does before.

Best wishes.

 

[ishvaaag]

First a simplified design for diagonal stiffening in shear of the panel.

I start this way the question because essentially the strength of a panel zone of rhomboidal shape would be that of a panel of such shape, supports and loadings, and not even for rectangular panels is the question entirely extant. We continue to address the design of connections by controlling fragmented aspects of the potential bad behavior ... serve this for a start.

A reasonable and today sound approach for the design of these things is the use of FEM, by using nonlinear material properties, initial imperfections, and geometrical nonlinearity. Within these requirements, we would be ensured of having attained a safe and stable final state at the limit state (when of course, both deformations and stresses are kept satisfactory in the design). However, 3D solid FEM is not much linked yet to more customary formulary specifications.

 

[ishvaaag]

Now, a part of the discussion was why axial compression would in any case be able to be forfeited. We decided it was not, just seeing it contemplated in the AISC 360-10 code ... well, that's exactly the same case for any transverse compression that may be extant in the panel, only that AISC seems to be (explicitly) content in neglecting it as long as the forces imparted by the flanges are efficiently dealt with by continuity stiffeners.

So the approach in the attachment is more or less an attempt to follow such philosophy, transversal compression effects of the inclined beam are neglected out of the continuity given by the (surmisedly efficient) stiffeners. Then a horizontal shear stress extant in the panel zone is derived, and the design would proceed along AISC 360-10 guidelines, for we have already the shear in the panel zone, and for axial load will take the worse of P1 and P2

Of course if I was still doubting the soundness of the design after these or other check would try to implement the FEM approach of above just to clarify.