Bent Plate Properties

[MDStruct]

Can anyone tell me how AISC calculates their properties for biaxial single angle flexure? I have a scenario where we need to use a long bent plate to carry brick. I need a 9" outstanding leg and angles only go to 8", so I need to calculate Swa, Swb, Swc, Sza, Szb and Szc.

Also, AISC referred me to their design example E.14 from their V14.1 design examples set. Their example is a single angle column with eccentric point load. In their example the eccentricities from z and w axes are intuitive since they are out of plane, but how do I adjust this for a vertical load on the plate that will be in plane with these axes?

 

[fegenbush]

It may be of interest for you to look at AISI 2007 - North American Specification for the Design of Cold-Formed Steel Structural Members to analyze these structures.

 

[MDStruct]

Can you be more specific? I just looked through it and am not finding anything about section properties. The only thing I can find which seems relevant is C3.1.2.1 which is LTB resistance of singly symmetric sections, but I do not have a singly symmetric section. I am looking at a 9x4 bent plate.

 

[JoshPlumSE]

In the back of the AISC manual (table 17-27: Properties of geometric sections) they give general formulas for calculating properties of single angles.

 

[Hokie93]

If I am understanding the situation correctly, you have a bent plate lintel spanning horizontally and supporting brick. I recommend you follow the requirements of AISC Specification section F10, resolving the bending moment from the applied load into components about the major and minor principal axes. You will also have torsion acting on the bent plate since the brick load is acting eccentrically. You should be able to find guidance on determing the moments of inertia and section modulii about the major and minor principal axes from your favorite mechanics of materials textbook. Chapter H3.3 of the AISC Specification provides guidance on combining torsion with bending and shear stresses.

 

[SAIL3]

using 8" leg on an available angle and it's properties should be close enough..back off your allowables to say 60 or 70% to account for the approximation...

 

[MDStruct]

Thanks for all of your answers.

SAIL3

I was able to figure out the I and r values, but it's the section moduli that have been stumping me. I suppose I could make the upturned leg 9" as well and look at it as an equal leg angle since AISC actually gives equations for equal leg angles. Is this the route you would go?

 

[RobertHale]

Those Sw moduli should be the Iw divided by the perpendicular distance from the W-Axis to the points A, B, and C (the ends of the legs and the intersection of the legs). I am a little confused about why you are messing with the Chapter E provisions when there was ostensibly be very little compression in the angle. Like hokie said, churn and burn with F10.

 

[Hokie93]

If you have computed I[sub]w[/sub] and I[sub]z[/sub], then the section modulii corresponding to points A, B, and C on the cross section are just I[sub]w[/sub]/c and I[sub]z[/sub]/c, where c is the perpendicular distance from the w- and z-axes to the point (a, B, or C) of interest. If you are having trouble with determination of I[sub]w[/sub] and I[sub]z[/sub], refer to Table 17-27 in the 13th edition AISC Steel Construction Manual for their respective equations. You can check yourself by verifying that I[sub]w[/sub] = I[sub]x[/sub] + I[sub]y[/sub] - I[sub]z[/sub]. What is the span of this bent plate? You might want to keep an eye on the rotation of the bent plate as well as the deflection of the outstanding leg. AISC Design Guide 9 provides guidance on determining the torsional rotation of an open shape such as a bent plate.

 

[MDStruct]

RobertHale, I'm not really touching Chapter E provisions, I am just using an example from the Ch. E set of examples because this is what AISC pointed me to when I contacted them. I contacted them asking if they had any examples for an unequal leg angle in biaxial bending and this is where they directed me. I fully agree and am trying to use F10 as much as possible, but it treats equal leg angles with far more respect than unequal. I'm trying to piece this together because I have never fully understood the unequal angle in biaxial bending.

Thank you all for your help.

 

[RobertHale]

Okay, In that case, I would decompose the geometric moments you calculated into the principle axes and then use the provisions of F.10 to design about each principle axis. The design examples show this in example F.11C. The only thing you would need to change is substitute Equation F10-5 for F10-4 in the example. I though the principle section moduli were not needed, but I forgot that you have to look at the combined elastic stress for cases like this. Those section moduli should be computed as Hokie or I suggested.

 

[MDStruct]

Can you help me out with βw? Looking at the commentary we have the integral for βw which when integrated will basically be A/Iw*(zw^2+z^3)-2zo.

The table provides zo as the coordinate along the z axis of the shear center with respect to the centroid, which makes sense when looking at Fig. C-F10.4.

What are the values z and w though? These appear almost as variable, but how do I decide what to plug in?

 

[Hokie93]

@MDStruct: the attached explanation for the determination of βw (or βz) may be of interest. Note that in the attached document, the major principal axis is denoted by "u", not "w".

 

[transmissiontowers]

The 9th edition of AISC ASD Manual has properties for L9x4x5/8; 9x4x9/16; and 9x4x1/2 listed on page 1-46 and you can probably get the properties on the AISC web site if you don't have the old manual.

_____________________________________
I have been called "A storehouse of worthless information" many times.

 

[MDStruct]

Thank you all. I finally made my way through the design....Lo and behold deflection controlled anyways. I guess that's SOP, hours working to prove a design works only to have deflection bump it up anyways.

Thanks for your help everyone.

 

[KootK]

Out of curiosity, how far does your plate span between points of support?

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[Denial]

If your "angle" is made out of "thin" sheet you really should follow up on fegenbush's suggestion.[ ] That will give you guidance on how much of your apparent cross section will actually be effective.