Unequal Leg Angles

[Vector1962]

Wondering how to calculate Swa,Swb, Swc, Sza, Szb and Szc for unequal angles. These values are listed in the AISC database and are used for problems involving principle axis of L shapes. For purpose of discussion, I have a L6x3.5x3/8 LLV and I can replicate all the data in the AISC spreadsheet regarding the angle of the principle axis, max and min Iw… Iz etc but the 'S' values in the table don't seem to come out... the 'Sw' values come "reasonably" close but the 'Sz' values are off. Looking for some general guidance/discussion that i'm calculating the 'S' values properly. appreciate the replies.

 

[SlideRuleEra]

The values for properties published by AISC are theoretical, based on certain assumptions... especially the properties for angles. Producers have freedom to vary, somewhat, from the published values. The AISC Manual will have a page explaining the concept. I don't know which page it is in recent manuals, but in the 9th Edition, the info is under "Dimensions and Properties" on page 1-9.

http://www.SlideRuleEra.net

 

[phamENG]

I'm going to have to admit that I'm not familiar with your notation. How do you have 6 different elastic section moduli?

 

[r13]

Were you working off the principle axes, and take measure from NA to the farthermost point for "y"?

 

[Vector1962]

Yes, to the best of my knowledge I've used standard procedures referenced from the principle axes to the extreme points (tips of toes and leg/leg intersection perpendicular to the principle planes). I calculated and verified the Xbar, Ybar. Subsequently, rotated the geometric axes to align with the principle planes. Then S=Iw/c for each of the c values. S=Iz/c for each of those values. The Sw values are reasonable. The Sz values are not even close.

 

[r13]

rotated the geometric axes to align with the principle planes

This probably causes the problem. Why rotate axes? you calculate I based on the principle axes, and measure the distances (c) off the principle axes too, then S = I/c. Since this been a long time for me, so I could be wrong. Strongly suggest to review AISC manual as pointed out by SRE.

 

[BridgeSmith]

I think all the major CAD packages will calculate section properties for any shape. You just have to draw it up and then rotate it so you get the section properties about the axis that's of interest.

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

 

[skeletron]

I believe McNulty's "Single Angle Design Manual" gives a procedure for these values. Admittedly, I couldn't be bothered with programming this into my sheet, so I just grab from the AISC database since they are calculated anyways.

 

[Hokie93]

Do your manual computation of W_A, W_B, W_C, Z_A, Z_B, and Z_C agree with the values in the AISC Shapes Database? Those values are based are measured from the major and minor principal axes to the tip of each leg (centerline of tip) and to the corner of the heel. If the manual computations for I_W and I_Z agree with the Shapes Database and dimensions to the leg tips and heel agree, then you should be set. For example, S_WA = I_W/Z_A and S_ZA = I_Z/W_A. Note that point 'A' is the short leg tip, point 'B' is the heel, and point 'C' is the long leg tip. Also note that AISC measures points 'A' and 'C' to the centerline of the leg tip, not the extreme (inside or outside) corner. In his book, McNulty uses the extreme corner. You can check I_W and I_Z using Table 17-27 in the AISC Steel Construction Manual or by breaking out your favorite Advanced Mechanics of Materials textbook.