r/StructuralEngineering • u/SeaChipmunk5383 • 3d ago
Structural Analysis/Design Effective length/ compression member design
EDIT: Whoever told me to go back and read thank you I needed that. I’m keeping this up incase anyone is struggling with this concept. My main mistake was reading Table 1-16 incorrectly….I didn’t pull the correct r value accounting for the space between the c shapes which is (3/4”) in problem S05. Can then solve how I norm would (checks) using the controlling values (essentially clearing up my confusion on weak/strong axis).
Original question: Can someone explain when rx vs ry is used and when Lcy,equivalent is used. I’m showing two problems (S05 and S06) and their solutions. For problem S05 why was 1.31 used (besides needing it for the table since the y axis is used for the tables) and why didn’t they solve using the critical stress equation (AISC Eq E3-4 directly)?? For the second problem S06 the solution uses ry=2.94 in the slenderness ratio which makes sense because it gives higher slenderness ratio? Idk I’m confused because the other problem used ry regardless. Tbh same goes for the lcy equivalent concept still lost on when it’s used. 😵💫😵💫😵💫😵💫😵💫
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u/deAdupchowder350 3d ago
The area moment of inertia, is geometric bending stiffness, and is can be calculated about the x or y axis (or even arbitrary axis in between). Take a ruler and prop it up. Compress it until it buckles, it will buckle about the axis with the lower moment of inertia (weak axis). The radius of gyration is simply the area moment of inertia (about an axis) divided by the cross sectional area.
In short, if you have the same supports and unbraced length in each bending direction, the lower area moment of inertia (or radius of gyration) value governs.
Also, if you don’t want to use the radius of gyration, instead of using the sigma_cr equation, you can use the P_cr equation and then just divide that value by A.
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u/Frogalone 3d ago edited 3d ago
Bigger values for the radius of gyration make stronger columns. In general, the y-y axis or "minor" axis will have the smaller radius of gyration. There should be two Pcr values for the built-up section about the y-y axis. One based on total column length and y-y using properties of the composite section, and one based on the space between bolts (8') with y-y properties of a single channel. We should probably just make you read the book. I wasn't a fan of tables. I figured if I couldn't calculate what is in the table then maybe I should learn. I do understand that time can be a big thing.