Braced column under compressive load

In summary, the problem involves finding the effective lengths for a column with given dimensions and support conditions. The radiuses of gyration for both axes have been calculated, and the larger slenderness ratio should be used in the buckling formula. The effective length factor of k=1 should be used for both axes due to member rotation at the braced support. The buckling formula should also be checked for correct use of L^2 instead of just L.
  • #1
sukibelle
10
0
Screen Shot 2012-05-27 at 10.21.09 PM.png

Homework Statement



Homework Equations



P = EI pi^2 / Leff radius of gyration: SQRT (I/A), slenderness ratio: Leff/r

The Attempt at a Solution



So I've found Ixx = 240.81 x 10^6 mm^4, Iyy = 71.9 x 10^6 A = 9600 finding the radiuses of gyration rx = 158.38, ry = 86.54
effective length of x-axis : (one end pinned, I'm assuming the buckling = fixeed and do i use the longer length?) 6*0.7 = 4.2
efective length of y: 10*1 (both ends pinned)
I'm not sure about the effective length part, I know I'm meant to find the larger slenderness ratio (which identifies the weaker axis) and then plug that into the P = EI pi^2 / Leff . I don't know how to address a column supported in this way. do I average the lengths or something?
 
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  • #2
You should use k = 1 as the effective length factor in both cases, where L = 10 for major axis and L = 6 for minor axis. This is due to member rotation at the braced support at the buckling mode. See which controls. Also check your buckling formula the L should be squared, Pcr = pi^2 EI/L^2
 

1. What is a braced column under compressive load?

A braced column under compressive load is a structural element that is designed to support and resist compressive forces. It is reinforced with braces or diagonals to prevent buckling.

2. How does a braced column under compressive load work?

The braces or diagonals in a braced column under compressive load act like a frame, providing lateral stability and preventing the column from buckling under the applied load.

3. What are the advantages of using a braced column under compressive load?

The main advantage of using a braced column under compressive load is its ability to resist buckling, making it a more efficient and reliable structural element. It also allows for longer and taller columns to be used, reducing the need for additional support.

4. What factors affect the design of a braced column under compressive load?

The design of a braced column under compressive load is affected by several factors, including the type of material used, the magnitude and direction of the applied load, the height and slenderness of the column, and the location and spacing of the bracing members.

5. Are there any limitations to using a braced column under compressive load?

While braced columns under compressive load are efficient and reliable, they may not be suitable for all types of structures. The use of braces may limit the usable space within a structure and may also require additional maintenance and inspection to ensure their effectiveness.

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