Why Does ECL Analysis Give Such High k Factors?

The effective length of a given member in a frame is the length of an equivalent pin-ended member whose Euler load equals the buckling load of the frame member. The effective length factors, kx and ky, are factors by which we multiply the actual length of the member in order to obtain the effective lengths for buckling about the section XX and YY axes, respectively. When designing the frame member by traditional methods, we take account of the stiffness of connected members to obtain the effective length and then we consider it as if it were an isolated member of an appropriate length. We could then determine the axial load required to cause column buckling in this equivalent member.

ECL analysis allows us to determine the frame buckling load factor for a given load case. Frame buckling occurs when the axial forces for the given load case are factored to the point where the frame collapses. Display the buckling mode shape of the frame and you can see how the frame buckles. Frame buckling for a given load case is usually a complex interaction of several members - there is not necessarily any one member which causes the buckling of the frame. In this situation, if we apply our definition of effective length, we find that the effective length of a given member for a given load case is the length of an equivalent pin-ended member whose Euler load equals the load in that member when frame buckling occurs. Thus, any member carrying a small axial load at frame buckling will have a large effective length. Also, the effective length of a member will vary from one load case to another. It is only where a member could be said to be critical (i.e. participating to a large degree in the buckling mode), that the effective length factor could be compared with the value used in traditional methods.

In general, traditional effective length factors relate to the buckling load of the member being considered whereas the effective length factor computed by ECL analysis relates to frame buckling.

What Effective Length Factor Should I Use for Design?

ECL analysis computes effective length values for each member, for each load case. These may be input automatically to steel design procedures, or you may input values yourself. Can you use ECL analysis to determine the "effective length" of a member for design? Yes, but you must interpret the values carefully.

To determine the traditionally accepted effective length of a given member of a frame, you could use either of two approaches:

• Examine the buckling mode shapes for appropriate load cases and choose a k factor by relating the behaviour of the member in question to the simple buckled shapes used in the design code for classification of effective lengths.

• Construct a load case whose frame buckling mode involves the primary buckling of the member in question and use the computed value.

See Also

RAM Elements Unbraced Lengths

RAM Elements Effective Length Factors