Civil Engineer needs help getting head round a graph

[funkydunky20]

Hi, new to the forum, although i have read some posts before.

I am in the process of completing a structural mechanics report based upon buckling of a slender column.

In the brief they asked us to plot a graph of Critical Buckling Load derived from Euler's Buckling Theory and actual (all in Newtons) against 1/L^2.

I am trying to understand what this graph shows us, however firstly i thought i would look at the units of the gradient. in my mind the gradient of the graph will have units of N.m^2 (not (N/m^2). I can't for the life of me think what these units represent and this is confusing my understanding of the graph.

The graph basically has three linear lines which increase as 1/L^2 increases.

Can anyone shed any light on this?

 

[nvn]

What do you mean by "and actual"? Could you list the three functions you are plotting?

 

[jefswat]

Euler buckling equation predicts higher than experimentally observed critical buckling loads. In the elastic buckling region this is due to initial out of straightness of the column. In the inelastic buckling region, the lower than expected load is predominately caused by residual stresses left in the metal from forming (for steel). That is most likely what the question is driving at.