Last Updated on October 26, 2024 by Maged kamel
Steel columns and Euler’s formula and k factors.
Introduction to Compression members. Euler’s formula gives a relation between the load-carrying capacity of the columns and their slenderness ratio, the slenderness ratio of height to the radius of gyration, the higher the slenderness ratio the lower load carry capacity.
According to Euler’s formula, the critical stress for a column can be evaluated as Fe=π^2 EI/(L/r)^2, where KL/r is called the slenderness ratio, K is the effective length factor, Fe is the critical stress, E is the modulus of elasticity.
The use of KL instead of L takes into consideration, the actual column length and support conditions. There are six conditions that columns may exist.
For each case a different k value is to be considered, for columns, these conditions are shown in the next picture, K factor cases for columns.
A detailed description of the Content of the lecture
Our subject will be the compression members, especially columns.
The first point. What is the definition of compression members?
The second point will be An illustration of the different modes of failures.
The third point illustrates where to use the different steel section for compression members.
The fourth point is how do we drive the expression for Euler’s equation.
The fifth point what is the difference between local buckling and general buckling?
The sixth point is what are the different modes for failures for short columns?The last point is the Torsional buckling.
Definition of the compression member.
From Prof Alan William’s book steel structure design LRFD -ASD. for the definition of Compression member.
What is a compression member? A compression member is a structural member that carries loads along its longitudinal axis.
Usually, the compression member is free from the effect of the bending moment.
He explored the different types of compression members, for instance, columns, in a framed structure. If you have braced frames, then the bracing themselves are compression members, as for the truss. the top chords of simply supported trusss are compression members.
The strut has a compression force, then is a compression member. As you can see in the figure, the strut has a compression force, then is a compression member on the right side as well as the diagonal member, and of course, the upper chord can be regarded as a compression member.
From Professor Varma’s lectures, he shows the formula used to compute stress.l He defined compression members as the structural elements that are subjected to axial compressive forces loaded through the centroid.
The stress can be evaluated as the division of the compression load by the area.
But in reality, the situation might vary. it is rare how to have a concentric load.
Causes of additional stress to compression members.
1 -The accidental eccentricity of loading concerning the centroid.
2-Residual stresses in the member due to the fabrication process.
3- Member out of straightness which is called crookedness, there is no 100% plumb column section..
Members with compression and moment can be called beam-columns.
A link to the next post-1a-Steel columns and Euler’s formula-part 2.
This is a link to an external resource-chapter 7– Concentrically Loaded Compression, Members