IntermediateTopic 65 of 106Engineering Mechanics
Buckling of columns
Slender members fail by instability at Euler load π²EI/(KL)².
In depth
A slender column fails by buckling at the critical load P_cr=π²EI/(KL)², with K=1 pinned-pinned, 0.5 fixed-fixed, 2 cantilever. Slenderness ratio KL/r above about 100 means elastic buckling. Imperfections and eccentricity reduce capacity.
Key points
- Buckling occurs about the weaker axis
- Bracing shortens effective length
- Johnson formula for intermediate columns
ExampleA 3 m pinned steel rod, 20 mm diameter, buckles near 17 kN.
What is Buckling of columns?
Slender members fail by instability at Euler load π²EI/(KL)².
Why is it important to understand buckling of columns?
Slender members can fail suddenly by buckling at loads far below yield, so buckling checks are essential for columns and struts.
What does the effective length factor K do?
It accounts for end conditions. Pinned-pinned gives K equal to one, fixed-fixed gives a lower value and fixed-free gives a higher value.
Why does buckling happen suddenly?
Beyond a critical load, the straight shape becomes unstable, and small imperfections cause large lateral deflection with little extra load.
How is Buckling of columns used in practice?
Typical applications include sizing a steel column in a building to avoid buckling under load, checking a long tube used as a compression strut in a frame and designing a telescopic support that must carry a set load without bending.
What should I learn before Buckling of columns?
Study "Failure theories" first (topic 64 of 106 in Engineering Mechanics). It covers the groundwork this topic builds on.
What are the key points of Buckling of columns?
Buckling occurs about the weaker axis. Bracing shortens effective length. Johnson formula for intermediate columns.
Can you give an example of Buckling of columns?
A 3 m pinned steel rod, 20 mm diameter, buckles near 17 kN.
What comes after Buckling of columns?
The next topic is "Strain energy", which builds directly on this one.
How difficult is Buckling of columns?
It is classed as Intermediate in Engineering Mechanics (topic 65 of 106). It is an intermediate topic. Work through the beginner topics in Engineering Mechanics first.