Buckling Q

Q: A beam is supported by two columns and at the center of the beam is a force applied. Are these two columns going to buckle?

A: Equation used is → Euler Criticial Buckling Load Equation P_cr also known as the critical buckling load (the compressive force on the column that will cause it to buckle), E is the modulus of elasticity/stiffness of the columns material. I is a measure of stiffness/moment of intertia but due to the cross-sectional shape of the column (In this case an I column is used). K is a constant that represents the connection (fixed connection, pinned connection, in this example it is assumed to be fixed). L is the length of the column.

Using all these variables we can figure out at what point the columnwill fail/buckle. If there is a force acting downards on the beam then there needs to be a reaciton force from the columns (half of the downward force on each end eg 80,000) holding the beam up. That means the beam is pushing down additionally on one of the columns half of the total downard force 160,000 + 80,000 due to newtons 3rd law. So the column is being compressed with a force of 80,000.

So that downwards 80,000 force is the force that will be compared to the P_CR value to see if it exceeds that number. P actual is less than P critical which means the column will not buckle.