Enter the modulus of elasticity, the moment of inertia, and the length of the column into the calculator to determine the critical force/load.

Critical Force Formula

The following equation is used to calculate the Critical Force.

CL = (pi^2 * E * I) / L^2
  • Where CL is the critical load (force)
  • E is the modulus of elasticity (force/length^2)
  • I is the moment of inertia (length^4)
  • L is the length

To calculate the critical load, multiply pi squared by the modulus of elasticity and the moment of inertia, then divide by the length squared.

What is a Critical Force?

Definition:

A critical force is a measure of the force required to buckle a column with a given modulus of elasticity, moment of inertia, and length.

How to Calculate Critical Force?

Example Problem:

The following example outlines the steps and information needed to calculate Critical Force.

First, determine the modulus of elasticity. In this example, the modulus of elasticity is found to be 500 lbf/in^2.

Next, determine the momentum of inertia. For this problem, the momentum of inertia is found to be 20 in^4.

Next, determine the length. In this case, the length is measured to be 5 in.

Finally, calculate the Critical Force using the formula above:

CL = (pi^2 * E * I) / L^2

CL = (3.14159^2 * 500 * 20) / 5^2

CL = 3947.83 lbf

FAQ

What factors can affect the modulus of elasticity in materials?

The modulus of elasticity, a measure of a material’s stiffness or rigidity, can be affected by several factors including temperature, the material’s composition, and the presence of impurities or defects within the material. For metals, the modulus typically decreases with an increase in temperature.

How does the length of a column influence its critical force?

The length of a column significantly influences its critical force; as the length increases, the critical force required to buckle the column decreases. This relationship is inversely proportional to the square of the length, meaning that doubling the length of a column reduces its critical force by a factor of four, making longer columns more susceptible to buckling under lower forces.

Can the moment of inertia be changed to increase a column’s critical force?

Yes, the moment of inertia is a geometrical property that represents how a column’s cross-sectional area is distributed. By changing the shape or distribution of material across the column’s cross-section, the moment of inertia can be increased, thereby increasing the column’s resistance to buckling and its critical force. For example, making a column’s cross-section wider or using a hollow tube shape can significantly increase the moment of inertia.