Critical Force Calculator, Formula, CF Calculation

Critical Force Calculator

Enter the values of modulus of elasticity, E_(lbf/in2), moment of inertia, I_(in4) and unsupported length, L_(in) to determine the value of critical load, CL_(lbf).

Critical Force Formula

The critical load (CL) is the maximum load that a slender column can bear while staying straight. When this load is exceeded, the column will buckle. The calculation of the critical load helps in ensuring the stability of structures under compression.

Critical load, CL_(lbf) in pound-force is equated by dividing the product of pi square, modulus of elasticity, E_(lbf/in2) in pound-force per square inch and moment of inertia, I_(in4) in inches to the fourth power by square of unsupported length, L_(in) in inches.

Critical load, CL_(lbf) = 9.8596 * E_(lbf/in2) * I_(in4) / L²_(in)

CL_(lbf) = critical load in pounds-force, lbf.

E_(lbf/in2) = modulus of elasticity in pounds-force per square inch, lbf/in².

I_(in4) = moment of inertia  in inches to the fourth power, in⁴.

L_(in2) = length in inches, in.

Critical Force Calculation:

1. Calculate the critical load for a steel column with a modulus of elasticity of 29,000,000 lbf/in² a moment of inertia of 100 in⁴ and an unsupported length of 120 inches.

Given: E_(lbf/in2) = 29,000,000l lbf/in², I_(in4) = 100 in⁴, L_(in2) = 120in.

Critical load, CL_(lbf) = 9.8596 * E_(lbf/in2) * I_(in4) / L²_(in)

CL_(lbf) = 9.8596 * 29,000,000 * 100 / 120²

CL_(lbf) = 1,982,350lbf.

2. Suppose you have a column with a critical load of 200,000 lbf, a moment of inertia of 30 in⁴, and an unsupported length of 100 inches. Find the modulus of elasticity.

Given: I_(in4) = 30 in⁴, CL_(lbf) = 200,000lbf, L_(in2) = 100in.

Critical load, CL_(lbf) = 9.8596 * E_(lbf/in2) * I_(in4) / L²_(in)

E_(lbf/in2) = CL_(lbf) * L²_(in) / 9.8596 * I_(in4)

E_(lbf/in2) = 200,000 * 100² / 9.8596 * 30

E_(lbf/in2) = 6,751,592.73 lbf/in².

Understanding Critical Power and W’