Enter the column diameter, length, and modulus of elasticity into the calculator to determine the critical load using Johnson’s Formula. This calculator helps in evaluating the buckling load of a column.
Johnson’s Formula
The following formula is used to calculate the critical load of a column.
P_{text{cr}} = frac{pi^2 cdot E cdot (r^4)}{8 cdot (L^2)}
Variables:
- P_cr is the critical load (pounds)
- E is the modulus of elasticity (psi)
- r is the radius of the column (inches)
- L is the length of the column (feet)
To calculate the critical load using Johnson’s Formula, square the value of pi, multiply by the modulus of elasticity and the fourth power of the radius of the column, and divide the result by eight times the square of the column’s length.
What is Johnson’s Formula?
Johnson’s Formula is an engineering calculation used to predict the buckling load of a column. It is particularly useful for long, slender columns where the Euler’s critical load formula is not applicable. The formula takes into account the material’s modulus of elasticity and the geometric properties of the column to determine the load at which the column will buckle.
How to Calculate Critical Load using Johnson’s Formula?
The following steps outline how to calculate the critical load of a column using Johnson’s Formula.
- First, determine the modulus of elasticity (E) of the column material in psi.
- Next, measure the diameter of the column and calculate the radius (r) in inches.
- Measure the length (L) of the column in feet.
- Use the formula from above to calculate the critical load (P_cr).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Column Diameter (d) = 4 inches
Column Length (L) = 10 feet
Modulus of Elasticity (E) = 29,000,000 psi
