The Euler’s crippling load for a 2 m long slender steel rod of uniform cross-section hinged at both the ends is 1 kN. The Euler’s crippling load for a 1 m long steel rod of the same cross-section and hinged at both the ends will be

Concept:

Euler’s crippling load:

Euler’s crippling load formula is used to find the buckling load of long columns.

It is given by

Where E = Modulus of elasticity, I = moment of inertia, l_e = Effective length of the column

The Effective length of the column depending on ends conditions is as follows:

Calculation:

Given data

Condition- I

l₁ = 2 m

l_e1 = l (Both ends hinged) = 2m

Now

P_e1 = 1 kN

 ........(i)

Condition- II

l₂ = 1 m

l_e2 = l₂ (Both ends hinged) = 1m

Using equation (i)

P_e2 = 4 kN