Critical Stress For Elastic Buckling Of Euler Column Should Be

Answer: B. π²E/λ²

Critical stress for elastic buckling of Euler column should be π²E/λ².

Solution

We know that, from Euler’s formula

P_e=π²EI_min/l²_eff

Where P_e= Bulking load

I_min = Minimum moment of inertia about centroidal axis

l_eff= Effective length of column

Pe=π²Ar²_min/l²_eff

We also know that,

σ_critical=P_e/A

=π²EAr²_min/l²_eff×A

=π²E/(l²_eff/r_min)²

σ_critical=π²E/λ²_c= critical stress

 l_eff/r_min= Critical slenderness ratio

Note :-

Euler’s formula is applicable when,

Crushing strength Buckling stress.

Hence, Critical stress for elastic buckling of Euler column should be π²E/λ².

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