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Column Loading and Elastic Stability Case 2a Formulae and Calculator

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Strength Mechanics of Materials
Beam Deflections, Stress Analysis and Engineering

Column Loading and Elastic Stability Formulae and Calculator Case 2a

Stepped straight bar under end load P₁ and intermediate load P₂; both ends fixed

Preview: Column Loading and Elastic Stability Calculator Case 2a

NOTATION:

P₁ = Load (force) (lbs, N);
P₂ = Load load (force) (lbs, N);
p' = critical unit load (force per unit length), (lbs, N);
T' = critical torque (force-length A.R.) (in-lbs, N-mm);
M' critical bending moment (force-length);
E = modulus of elasticity (force per unit area) (psi, Pa);
I = moment of inertia of cross section about central axis perpendicular to plane of buckling ( in⁴, mm⁴ )
l = Length of bar (in, mm),
K₂ = Derived from ratios as follows (see table):
1.) ( E₂ I₂ ) / ( E₁ I₁ )
2.) a / l
3.) P₁ / P₂

Formulae:

P'₂ = ( K₂ π² E₁I₁ ) / l²

References:

Roark's Formulas for Stress and Strain, Eight Edition