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Column Loading Elastic Case 1b Formulae and Calculator

Strength Mechanics of Materials
Beam Deflections, Stress Analysis and Engineering

Column Loading and Elastic Stability Formulae and Calculator Case 1b

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

Preview: Column Loading and Elastic Stability Calculator Case 1b

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),
K₁ = Derived from ratios as follows (see table):
1.) ( E₂ I₂ ) / ( E₁ I₁ )
2.) a / l
3.) P₂ / P₁

Formulae:

P'₁ = ( K₁ π² E₁I₁ ) / l²

References:

Roark's Formulas for Stress and Strain, Eight Edition