Related Resources: calculators

Column Loading and Elastic Stability Case 2d Formulae and Calculator

Strength Mechanics of Materials
Beam Deflections, Stress Analysis and Engineering

Column Loading and Elastic Stability Formulae and Calculator Case 2d

Stepped straight bar under tensile end load P₁ and intermediate load P₂; upper end pinned, lower end fixed.

Preview: Column Loading and Elastic Stability Calculator Case 2d

NOTATION:

P₁' = critical 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.) P₁ / P₂

Formulae:

P'₂ = ( K₂ π² E₁I₁ ) / l²

References:

Roark's Formulas for Stress and Strain, Eight Edition