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Column Loading and Elastic Stability Case 3a1 Formulae and Calculator

Strength Mechanics of Materials
Beam Deflections, Stress Analysis and Engineering

Column Loading and Elastic Stability Formulae and Calculator Case 3a1

Uniform straight bar under end load P and a uniformly distributed load p over a lower portion of the length; several end conditions. Upper end free, lower end fixed.

Preview: Column Loading and Elastic Stability Calculator Case 3a1

NOTATION:

P = Load (force) (lbs, N);
(pa)' = Critical unit load (force per unit length), (lbs, N);
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),
K = Derived from ratios as follows (see table):
1.) a / l
2.) P / pa

Formulae:

(pa)' = K ( π² E I  ) / l²

(a negative value for P/pa means the end load is tensile)

References:

Roark's Formulas for Stress and Strain, Eight Edition