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Column Loading and Elastic Stability Case 3C1 Formulae and Calculator

Strength Mechanics of Materials
Beam Deflections, Stress Analysis and Engineering

Column Loading and Elastic Stability Formulae and Calculator Case 3C1.

Stepped straight bar under end load P and a distributed load of maximum value p at the bottom linearly decreasing to zero at a distance a from the bottom Upper end free, lower end fixed.
(a negative value for P/pa means the end load is tensile)

Preview: Column Loading and Elastic Stability Calculator Case 3C1

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