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Column Loading & Elastic Stability Case 3B1 Formulae and Calculator
Column Loading and Elastic Stability Formulae and Calculator Case 3B1.
Uniform straight bar under end load P and a uniformly distributed load p over an upper portion of the length; several end conditions Upper end free, lower end fixed.
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
(pa)' = K ( π2 E I ) / l2
(a negative value for P/pa means the end load is tensile)
Roark's Formulas for Stress and Strain, Eight Edition