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Column Loading and Elastic Stability Case 2a Formulae and Calculator

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Strength Mechanics of Materials
Beam Deflections, Stress Analysis and Engineering

Column Loading and Elastic Stability Formulae and Calculator Case 2a

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

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

Preview: Column Loading and Elastic Stability Calculator Case 2a

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),
K2 = 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

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