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### Column Loading Elastic Case 1b Formulae and Calculator

**Strength Mechanics of Materials **

**Beam Deflections, Stress Analysis and Engineering **

**Column Loading and Elastic Stability Formulae and Calculator Case 1b **

Stepped straight bar under end load P_{1} and intermediate load P_{2}; both ends pinned

Preview: **Column Loading and Elastic Stability Calculator Case 1b **

NOTATION:

P_{1} = Load (force) (lbs, N);

P_{2} = 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 ( in^{4}, mm^{4} )

l = Length of bar (in, mm),

K_{1} = Derived from ratios as follows (see table):

1.) ( E_{2} I_{2 } ) / ( E_{1} I_{1} )

2.) a /* l
3.) P _{2} / P_{1} *

Formulae:

P'_{1} = ( K_{1} π^{2} E_{1}I_{1} ) / *l*^{2}

References:

Roark's Formulas for Stress and Strain, Eight Edition