**Related Resources: calculators**

### Column Loading and Elastic Stability Case 3C3 Formulae and Calculator

**Strength Mechanics of Materials **

**Beam Deflections, Stress Analysis and Engineering **

**Column Loading and Elastic Stability Formulae and Calculator Case 3C3.**

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 pinned, lower end fixed.

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

Preview: **Column Loading and Elastic Stability Calculator Case 3C3 **

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 ( in^{4}, mm^{4} )

*l* = Length of bar (in, mm),

K = Derived from ratios as follows (see table):

1.) a /* l
2.) P / pa *

Formulae:

(pa)' = K ( π^{2} E I ) / *l*^{2}

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

References:

Roark's Formulas for Stress and Strain, Eight Edition