**Related Resources: calculators**

### Column Loading and Elastic Stability Case 2d Formulae and Calculator

**Strength Mechanics of Materials **

**Beam Deflections, Stress Analysis and Engineering **

**Column Loading and Elastic Stability Formulae and Calculator Case 2d**

Stepped straight bar under tensile end load P_{1} and intermediate load P_{2}; upper end pinned, lower end fixed.

Preview: **Column Loading and Elastic Stability Calculator Case 2d **

NOTATION:

P_{1}' = critical 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 _{1} / P_{2} *

Formulae:

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

References:

Roark's Formulas for Stress and Strain, Eight Edition