Formula Home Buckling of Columns Introduction Critical Load Elastic Buckling Inelastic Buckling Column Related Eccentric Loads Initially Curved Beam-Columns Calculators Critical Load Struc. Steel Columns Related Subjects Materials Mechanics Beams Resources Bibliography
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more free magazines       Beam-Column Equation The out-of-plane transverse displacement w of a beam subject to in-plane loads is governed by the equation, where p is a distributed transverse load (force per unit length) acting in the positive-y direction, f is an axial compression force, E is the Young's modulus of the beam, and I is the area moment of inertia of the beam's cross section. The above equation is sometimes referred to as the beam-column equation, since it exhibits behaviors of both beams and columns. If E and I do not vary with x across the length of the beam and f remains constant, denoted as F, then the beam-column equation can be simplified to, Origin of the Beam-Column Equation Similar to the Euler-Bernoulli beam equation, the beam-column equation arises from four distinct subsets of beam-column theory: kinematics, consitutive, force resultants, and equilibrium. The outcome of each of these segments is summarized as follows:
 Kinematics: Constitutive: Resultants: Equilibrium:  In the equilibrium equations, N is the axial force resulting acting in a tensile manner (opposite in direction to the compressive resultant f). To relate the beam's out-of-plane displacement w to its pressure loading p, we combine the results of the four sub-categories in the following order:
 Kinematics => Constitutive => Resultants => Equilibrium => Beam-ColumnEquation
 This hierarchy can be demonstrated by working backwards. First combine the two equilibrium equations to eliminate V: Next replace the moment resultant M with its definition in terms of the direct stress s: Use the constitutive relation to eliminate s in favor of the strain e, and then use kinematics to replace e in favor of the normal displacement w:  As a final step, recognizing that the integral over y2 is the definition of the beam's area moment of inertia I, We arrive at the beam-column equation based on the Euler-Bernoulli beam theory, Since columns are usually used as compression members, engineers may be more familiar with the axial compression resultant f than the tensile resultant N. Let f = -N. The beam-column equation expressed with f is therefore,   Essentials of Manufacturing

Information, coverage of important developments and expert commentary in manufacturing. 3D Scanners

A white paper to assist in the evaluation of 3D scanning hardware solutions. Metal 3D Printing Design Guide

Direct Metal Laser Sintering (DMLS) 3D printing for parts with reduced cost and little waste. Salary Expectation

8 things to know about the interview question "What's your salary expectation"?