Reference Guide

Equation Reference 5-3
Columns and Beams (1)
Variable
Description
º
Eccentricity (offset) of load
σ cr
Critical stress
σ max
Maximum stress
θ
Slope at x
A
Cross-sectional area
a
Distance to point load
c
Distance to edge fiber (Eccentric Columns), or
Distance to applied moment (beams)
E
Modulus of elasticity
I
Moment of inertia
K
Effective length factor of column
L
Length of column or bean
M
Applied moment
Mx
Internal bending moment at x
P
Load (Eccentric Columns), or Point load (beams)
Pcr
Critical load
r
Radius of gyration
V
Shear force at x
w
Distributed load
x
Distance along beam
y
Deflection at x
For simply supported beams and cantilever beams (“Simple Deflection” through “Cantilever Shear”), the
calculations differ depending upon the location of x relative to the loads.
 Applied loads are positive downward.
 The applied moment is positive counterclockwise.
 Deflection is positive upward.
 Slope is positive counterclockwise
 Internal bending moment is positive counterclockwise on the left-hand part.
 Shear force is positive downward on the left-hand part.
Reference: 2.