Beam Formulas

Beam

Beam formulas may be used to determine the deflection, shear and bending moment in a beam based on the applied loading and boundary conditions.

Reference Documents:

  1. Formulas for Stress and Strain, Roark & Young, McGraw-Hill
  2. Formulas for Stress, Strain, and Structural Matrices, Pilkey, John Wiley & Sons.

Common Beam Formulas:

common beam formulas 
PINNED-PINNED BEAM WITH UNIFORM LOAD
 
FIXED-FIXED BEAM WITH UNIFORM LOAD		  
 
PINNED-FIXED BEAM WITH UNIFORM LOAD		  

FREE-FIXED BEAM WITH UNIFORM LOAD 		  
 
PINNED-PINNED BEAM WITH POINT LOAD		  
See definitions of < > step functions below.
 
FIXED-FIXED BEAM WITH POINT LOAD		  
See definitions of < > step functions below.
 
PINNED-FIXED BEAM WITH POINT LOAD		  
See definitions of < > step functions below.
 
FREE-FIXED BEAM WITH POINT LOAD		  
See definitions of < > step functions below.

Legend:

w = uniform load (force/length units)
V = shear
M = moment
d = deflection
E = modulus of elasticity
I = moment of inertia


Definitions of step functions:

If x < a then < x - a >0 = 0
If x < a then < x - a >n = 0
If x > a then < x - a >0 = 1
If x > a then < x - a >n = ( x - a )n