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Engineering Deflection Calculations
for beams with constant cross sections
 

 

Support Type Beam Type Diagram Critical Deflections
Support at both
ends

uniform load

 s ^ ^ ^ ^ ^ ^ s
 5WL^3 / 384*E*I  at center
Support at both
ends		 center load s       ^      s
 WL^3 / 48*E*I at load
Support at both
ends		 load at any point s    ^         s
a        b		 Wa^2*b^2 / 3*E*I*L at load
W*a*v^3/( 3*E*I*L)
where v =b*[(1/3+2a/3b)^ .5]		 at max (on longer segment b)
Support at both
ends		 2 even load s   ^      ^   s
a         a		 Wa/(24EI)*(3L^2-4a^2) at center
Fixed at one
end		 uniform load F ^ ^ ^ ^ ^ ^ ^ WL^3 / 8*E*I at end
Fixed at one
end		 load at other end F              ^ WL^3 / 3*E*I at end
Fixed at one
end		 load at any point F         ^    _
  l       b		 WL^3 / 3*E*I at load
WL^2 / 6*E*I(2L+3b) at end
Fixed at both
ends		 uniform load F ^ ^ ^ ^ ^ ^ F WL^3 / 384*E*I at center
Fixed at both
ends		 load at center F      ^        F WL^3 / 192*E*I at load
 
Variable Description

English Unit

Metric Unit
  W = Load on beam lb (pounds) N (newtons)
   L = Length of beam in inches in mm
  E = Modulus of elasticity of the material lb/in^2 N/mm^2
I = Moment of inertia of the cross section of beam in^4 mm^4

 

 

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