Cantilever Beams

Maximum reaction, deflection and moment - single and uniform loads

Cantilever Beam - Single Load

cantilever beam single load

Maximum Reaction

can be expressed as:

RA = F      (1a)

where

RA = reaction force in A (N, lb)

F = single acting force in B (N, lb)

Maximum Moment

can be expressed as

MA = - F a    (1b)

where

MA = maximum moment in A (N.m, N.mm, lb.in)

a = length between A and B (m, mm, in)

Maximum Deflection

at the end of the cantilever beam can be expressed as

δC = (F a3 / (3 E I)) (1 + 3 b / 2 a)    (1c)

where

δC = maximum deflection in C (m, mm, in)

E = modulus of elasticity (N/m2 (Pa), N/mm2, lb/in2 (psi))

I = moment of Inertia (m4, mm4, in4)

b = length between B and C (m, mm, in)

Maximum Deflection

at the action of the single force can  be expressed as

δB = F a3 / (3 E I)   (1d)

where

δB = maximum deflection in B (m, mm, in)

 

Cantilever Beam - Single Load Calculator

A generic calculator - use metric values based on m or mm, or imperial values based on inches. Default typical values are in metric mm.

F - Load (N, lb)

a - Length of beam between A and B  (m, mm, in)

b - Length of beam between B and C (m, mm, in)

I - Moment of Inertia (m4, mm4, in4)

E - Modulus of Elasticity (N/m2, N/mm2, psi)

Cantilever Beam - Uniform Load

cantilever beam uniform load

Maximum Reaction

can be expressed as:

RA = q L      (2a)

where

RA = reaction force in A (N, lb)

q = uniform load (N/m, N/mm, lb/in)

L = length of cantilever beam (m, mm, in)

Maximum Moment

can be expressed as

MA = - q L2 / 2    (2b)

Maximum Deflection

can be expressed as

δB = q L4 / (8 E I)    (2c)

where

δB = maximum deflection in B (m, mm, in)

Cantilever Beam - Uniform Load Calculator

A generic calculator - use metric values based on m or mm, or imperial values based on inches. Default typical values are in metric mm.

q - Uniform load (N/m, N/mm, lb/in)

L - Length of beam (m, mm, in)

I - Moment of Inertia (m4, mm4, in4)

E - Modulus of Elasticity (Pa, N/mm2, psi)

More than One Point Load and/or Uniform Load acting on a Cantilever Beam

With more than one point load and/or uniform load - the resulting maximum moment in A and resulting maximum deflection in B can be calculated by summarizing the maximum moment in A and maximum deflection in B for each point and/or uniform load. 

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Related Topics

  • Beams and Columns - Deflection and stress, moment of inertia, section modulus and technical information of beams and columns

Related Documents

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