HomeEngineeringCivilStructuralCantilever Beam - Uniformly Distributed Load
Print

Cantilever Beam - Uniformly Distributed Load

on . Posted in Structural Engineering

diagram Symbols

  • Bending moment diagram (BMD)  -  Used to determine the bending moment at a given point of a structural element.  The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
  • Free body diagram (FBD)  -  Used to visualize the applied forces, moments, and resulting reactions on a structure in a given condition.
  • Shear force diagram (SFD)  -  Used to determine the shear force at a given point of a structural element.  The diagram can help determine the type, size, and material of a member in a structure so that a given set of loads can be supported without structural failure.
  • Uniformly distributed load (UDL)  -  A load that is distributed evenly across the entire length of the support area.

 

cb 1A

Cantilever Beam - Uniformly Distributed Load formulas

\( R \;=\; V \;=\; w \; L  \) 

\( V_x \;=\; w \; x    \) 

\( M_{max} \; \left(at\; fixed \;end \right)  \;=\; w\; L^2\;/\;2  \) 

\( M_x   \;=\;  w\;x^2 \;/\;2  \)

\( \Delta_{max} \; (at\; free\; end )  \;=\; w\; L^4\;/\;8 \;\lambda\; I  \)

\( \Delta_x   \;=\; (w\;/\;48\; \lambda\; I) \; ( x^4 - 4\;L^3\;x - 3\;x^4 )   \)

C B - Uniformly Distributed Load - Solve for R

\(\large{ R = V =  w \; L  }\)

load per unit length, w
span length, L

C B - Uniformly Distributed Load - Solve for Vx

\(\large{ V_x =  w \; x    }\) 

load per unit length, w
distance from reaction, x

C B - Uniformly Distributed Load - Solve for Mmax

\(\large{ M_{max} \; \left(at\; fixed \;end \right)  =  \frac{w\; L^2}{2}  }\) 

load per unit length, w
span length, L

C B - Uniformly Distributed Load - Solve for Mx

\(\large{ M_x  =  \frac{ w \; x^2 }{2}   }\)

load per unit length, w
distance from reaction, x

C B - Uniformly Distributed Load - Solve for Δmax

\(\large{ \Delta_{max} \; \left(at\; free\; end \right)  =  \frac{w\; L^4}{8 \;\lambda\; I}  }\)

load per unit length, w
span length, L
modulus of elasticity, λ
second moment of area, I

C B - Uniformly Distributed Load - Solve for Δx

\(\large{ \Delta_x   =  \frac{w}{48\; \lambda\; I} \; \left(  x^4 - 4\;L^3\;x - 3\;x^4  \right)     }\)

load per unit length, w
modulus of elasticity, λ
second moment of area, I
distance from reaction, x
span length, L

Symbol English Metric
\( R \) = reaction load at bearing point \(lbf\) \(N\)
\( V \) = maximum shear force \(lbf\) \(N\)
\( M \) = maximum bending moment \(lbf-in\) \(N-mm\)
\( \Delta \) = deflection or deformation \(in\) \(mm\)
\( w \) = load per unit length \(lbf\;/\;in\) \(N\;/\;m\)
\( L \) = span length of the bending member \(in\) \(mm\)
\( x \) = horizontal distance from reaction to point on beam \(in\) \(mm\)
\( \lambda  \)   (Greek symbol lambda) = modulus of elasticity \(lbf\;/\;in^2\) \(Pa\)
\( I \) = second moment of area (moment of inertia) \(in^4\) \(mm^4\)

 

Piping Designer Logo Slide 1

Tags: Beam Support

Latest Articles