Two Member Frame - Fixed/Free Top Uniformly Distributed Load

on . Posted in Structural Engineering

2fff 4

Article Links

 

 

 

 

 

 

 

 

Two Member Frame - Fixed/Free Top Uniformly Distributed Load formulas

\(\large{ R_A  \;\;=\;\; w\;L  }\) 
\(\large{ H_A \;\;=\;\; 0  }\)
\(\large{ M_{max}  \left(at \;points\; A\; and \;B\right) \;\;=\;\; \frac{w\;L^2}{2}  }\) 
\(\large{ \Delta_{Cx}  \;\;=\;\; \frac{w\;h^2\;L^2}{4\; \lambda \; I}  }\)
\(\large{ \Delta_{Cy}  \;\;=\;\; \frac{w\;L^3}{8\; \lambda \; I} \; \left( L + 4\;h \right)  }\)

Where:

 Units English Metric
\(\large{ \Delta }\) = deflection or deformation \(\large{in}\) \(\large{mm}\)
\(\large{ h }\) = height of frame \(\large{in}\) \(\large{mm}\)
\(\large{ H }\) = horizontal reaction load at bearing point \(\large{lbf}\) \(\large{N}\)
\(\large{ I_h }\) = horizontal member second moment of area (moment of inertia) \(\large{in^4}\) \(\large{mm^4}\)
\(\large{ I_v }\) = vertical member second moment of area (moment of inertia) \(\large{in^4}\) \(\large{mm^4}\)
\(\large{ w }\) = load per unit length \(\large{\frac{lbf}{in}}\) \(\large{\frac{N}{m}}\)
\(\large{ M }\) = maximum bending moment \(\large{lbf-in}\) \(\large{N-mm}\)
\(\large{ \lambda  }\)   (Greek symbol lambda) = modulus of elasticity \(\large{\frac{lbf}{in^2}}\) \(\large{Pa}\)
\(\large{ A, B, C }\) = point of intrest on frame - -
\(\large{ L }\) = span length under consideration \(\large{in}\) \(\large{mm}\)
\(\large{ R }\) = vertical reaction load at bearing point \(\large{lbf}\) \(\large{N}\)

 

diagrams

  • 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.

 

Piping Designer Logo 1

Tags: Frame Support