# Two Member Frame - Fixed/Pin Top Uniformly Distributed Load

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## Two Member Frame - Fixed/Pin Top Uniformly Distributed Load formulas

### Important Value

$$\large{ e \;\;=\;\; \frac{h}{L} }$$
$$\large{ \beta \;\;=\;\; \frac{I_h}{I_v} }$$

### Support reaction

$$\large{ R_A \;\;=\;\; \frac{w\;L}{2} \; \left( \frac{ 3\;\beta\;e \;+\; 5 }{3\; \beta\;e \;+\; 4 } \right) }$$
$$\large{ R_C \;\;=\;\; \frac{3\;w\;L}{2} \; \left( \frac{ \beta\;e \;+\; 1 }{3\; \beta\;e \;+\; 4 } \right) }$$
$$\large{ H_A = H_C \;\;=\;\; \frac{3\; w\;L^2 }{ 4\;h\; \left(3\; \beta\;e \;+\; 4 \right) } }$$

### Bending Moment

$$\large{ M_A \;\;=\;\; \frac{ w\;L^2 }{ 4\; \left(3\; \beta\;e \;+\; 4 \right) } }$$
$$\large{ M_B \;\;=\;\; \frac{ w\;L^2 }{ 2\; \left( 3\;\beta\;e \;+\; 4 \right) } }$$

### 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 $$\large{lbf-in}$$ $$\large{N-mm}$$ $$\large{ A, B, C }$$ = 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

• 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.
• 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.
• Uniformly distributed load (UDL)  -  A load that is distributed evenly across the entire length of the support area.

Tags: Frame Support