# Two Member Frame - Fixed/Free Free End Vertical Point Load

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## Two Member Frame - Fixed/Free Free End Vertical Point Load formulas

### Support Reaction

$$\large{ R_A \;\;=\;\; P }$$
$$\large{ H_A \;\;=\;\; 0 }$$

### Bending Moment

$$\large{ M_{max} \left(at \;points\; A\; and \;B\right) \;\;=\;\; P\;L }$$

### Deflection

$$\large{ \Delta_{Cx} \;\;=\;\; \frac{P\;L\;h^2}{2\; \lambda \; I} }$$
$$\large{ \Delta_{Cy} \;\;=\;\; \frac{P\;L^2}{3\; \lambda \; I} \; \left( L + 3\;h \right) }$$

### Slope

$$\large{ \theta_{C} \;\;=\;\; \frac{P\;L}{2\; \lambda \; I} \; \left( L + 2\;h \right) }$$

### 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) $$\large{in^4}$$ $$\large{mm^4}$$ $$\large{ M }$$ = 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 - - $$\large{ \theta }$$ = slope of member $$\large{rad}$$ $$\large{rad}$$ $$\large{ L }$$ = span length under consideration $$\large{in}$$ $$\large{mm}$$ $$\large{ P }$$ = total concentrated load $$\large{lbf}$$ $$\large{N}$$ $$\large{ R }$$ = 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.

Tags: Frame Support