Three Member Frame - Pin/Roller Central Bending Moment
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Three Member Frame - Pin/Roller Central Bending Moment formulas
\large{ R_A = R_B = \frac{M_C}{L} } | |
\large{ H_A = 0 } | |
\large{ M_{max} \;(at \; C) = \frac{M_C}{2} } | |
\large{ \theta \;(at \; C) = \frac{M_C\;L}{12 \; \lambda \; I} } |
Where:
Units | English | Metric |
\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, D, E } = point of intrest on frame | - | - |
\large{ \theta } = slope of member | \large{deg} | \large{rad} |
\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.