Simple Beam - Two Unequal Point Loads Unequally Spaced
Simple Beam - Two Unequal Point Loads Unequally Spaced Formulas |
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\(\large{ R_1 = V_1 \;\;=\;\; \frac {P_1 \; \left( L \;- \;a \right) \;+\; P_2\; b } { L } }\) \(\large{ R_2 = V_2 \;\;=\;\; \frac {P_1 \;a \;+\; P_2 \; \left( L\; - \;b \right) } { L } }\) \(\large{ V_x \; \left[ a < x < \left( L - b \right) \right] \;\;=\;\; R_1 - P_1 }\) \(\large{ M_1 \; \left(max.\; when\; R_1 < P_1 \right) \;\;=\;\; R_1\; a }\) \(\large{ M_2 \; \left(max.\; when\; R_2 < P_2 \right) \;\;=\;\; R_2\; b }\) \(\large{ M_x \; \left(max.\; when\; x < a \right) \;\;=\;\; R_1\; x }\) \(\large{ M_x \; \left[ max.\; when\; a < x < \;\left( L - b \right) \right] \;\;=\;\; R_1\; x - P_1\; \left( x - a \right) }\) |
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| Symbol | English | Metric |
| \(\large{ \Delta }\) = deflection or deformation | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ x }\) = horizontal distance from reaction to point on beam | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ a, b }\) = length to point load | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ M }\) = maximum bending moment | \(\large{lbf-in}\) | \(\large{N-mm}\) |
| \(\large{ V }\) = maximum shear force | \(\large{lbf}\) | \(\large{N}\) |
| \(\large{ \lambda }\) (Greek symbol lambda) = modulus of elasticity | \(\large{\frac{lbf}{in^2}}\) | \(\large{Pa}\) |
| \(\large{ I }\) = second moment of area (moment of inertia) | \(\large{in^4}\) | \(\large{mm^4}\) |
| \(\large{ R }\) = reaction load at bearing point | \(\large{lbf}\) | \(\large{N}\) |
| \(\large{ L }\) = span length of the bending member | \(\large{in}\) | \(\large{mm}\) |
| \(\large{ P }\) = total concentrated load | \(\large{lbf}\) | \(\large{N}\) |
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.
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Tags: Beam Support Equations