Beam Fixed at One End - Concentrated Load at Center
Beam Fixed at One End - Concentrated Load at Center formulas |
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\(\large{ R_1 = V_1 \;\;=\;\; \frac {5\;P} {16} }\) \(\large{ R_2 = V_2 max \;\;=\;\; \frac {11\;P} {16} }\) \(\large{ M_{max} \; \left(at \;fixed \;end \right) \;\;=\;\; \frac {3\;P\;L} {16} }\) \(\large{ M_1 \; \left(at\; point\; of \;load \right) \;\;=\;\; \frac {5\;P\;L} {32} }\) \(\large{ M_x \; \left( x < \frac {L}{2} \right) \;\;=\;\; \frac { 5\;P\;x} {16} }\) \(\large{ M_x \; \left( x > \frac {L}{2} \right) \;\;=\;\; P\; \left( \frac { L} {2} - \frac { 11\;x} {16} \right) }\) \(\large{ \Delta_x \; \left(at\; point\; of\; load \right) \;\;=\;\; \frac { 7\;P\;L^3} {768\; \lambda\; I} }\) \(\large{ \Delta_x \; \left( x < \frac {L}{2} \right) \;\;=\;\; \frac { P\;x} {96 \;\lambda\; I} \; \left( 3\;L^2 - 5\;x^2 \right) }\) \(\large{ \Delta_x \; \left( x > \frac {L}{2} \right) \;\;=\;\; \frac { P} {96 \;\lambda\; I}\; \left( x - L \right)^2 \; \left( 11\;x - 2\;L \right) }\) \(\large{ \Delta_{max} \; \left[ at \; x = L \; \left( \frac{1}{5} \right)^{\frac{1}{2}} \right] \;\;=\;\; \frac{P\;L^3}{48\; \lambda\; I \; \left( 5 \right)^{\frac{1}{2}} } }\) |
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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 | \(\large{in}\) | \(\large{mm}\) |
\(\large{ M }\) = 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 | \(\large{\frac{lbf}{in^2}}\) | \(\large{Pa}\) |
\(\large{ R }\) = reaction load at bearing point | \(\large{lbf}\) | \(\large{N}\) |
\(\large{ I }\) = second moment of area (moment of inertia) | \(\large{in^4}\) | \(\large{mm^4}\) |
\(\large{ L }\) = 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