Beam Fixed at One End - Concentrated Load at Center
- See Article Link - Beam Design Formulas
- Tags: Beam Support
diagram Symbols
- 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.
Beam Fixed at One End - Concentrated Load at Center formulas |
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\( R_1 \;=\; V_1 \;=\; 5\;P\;/\;16 \) \( R_2 \;=\; V_2 max \;=\; 11\;P\;/\;16 \) \( M_{max} \; (at \;fixed \;end ) \;=\; 3\;P\;L\;/\;16 \) \( M_1 \; (at\; point\; of \;load ) \;=\; 5\;P\;L\;/\;32 \) \( M_x \; ( x < \frac {L}{2} ) \;=\; 5\;P\;x\;/\;16 \) \( M_x \; ( x > \frac {L}{2} ) \;=\; P\; [\; ( L\;/\;2) - (11\;x\;/\;16) \;] \) \( \Delta_x \; (at\; point\; of\; load ) \;=\; 7\;P\;L^3\;/\;768\; \lambda\; I \) \( \Delta_x \; ( x < \frac {L}{2} ) \;=\; ( P\;x\;/\;96 \;\lambda\; I) \; ( 3\;L^2 - 5\;x^2 ) \) \( \Delta_x \; ( x > \frac {L}{2} ) \;=\; ( P\;/\;96 \;\lambda\; I ) \; ( x - L )^2 \; ( 11\;x - 2\;L ) \) \( \Delta_{max} \; ( at \; x = L \; \left( \frac{1}{5} \right)^{\frac{1}{2}} ) \;=\; P\;L^3\;/\;48\; \lambda\; I \; \left( 5 \right)^{\frac{1}{2}} \) |
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| Symbol | English | Metric |
| \( R \) = reaction load at bearing point | \(lbf\) | \(N\) |
| \( V \) = maximum shear force | \(lbf\) | \(N\) |
| \( M \) = maximum bending moment | \(lbf - in\) | \(N - mm\) |
| \( \Delta \) = deflection or deformation | \(in\) | \(mm\) |
| \( P \) = total concentrated load | \(lbf\) | \(N\) |
| \( L \) = span length of the bending member | \(in\) | \(mm\) |
| \( x \) = horizontal distance from reaction to point on beam | \(in\) | \(mm\) |
| \( \lambda \) (Greek symbol lambda) = modulus of elasticity | \(lbf\;/\;in^2\) | \(Pa\) |
| \( I \) = second moment of area (moment of inertia) | \(in^4\) | \(mm^4\) |
Tags: Beam Support