Simple Beam - Load Increasing Uniformly to One End

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• 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.

 

Simple Beam - Load Increasing Uniformly to One End formulas
\( R_1 \;=\ V_1 \;=\; W \;/\;3\) \( R_2 \;=\ V_2 \;=\; 2\;W \;/\;3\) \( V_x \;=\ (W\;/\;3)  - (W\;x^2\;/\;L^2)\) \( M_{max} \; (at \;  x = L\;/\; \sqrt{3}\; ) \;=\; 2\;W\;L \;/\; 9\; \sqrt{3}   \) \( M_x \;=\; (W \;x\;/\;3\;L^2)  \; ( L^2  - x^2 )   \) \( \Delta_{max} \; ( \;at \; x = L\; \sqrt{1 - ( 8/15 )^{\frac{1}{2} } } \;)  \;=\; 0.01304 \; ( W \;L^3\;/\; \lambda \;I ) \) \( \Delta_x \;=\; (W \;x\;/\; 180\; \lambda \;I \;L^2 ) \; ( 3\;x^4 - 10\;L^2\;x^2 + 7\;L^4 )  \)
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	\(in\)	\(mm\)
\( W \) = total load or \( w\;L\;/\;2 \)	\(lbf\)	\(N\)
\( w \) = highest load per unit length of UIL	\(lbf\;/\;in\)	\(N\;/\;m\)
\( L \) = 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)	\(in^4\)	\(mm^4\)