# Simple Beam - Two Point Loads Equally Spaced

on . Posted in Structural Engineering

### 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 - Two Point Loads Equally Spaced formulas

$$R \;=\; V \;=\; P$$

$$M_{max} \; ( between\; loads ) \;=\; P\;a$$

$$M_x \; ( x < a ) \;=\; P\;x$$

$$\Delta_{max} \; ( at \;center ) \;=\; ( P\;x \;/\;24\; \lambda\; I ) \;l \; ( 3\;L^2 - 4\;a^2 )$$

$$\Delta_x \; ( x < a ) \;=\; ( P\;x \;/\;6\; \lambda \;I) \; ( 3\;L\;a - 3\;a^2 - x^2 )$$

$$\Delta_x \; [\; a < x < ( L - a ) \;] \;=\; ( P\;a \;/\;6\; \lambda\; I) \; ( 3\;L\;x - 3\;x^2 - a^2 )$$

Symbol English Metric
$$\Delta$$ = deflection or deformation $$in$$ $$mm$$
$$x$$ = horizontal distance from reaction to point on beam $$in$$ $$mm$$
$$a$$ = length to point load $$in$$ $$mm$$
$$M$$ = maximum bending moment $$lbf-in$$ $$N-mm$$
$$V$$ = maximum shear force $$lbf$$ $$N$$
$$\lambda$$   (Greek symbol lambda) = modulus of elasticity $$lbf\;/\;in^2$$ $$Pa$$
$$R$$ = reaction load at bearing point $$lbf$$ $$N$$
$$I$$ = second moment of area (moment of inertia) $$in^4$$ $$mm^4$$
$$L$$ = span length of the bending member $$in$$ $$mm$$
$$P$$ = total concentrated load $$lbf$$ $$N$$

Tags: Beam Support