# Simple Beam - Two Equal Point Loads Unequally 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 Equal Point Loads Unequally Spaced formulas

$$R_1 \;=\; V_1 \; ( max.\; when\; a < b ) \;=\; (P\;/\;L) \; ( L - a + b )$$

$$R_2 \;=\; V_2 \; ( max.\; when\; a < b ) \;=\; (P\;/\;L) \; ( L - b + a )$$

$$V_x \; [\; a < x < ( L - b ) \;] \;=\; (P\;/\;L) \; ( b - a )$$

$$M_1 \; ( max.\; when\; a > b ) \;=\; R_1 \;a$$

$$M_2 \; (max.\; when\; a < b ) \;=\; R_2 \;b$$

$$M_x \; ( max.\; when\; x < a ) \;=\; R_1 \;x$$

$$M_x \; [\; max. \; when \; a < x < ( L - b ) \;] \;=\; (R_1 \;x) - [\;P\; ( x - a )\;]$$

Symbol English Metric
$$x$$ = horizontal distance from reaction to point on beam $$in$$ $$mm$$
$$a, b$$ = 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