# Simple Beam - Two Unequal Point Loads Unequally Spaced

on . Posted in Structural Engineering

## Simple Beam - Two Unequal Point Loads Unequally Spaced Formulas

$$\large{ R_1 = V_1 \;\;=\;\; \frac {P_1 \; \left( L \;- \;a \right) \;+\; P_2\; b } { L } }$$

$$\large{ R_2 = V_2 \;\;=\;\; \frac {P_1 \;a \;+\; P_2 \; \left( L\; - \;b \right) } { L } }$$

$$\large{ V_x \; \left[ a < x < \left( L - b \right) \right] \;\;=\;\; R_1 - P_1 }$$

$$\large{ M_1 \; \left(max.\; when\; R_1 < P_1 \right) \;\;=\;\; R_1\; a }$$

$$\large{ M_2 \; \left(max.\; when\; R_2 < P_2 \right) \;\;=\;\; R_2\; b }$$

$$\large{ M_x \; \left(max.\; when\; x < a \right) \;\;=\;\; R_1\; x }$$

$$\large{ M_x \; \left[ max.\; when\; a < x < \;\left( L - b \right) \right] \;\;=\;\; R_1\; x - P_1\; \left( x - a \right) }$$

Symbol English Metric
$$\large{ \Delta }$$ = deflection or deformation  $$\large{in}$$ $$\large{mm}$$
$$\large{ x }$$ = horizontal distance from reaction to point on beam $$\large{in}$$ $$\large{mm}$$
$$\large{ a, b }$$ = length to point load $$\large{in}$$ $$\large{mm}$$
$$\large{ M }$$ = 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 $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ I }$$ = second moment of area (moment of inertia) $$\large{in^4}$$ $$\large{mm^4}$$
$$\large{ R }$$ = reaction load at bearing point $$\large{lbf}$$ $$\large{N}$$
$$\large{ L }$$ = 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. 