Beam Load Calculator

For a simply supported beam with a total length or span (Span), loads ($M_n$) are applied at specific distances ($T_n$) from the left support. The calculator uses static equilibrium equations—specifically the sum of moments and forces—to find the reaction forces at both supports (typically designated as reaction $B$ for the right support and reaction $A$ for the left support). The right support reaction for a series of loads is calculated by taking the sum of each load multiplied by its distance from the left support, all divided by the total span: $B = \frac{\sum (M_n \times T_n)}{\text{Span}}$. Subsequently, the left reaction is determined by summing all applied loads and subtracting the right reaction: $A = \sum M_n - B$. This ensures that both vertical force equilibrium and rotational equilibrium are fully satisfied.

Consider a simply supported wooden beam with a total span of 6 meters. Two concentrated downward loads are applied along the span: a load of $M_1 = 10\text{ kN}$ located at a distance $T_1 = 2\text{ m}$ from the left support, and a second load of $M_2 = 15\text{ kN}$ located at $T_2 = 4\text{ m}$ from the left support. First, we calculate the right support reaction ($B_2$): \(B_2 = \frac{(10 \times 2) + (15 \times 4)}{6} = \frac{20 + 60}{6} = \frac{80}{6} \approx 13.33\text{ kN}\). Next, we find the left support reaction ($A_2$) by subtracting the right reaction from the total applied loads: \(A_2 = (10 + 15) - 13.33 = 25 - 13.33 = 11.67\text{ kN}\). Thus, the left support bears 11.67 kN and the right support bears 13.33 kN.

Always maintain consistent units throughout your calculation—mixing meters and millimeters or kilonewtons and pounds will yield erroneous results. Pay close attention to the reference point; distances ($T$) must always be measured consistently from the exact same datum point (usually the left support). Additionally, remember that these formulas apply specifically to statically determinate simply supported beams and should not be used directly for continuous beams or fixed-end supports without accounting for bending moments.