Simply supported beam with multiple point loads.

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Use one statics model for several point-load layouts.

The calculator accepts three load slots and sorts active loads by position. Loads at the same position are added, so the same page can represent a single central load or a group of independent wheel, joist, or reaction loads.

Governing equations

For active loads P_i at x_i, R_B = ΣP_ix_i/L and R_A = ΣP_i - R_B. At a section x, M(x) = R_Ax - ΣP_i(x - x_i) for loads to the left of x. The displayed governing moment is checked at each load position and support.

Classic variants covered

This parameterised page covers a central point load, one arbitrary point load, equally spaced or unequally spaced loads, and unequal load magnitudes. It is a statics screen; it does not calculate elastic deflection.

Keep it as a statics load-case screen.

• Use positive L and keep every x_i between 0 and L.
• Loads are downward and non-negative; zero loads are ignored.
• Do not add a distributed load here or interpret the result as a fatigue, vibration, stress, or design check.
• Loads at a support are treated as input point actions at that coordinate; confirm the physical load path separately.