Simply supported beam with partial UDL zones.

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Build common partial-load variants from two zones.

Each zone is a downward UDL with intensity w_i, start a_i, and end b_i. The zones may be central, at an end, at both ends, separated, touching, or overlapping.

Governing equations

For zone i, W_i = w_i(b_i - a_i) and its centroid is x̄_i = (a_i + b_i)/2. Equilibrium gives R_A = ΣW_i(L - x̄_i)/L and R_B = ΣW_i - R_A. Within each interval, shear changes linearly and the critical moment is checked at zone boundaries and zero-shear positions.

Classic variants covered

This parameterised page covers a central partial UDL, an end partial UDL, partial UDLs at both ends, two separated zones, and overlapping uniform-load zones. Overlap means the intensities are added.

Keep it as a statics load-case screen.

• Use positive L; keep every a_i and b_i between the supports with b_i ≥ a_i.
• Loads are downward and non-negative; a zero-intensity zone is ignored.
• Deflection, stress, self-weight unless entered, load factors, stability, and code limits are not checked.
• This is elastic-load analysis terminology, not member or connection design.