Simply Supported Beam Load Balance

How to use Simply Supported Beam Load Balance

Balance total force and first moment to find the two support reactions. Integrate the explicit point and uniform loads piecewise, then inspect breakpoints and every interior zero-shear station for moment extrema.

1. Use the example as the schema; replace its labels and entered model assumptions.
2. Balance total force and first moment to find the two support reactions. Integrate the explicit point and uniform loads piecewise, then inspect breakpoints and every interior zero-shear station for moment extrema.
3. Calculate, inspect the complete witnesses and limitations, then copy or download the JSON report.

Good to know

• Positive span at most 1,000,000 m, 0–50 signed point loads, 0–50 positive-length UDL segments and 0–100 query stations. Forces are in N, intensities N/m, coordinates m; load magnitudes are at most 1,000,000,000.
• One pin/roller span with no applied couples or overhang. No deflection, stress, material, strength, allowable load, safety factor, building-code approval or structural recommendation. Flat extrema intervals are represented by endpoints.
• Local calculation with no upload, input persistence or outside lookup. Model JSON is limited to 30,000 characters and 10,000 values. Decimal quantities are strings with up to six places; count fields use plain JSON integers. Exact fractions are capped at 8,192 bits. The complete JSON output is limited to 1,000,000 characters; approximate numbers preserve their stored values. Unsupported states fail explicitly.