Formula Used
The calculator uses static equilibrium first. For a two-support beam, the equations are ΣFy = 0 and ΣMA = 0.
RB = [Σ(Wi × (xi − xA)) + ΣMi] ÷ (xB − xA). Then RA = ΣWi − RB.
For a fixed left cantilever, RA = ΣWi. The fixed moment is −Σ(Wi × xi) − ΣMi.
Shear is found by summing reactions and subtracting all loads to the left of a station. Moment is found by summing reaction moments, load moments, and applied point moment jumps to the left of that station.
For a uniform load over a partial length a, W = w × a and the centroid is at a ÷ 2 from the loaded segment start.
For a linearly varying load, W = (w1 + w2) × a ÷ 2. Its centroid from the start is a(w1 + 2w2) ÷ [3(w1 + w2)].
How to Use This Calculator
Enter the beam length first. Choose two supports or a fixed left cantilever. Add support positions when the beam has two supports.
Enter loads using the shown formats. Use one load per line. Enter downward loads as positive. Use negative values for upward loads.
Press the calculate button. The result appears above the form and below the header. Review reactions, critical values, zero shear locations, and station values.
Use the CSV button for spreadsheet work. Use the PDF button for a compact report file.
Why This Calculator Helps
A shear force and bending moment diagram shows how a beam carries load. It turns raw loading data into values at many stations. That makes design checks easier. It also helps students see how equilibrium works along a beam. This calculator accepts point loads, uniform loads, varying loads, support positions, and applied couples. It then solves reactions and reports shear and moment values.
Reading the Results
Positive shear means the left segment tends to move upward. Negative shear means the left segment tends to move downward. Positive bending moment usually represents sagging. Negative moment usually represents hogging. The table gives station values from the left end. Peak values can show where bending stress may control. Zero shear points often mark local maximum or minimum moment locations.
Useful Engineering Checks
Use the maximum absolute moment with the section modulus to estimate bending stress. Use maximum absolute shear with the selected shear area to estimate shear stress. Compare both results with allowable material limits. A diagram is not a complete design by itself. It is a fast starting point. Real beams also need deflection checks, connection checks, bearing checks, and code review.
Data Quality Tips
Keep units consistent through the whole entry. If length is in meters, use load units that match meters. Enter downward loads as positive values. Use negative loads for upward actions. Place loads inside the beam span. For overhanging beams, supports may be inside the total length. This is common for balcony, crane, and bracket style checks.
Common Use Cases
The tool is useful for classroom work, quick estimates, and report tables. It can compare alternate load positions. It can also show how a distributed load changes diagram shape. Export the CSV file when spreadsheet editing is needed. Export the PDF file when a compact record is useful. Always review assumptions before using results for final construction decisions.
Limitations To Remember
The calculation assumes small deflection behavior. It also treats loads as static and vertical. Dynamic impact, lateral torsion, buckling, and support settlement are outside the simple model. Use refined analysis for long spans, unusual sections, moving loads, or safety critical work. When in doubt, ask a qualified engineer to review the beam first.
FAQs
What is a shear moment diagram?
It is a pair of diagrams showing internal shear force and bending moment along a beam. They help locate critical sections for stress and deflection checks.
Can I enter more than one point load?
Yes. Add one point load per line. Use the format P@x, such as 12@3. Downward loads should be positive.
Does this handle uniform distributed loads?
Yes. Enter each load as w@start-end. The calculator converts each segment to its resultant and also integrates it for station values.
What does a negative reaction mean?
A negative reaction means the support force acts opposite to the assumed upward direction. It can happen with uplift, overhangs, or applied moments.
Can I use feet and pounds?
Yes, if all entries use consistent units. For example, use feet for length, pounds for point loads, and pounds per foot for distributed loads.
Why are zero shear points useful?
Zero shear points often indicate where bending moment reaches a local maximum or minimum. These locations can control beam sizing.
Does the PDF include every result row?
Yes. The generated PDF lists the summary and station values. For larger data work, the CSV export is usually easier to edit.
Is this a final structural design tool?
No. It is an analysis aid. Final design should include code rules, deflection, stability, connections, load factors, and professional review.