| Beam type | Load case | Span (m) | Loading | Approx. max moment (kN·m) |
|---|---|---|---|---|
| Simply supported | Uniform load | 10 | w = 12 kN/m | 150.0 |
| Simply supported | Point load | 8 | P = 90 kN at a = 3 m | 168.8 |
| Simply supported | Two point loads | 12 | 80 kN @3 m, 60 kN @8 m | 310.0 |
| Cantilever | Uniform load | 6 | w = 8 kN/m | 144.0 |
| Cantilever | Point load | 5 | P = 40 kN at a = 4 m | 160.0 |
Examples are for learning and scoping. Always verify against project drawings and governing design standards.
Simply supported with uniform load over full span
- Reactions: R1 = R2 = wL/2
- Maximum moment at midspan: Mmax = wL²/8
Simply supported with a point load
- Let a be distance from left, b = L − a
- Reactions: R1 = P·b/L, R2 = P·a/L
- Maximum moment under the load: Mmax = P·a·b/L
Simply supported with two point loads
- Reaction right: R2 = (P1·a1 + P2·a2)/L
- Reaction left: R1 = (P1 + P2) − R2
- Peak moment is commonly at a load location; this tool checks moments at a1 and a2.
Cantilever (fixed at left)
- Uniform load: fixed-end moment Mmax = wL²/2
- Point load at distance a: fixed-end moment Mmax = P·a
- Two point loads: fixed-end moment Mmax = P1·a1 + P2·a2
- Select the beam type that matches your girder support condition.
- Choose the load case that best represents the governing scenario.
- Enter span length and load magnitudes using your preferred units.
- For point loads, enter the correct distance from the reference end.
- Press the calculate button to show reactions and peak moment.
- Use CSV or PDF export to attach results to site notes.
Why bending moment governs girder design
Bending moment represents the internal turning demand caused by applied loads and support reactions. It drives flexural stress, required section modulus, and reinforcement or flange sizing. On site, bending moment also guides temporary works decisions because overstressed girders can crack, deflect excessively, or compromise bearing details. This calculator provides repeatable moment estimates to support preliminary checks, comparisons, and reporting during concept planning.
Selecting a realistic load case
Start by matching the beam type to the actual restraint: simply supported for bearings with rotation, or cantilever for fixed-end connections. Then select the loading pattern that best reflects the governing condition. Uniform load is suitable for distributed deck weight or continuous backfill pressure. Point loads represent cranes, lifted components, or concentrated equipment. Two point loads approximate paired wheel loads or tandem lifting and sequencing.
Interpreting reactions and peak moment
Reactions quantify how total load is shared by supports and are useful for bearing checks, shoring layout, and load paths into columns. The maximum bending moment is reported with its location along the span, enabling quick section checks at critical positions. For a full-span uniform load on a simply supported girder, the peak occurs at midspan. For point loads, the peak typically occurs under a load for inspections.
Unit control and input validation
Construction calculations often mix units, so the tool normalizes forces to kN and lengths to meters internally. Keep unit choices consistent with drawings and specifications, and confirm that load positions fall within the span. Negative loads are blocked to prevent sign confusion in basic checks. If a case involves partial uniform loading, multiple supports, or moment releases, treat the output as a screening value only before submission.
Using results in design documentation
Use the exported CSV or PDF as a calculation attachment for method statements, temporary works notes, or coordination emails. Record assumptions: span definition, load magnitude, and position reference. Compare calculated moments against allowable capacities from steel tables or reinforced concrete design outputs, factoring applicable load combinations. When values are close to limits, refine the model using structural analysis software and confirm with the engineer of record and approvals.
1) What does “maximum bending moment” mean?
It is the largest internal flexural demand along the member for the selected case. It is commonly used to size the girder section and check bending stresses.
2) Where does the maximum moment usually occur?
For a simply supported girder with full-span uniform load, it occurs at midspan. For a single point load, it occurs directly under the load. For a cantilever, it occurs at the fixed end.
3) Why are support reactions shown?
Reactions help verify load distribution to bearings, shoring, and columns. They also support checks for uplift, base plate demands, and temporary support sizing in construction staging.
4) Can I use this for partial uniform loads or multiple spans?
Not directly. The calculator uses standard closed-form solutions for full-span uniform load and up to two point loads on a single span. Use structural analysis for partial loading, continuity, or complex restraint.
5) How accurate is the two point loads option?
It is accurate for the stated assumptions and evaluates moments at the load positions, which commonly govern. If loads are close together or other distributed loads exist, a full moment diagram check is recommended.
6) What should I document with exported results?
Include span definition, beam type, load case, units, and reference points for load locations. Note any omitted effects such as self-weight factors, dynamic impact, lateral torsional buckling, or load combinations.