Beam and Load Inputs
Enter both concentrated loads as downward loads. Their positions must fall between the two supports.
Example Data Table
| Input or result | Example value | Meaning |
|---|---|---|
| Span, L | 8.00 m | Support A to support B distance. |
| P1 at x1 | 12.00 kN at 2.50 m | First applied point load. |
| P2 at x2 | 18.00 kN at 5.50 m | Second applied point load. |
| Load multiplier | 1.20 | Creates 14.40 kN and 21.60 kN design loads. |
| Maximum moment | 48.38 kN·m | Occurs at the second load position. |
Formula Used
Take upward support reactions as positive. Let L be the span. Let x1 and x2 be measured from the left support.
RA = [P1(L − x1) + P2(L − x2)] / L
RB = P1 + P2 − RA
M(x) = RAx − P1max(0, x − x1) − P2max(0, x − x2)
The calculator checks the moment at both load positions. For two downward point loads on a simple span, the peak normally occurs under a load where shear changes sign.
How to Use This Calculator
- Enter the clear support-to-support span.
- Enter each point load and its left-support position.
- Select consistent load and length units.
- Enter 1.00 for direct values or apply your chosen multiplier.
- Choose the preferred result precision.
- Press Calculate Moment Diagram.
- Review reactions, load-point moments, peak moment, and the plotted diagram.
- Export the results or print the summary for your working file.
Two Point Loads on a Simple Beam
Two point loads create a simple but important beam case. A simply supported beam carries vertical reactions at both ends. Each load changes the shear force at its location. The bending moment remains continuous across the beam. It rises where shear is positive. It falls where shear becomes negative. The largest moment often occurs under one load. Its location depends on load sizes and positions. This calculator evaluates the complete load path quickly. It reports reactions, moment values, and the critical location. These results support preliminary framing choices before detailed design checks.
Reading the Moment Shape
The moment diagram begins at zero at the left support. It returns to zero at the right support. Straight segments join the load locations. That shape occurs because no distributed load exists between points. The slope of each moment segment equals the internal shear force. A downward point load causes a vertical shear change. It does not create a jump in bending moment. A higher reaction makes the first segment rise faster. Load position changes both reactions. Moving a load toward one support reduces its moment lever arm. However, it may increase the reaction at that nearby support.
Useful Construction Checks
Use consistent units throughout the calculation. Pair kN with metres for kN·m results. Pair pounds with feet for lb·ft results. Confirm that both positions sit within the support span. Check that field load locations match plans. Include applicable load factors only when your workflow requires them. The multiplier affects both reactions and moments. It does not change the load positions. Compare the peak moment against the member capacity from an approved design method. Also check shear, deflection, bearing, connections, and lateral stability. A moment result alone never completes a beam design.
Limits of This Model
This model assumes simple supports and vertical downward loads. It does not model fixed ends, overhangs, distributed loads, moving loads, or applied moments. It also excludes member self-weight unless you add it to the loading plan separately. Real structures may need multiple load combinations. Material properties and support details also matter. Use the diagram as a transparent calculation record. Then apply the relevant project standard before construction decisions. It never replaces a licensed engineer’s review for critical onsite field conditions.
Frequently Asked Questions
1. What beam condition does this calculator use?
It uses a simply supported beam. The left and right supports provide vertical reactions. End moments are assumed to be zero. This is suitable for a basic span without fixed support restraint or an overhang.
2. Can the two load positions be entered in either order?
Yes. Enter P1 and P2 at any valid locations inside the span. The calculation evaluates both positions correctly. The diagram sorts their locations visually from left to right.
3. Why does the calculator apply a load multiplier?
The multiplier lets you review an adjusted load case without changing source values. Enter 1.00 for direct input loads. Use another value only when it matches your chosen calculation procedure.
4. Where does the maximum bending moment occur?
For this load pattern, it normally occurs at one point-load location. The controlling location is where the shear force changes from positive to negative. The calculator compares both load-point moments automatically.
5. Why are the support reactions important?
Reactions confirm vertical equilibrium. Their sum should equal the two design loads. They also determine shear and bending moment everywhere along the beam. Incorrect reactions produce an incorrect diagram.
6. Can I use mixed units?
No. Keep every load in the selected load unit. Keep every distance in the selected length unit. Mixed units can create incorrect reaction and moment values without an obvious warning.
7. Does this calculator include beam self-weight?
No. It only calculates the two entered point loads. Add self-weight through a separate load model or convert it into an appropriate equivalent loading method for your analysis.
8. Does a point load cause a jump in the bending moment diagram?
No. A point load creates a jump in the shear force diagram. The bending moment remains continuous. Its line slope changes immediately at the point load.
9. Can this tool analyse fixed-end beams?
No. Fixed ends develop end moments and require a different model. Use a structural-analysis method that includes rotational restraint, support stiffness, and the correct boundary conditions.
10. What does a negative bending moment mean here?
A negative value follows the chosen sign convention and indicates hogging. With two downward loads on a simple span, results are usually sagging and positive. Other beam conditions can produce negative moments.
11. Is this result enough to approve a beam?
No. It supports early checks and learning. Confirm member capacity, connections, deflection, stability, load combinations, and local requirements separately. Use verified design standards before approving any beam work.