Example Data
| Input | Example value | Meaning |
|---|---|---|
| Total span | 10 m | Distance from Support A to Support C. |
| Support B location | 4 m | Intermediate roller before the hinge. |
| Internal hinge location | 6 m | Moment release separating the beam segments. |
| Point load 1 | 18 kN at 2 m | Downward load on the left segment. |
| UDL 1 | 4 kN/m from 0 m for 4 m | Uniform load carried by the left segment. |
| Point load 2 | 12 kN at 8 m | Downward load on the right segment. |
Formula Used
This calculator applies static equilibrium to each side of the internal hinge. The hinge carries axial and vertical force, but it carries no bending moment.
Right segment moment equation: Cy(L − xh) − Σ[Wr(x − xh)] + ΣMr = 0
Right segment vertical equation: Hr + Cy − ΣWr = 0
Left segment moment equation: ByxB + Hlxh − Σ(Wlx) + ΣMl = 0
Left segment vertical equation: Ay + By + Hl − ΣWl = 0
For a uniform load, the calculator replaces q over length a with a resultant W = qa. It places that resultant at the loaded length midpoint. A distributed load spanning the hinge is divided into two separate resultants before solving.
How to Use This Calculator
- Enter the total beam span from Support A to Support C.
- Set Support B before the internal hinge location.
- Enter point loads using downward positive values.
- Enter each UDL intensity, start position, and loaded length.
- Enter applied moments as positive for counterclockwise rotation.
- Add horizontal loads only when axial reactions are needed.
- Click Calculate Reactions and review force directions carefully.
- Check the displayed equilibrium residuals before using results.
Use consistent units throughout. For example, combine metres with kilonewtons and kilonewton-metres. This tool supports preliminary analysis, not final code design.
Internal Hinge Beam Analysis
An internal hinge divides a beam into two connected free bodies. The connection transfers vertical force and axial force. It does not transfer bending moment. This release changes how reactions are found. Each beam side can be isolated. Engineers then apply equilibrium to each isolated segment.
The calculator uses a stable three-support arrangement. Support A is pinned. Support B is a roller on the left segment. Support C is a roller on the right segment. The internal hinge lies between B and C. This layout is statically determinate when the supports are correctly positioned.
Start with the right segment. Take moments about the hinge. The hinge force has no lever arm there. This produces the reaction at Support C. Use vertical equilibrium next. The result is the vertical hinge force acting on the right segment. The equal opposite force then acts on the left segment.
Next, isolate the left segment. Include Support A, Support B, left-side loads, and the transferred hinge force. Take moments about Support A. This finds the reaction at Support B. Then apply vertical equilibrium. That determines the vertical reaction at Support A. Horizontal loads are solved separately because the roller supports do not resist horizontal force.
Distributed loads need careful treatment. A uniform load becomes one equivalent point load. Its magnitude equals intensity times loaded length. Its position is the midpoint of that loaded length. A load crossing the hinge must be split. Each portion belongs to the segment where it acts. This calculator performs that split automatically.
Applied couples affect moment equations directly. They do not change vertical force totals. Counterclockwise applied moments are entered as positive. Clockwise values should be negative. Keep your units consistent. Use force, length, and moment units that match one another.
Always inspect the equilibrium checks. Values near zero show that the calculated forces balance. A negative reaction is not automatically an error. It may indicate uplift or a reversed support action. Confirm that the physical support can provide that reaction. For final design, check deflection, connection capacity, member strength, load combinations, and applicable structural codes.
Reaction signs need careful interpretation during review. Upward reactions resist downward loads. Downward reactions may require anchors. Hinge forces act with opposite signs on adjoining free body diagrams.
Frequently Asked Questions
1. What does an internal hinge do in a beam?
An internal hinge releases bending moment at its location. It can transmit axial and shear force. It allows relative rotation between the connected beam segments.
2. Why must Support B be left of the hinge?
This calculator uses a determinate three-support arrangement. Support B stabilizes the left segment. Support C stabilizes the right segment. The stated order keeps the included equations valid.
3. Can I use upward loads?
Yes. Enter upward vertical loads as negative values. The calculator will include their sign in force and moment equilibrium.
4. Can a UDL cross the hinge?
Yes. The calculator divides the UDL at the hinge. It replaces each portion with its own equivalent point load.
5. Why is the hinge moment always zero?
An ideal hinge cannot resist a bending couple. Therefore, the moment at the released connection is zero, even while shear and axial force pass through it.
6. What sign is used for applied moments?
Counterclockwise applied moments are positive. Clockwise applied moments are negative. Use the same convention when reviewing your hand calculations.
7. What does a negative vertical reaction mean?
It means the calculated reaction acts downward. This can indicate uplift at a support. Verify that the real support, anchor, or bearing detail can resist it.
8. Does this calculator include beam deflection?
No. It calculates static reactions and internal hinge actions only. Deflection needs stiffness, section properties, material properties, and compatibility analysis.
9. Can I enter horizontal loads?
Yes. Positive horizontal loads act rightward. The calculator reports the pin reaction at Support A and the matching hinge axial transfer.
10. What units should I use?
Use one consistent system. For example, use kN, m, kN/m, and kN·m together. The calculator does not convert units automatically.
11. Is this suitable for final structural design?
Use it for checking and preliminary analysis. Final design requires load combinations, code requirements, member design, connection checks, and review by a qualified engineer.