Calculator Form
Example Data Table
| Case | Span | Load | E | I | Max Deflection |
|---|---|---|---|---|---|
| Fixed-Fixed Center Point Load | 6 m | 30 kN | 200 GPa | 80,000,000 mm4 | 2.109 mm |
| Fixed-Fixed Uniform Load | 5 m | 12 kN/m | 210 GPa | 60,000,000 mm4 | 1.550 mm |
| Fixed-Fixed Center Point Load | 4 m | 18 kN | 70 GPa | 35,000,000 mm4 | 2.449 mm |
Formula Used
Case 1: Fixed-Fixed Beam with Center Point Load
Support reactions: RA = RB = P / 2
Fixed end moments: MA = MB = P L / 8
Maximum deflection: δmax = P L3 / (192 E I)
Left half curve: y(x) = P x2 (3L - 4x) / (48 E I)
Right half curve: y(x) = P (L - x)2 (4x - L) / (48 E I)
Case 2: Fixed-Fixed Beam with Full-Span Uniform Load
Support reactions: RA = RB = w L / 2
Fixed end moments: MA = MB = w L2 / 12
Maximum deflection: δmax = w L4 / (384 E I)
Deflection curve: y(x) = w x2 (L - x)2 / (24 E I)
Variable meanings
P = point load, w = uniform load per unit length, L = span length, E = elastic modulus, I = second moment of area, and EI = flexural rigidity.
How to Use This Calculator
- Select the fixed-fixed beam case that matches your loading.
- Enter the beam span and choose the matching length unit.
- Enter the load value and the correct load unit.
- Provide the elastic modulus and second moment of area.
- Choose how many graph points you want for the curve.
- Press the calculate button to show reactions, end moments, and maximum deflection above the form.
- Use the CSV buttons to save summary data or graph points.
- Use the PDF button to export the visible result section.
Important Scope Note
This calculator handles two common statically indeterminate fixed-fixed beam cases. It is not a general solver for varying sections, moving loads, multiple point loads, settlement, thermal effects, or changing support stiffness.
FAQs
1. What makes a beam statically indeterminate?
A beam is statically indeterminate when equilibrium equations alone cannot find every reaction. Extra compatibility conditions and stiffness relations are needed to complete the solution.
2. Which beam cases are included here?
This page solves two fixed-fixed beam cases: a center point load and a full-span uniform load. Both are classic indeterminate bending problems.
3. Why do E and I matter so much?
E measures material stiffness and I measures section stiffness. Their product, EI, controls how strongly the beam resists curvature and vertical deflection.
4. Can I mix unit systems?
Yes. The calculator converts the entered units to a common internal system, then reports the main deflection in your chosen length unit and in millimeters.
5. Why is fixed-fixed deflection smaller than simply supported deflection?
Fixed ends restrain rotation, which increases overall stiffness. That restraint reduces curvature and usually produces smaller maximum deflection under the same loading and span.
6. What does the graph show?
The graph shows the downward deflection magnitude along the beam span. It helps you see where the beam bends most and how the curve changes with load type.
7. Can I use this for several loads at once?
Not directly. This version covers one standard loading pattern at a time. For combined loads, you would need superposition or a broader beam analysis model.
8. Why would I download CSV or PDF results?
CSV is useful for checking, archiving, or sharing numbers in spreadsheets. PDF is helpful when you want a clean record for reports, reviews, or design notes.