Fixed-end Beam (UDL)
Compute fixed-end moment M and reaction R of a beam fixed at both ends under full-span UDL w.
Inputs
Formula
M = w·L²/12; R = w·L/2
Fixity lowers mid-span moment but raises end negative moment.
Fundamentals
Compute fixed-end moment M and reaction R of a beam fixed at both ends under full-span UDL w.
This tool computes Fixed-end Beam (UDL) from the formula: M = w·L²/12; R = w·L/2
History
Soil and structural mechanics were systematised in the 19th century, supporting modern civil design.
Engineering applications
Used for retaining, foundation and structural member design.
Glossary
| UDL w | Input parameter |
| Span L | Input parameter |
| Fixed-end moment M | Output result |
| Reaction R | Output result |
How to use
- Fill in UDL w, Span L in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Fixed-end moment M, Reaction R in the results area.
Formula · Worked Example · Knowledge
Formula
核心计算关系：M = w·L²/12; R = w·L/2
输入变量：
- UDL w
w— kN/m - Span L
L— m
输出结果：
- Fixed-end moment M
M— kN·m - Reaction R
R— kN
假设/适用：Earth pressure uses Rankine/Coulomb active assumptions; passive & surcharge handled separately.
Worked Example
根据公式 M = w·L²/12; R = w·L/2，取 UDL w = 5 kN/m；Span L = 6 m。
代入计算得：Fixed-end moment M = 15 kN·m；Reaction R = 15 kN。
Key Points
- Earth pressure uses Rankine/Coulomb active assumptions; passive & surcharge handled separately.
- Check both strength and stability (overturning, sliding).
- Support reactions from static equilibrium; continuous structures need force/displacement method.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| UDL w (kN/m) | w | kN/m | 5 |
| Span L (m) | L | m | 6 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Fixed-end moment M | M | kN·m |
| Reaction R | R | kN |
Applications
- Simply-supported/cantilever reactions
- Structural equilibrium analysis
- Shear & moment distribution
FAQ
What formula does this tool use?
This tool computes per ISO / AGMA / ASME standard formulas: M = w·L²/12; R = w·L/2
How accurate are the results?
Results match input precision, based on SI units and common engineering approximations; for critical duty re-check with a safety factor.
Where is it used?
Simply-supported/cantilever reactions