Calculator
Example Data Table
| Case | Span | Section | Load | Max Moment | Section Modulus | Bending Stress |
|---|---|---|---|---|---|---|
| Simply supported, midspan point load | 4.0 m | 90×190 mm | 8 kN | 8.000 kN·m | 54.150 cm³ | 147.78 MPa |
| Simply supported, UDL | 3.6 m | 100×250 mm | 2.2 kN/m | 3.564 kN·m | 104.167 cm³ | 34.21 MPa |
| Cantilever, end point load | 1.8 m | 75×200 mm | 3 kN | 5.400 kN·m | 50.000 cm³ | 108.00 MPa |
| Cantilever, UDL | 2.2 m | 140 mm round | 1.0 kN/m | 2.420 kN·m | 269.393 cm³ | 8.98 MPa |
Values are illustrative. Always verify assumptions against your design standard.
Formula Used
- Simply supported + midspan point load: M = P·L / 4
- Simply supported + UDL: M = w·L² / 8
- Cantilever + end point load: M = P·L
- Cantilever + UDL: M = w·L² / 2
How to Use This Calculator
- Select a section shape and enter its dimensions.
- Pick the load case that matches the beam support condition.
- Enter span length and the required load magnitude.
- Optionally add allowable stress and an adjustment factor.
- Press Calculate to view moment, modulus, and stress.
- Use CSV or PDF buttons for a quick site report.
This tool computes bending stress only. Deflection, shear, and stability checks are not included.
Material stresses in timber members
Bending stress reflects the extreme fiber demand produced by a bending moment. The calculator reports stress in MPa (N/mm²), so values can be compared with timber design stresses. Timber properties vary with species, grade, moisture, and grain direction, therefore field checks should reference the same basis as the allowable stress you enter.
Choosing realistic beam loading cases
Four beam cases are provided to match common construction situations. For simply supported beams, the maximum moment occurs at midspan, making checks straightforward for joists and lintels. For cantilevers, the peak moment is at the fixed face, which is critical for balconies, overhangs, and canopy framing. For uniform loads, ensure the intensity includes self-weight and finishes too. Point loads should include any concentrated reactions from secondary framing members. Select the case that matches how the member is supported in the field.
Geometry control through section modulus
Section modulus converts moment into stress, and geometry dominates capacity. Rectangular modulus uses S = b·h²/6, so increasing depth is usually the most effective strengthening option. Circular modulus uses S = π·d³/32, which shows how quickly capacity grows with diameter. Keep dimensions consistent with the bending axis; rotating a rectangular member changes h and therefore stress.
Allowable stress and adjustment factor use
When an allowable bending stress is entered, the calculator computes utilization as σ divided by the adjusted allowable value. The adjustment factor can represent design modifiers such as load duration, service class, or safety reductions required by your standard. Use K = 1.0 when you want a direct comparison without modifiers, and document any modifiers used in your report.
Practical workflow for site checks and reports
Measure span, verify the member size, and enter the governing load magnitude. Confirm whether loads are service-level or factored so the allowable value matches the same level. Review the moment, modulus, and stress outputs, then interpret utilization to decide if strengthening is needed. Export CSV for job logs or PDF for submittals and inspections.
FAQs
1. What bending axis is assumed for rectangular timber?
The calculator assumes strong-axis bending, using breadth b and depth h in S = b·h²/6. If the member is rotated, swap the dimensions so h represents the bending depth.
2. Which units are used in the results?
Internally, the tool converts inputs to millimeters and Newtons. It reports moment in kN·m, section modulus in cm³, and bending stress in MPa for easy comparison.
3. How do I choose between point load and uniform load cases?
Use a point load case for a concentrated load at midspan or at a cantilever tip. Use the uniform load case for loads spread evenly along the span, including self-weight and finishes.
4. What should I enter for allowable bending stress?
Enter the allowable bending stress from your project’s timber grade and design standard. Ensure the value corresponds to the same load level you are checking, and apply modifiers through the adjustment factor if required.
5. What does an adjustment factor greater than 1 mean here?
The factor multiplies the allowable stress shown in the utilization check. Use it only when your design method permits increasing allowable stress for conditions such as short-duration loads; otherwise keep it at 1.0.
6. Does this calculator verify shear or deflection?
No. It focuses on bending stress from common beam formulas. For design decisions, also check shear, bearing, deflection limits, lateral stability, and connection capacity using your governing standard.
FAQ answers are general guidance. Always follow your applicable code and project specifications.