Tools — Beam Notch
How much section is left
after the notches?
A girder carrying joists from both sides with a column tenon at mid-span — the most common junction in Japanese timber framing, and a tedious one to work out by hand. Pick the sizes and see how much area, moment of inertia and section modulus survive. Everything runs in your browser.
Girder
×mm
What lands on it
Joist depth (mm)
Joist depth (mm)
Full-depth material left: 6 mm
Section properties after notching
| Property | Before | After | Ratio |
|---|---|---|---|
| Area (cm²) | 315.0 | 237.3 | 0.75 |
| Moment of inertia (cm⁴) | 23625 | 11982 | 0.50 |
| Section modulus (cm³) | 1575 | 653 | 0.41 |
| Centroid y_c (mm) | 116.6 | ||
How it works
- 01Choose the girder size. Width is 105 / 120 / 135; enter the depth directly.
- 02Choose the joist on each side. Joist width is fixed at 105; depth comes from the machining table (values in between are not interpolated).
- 03Say whether a column tenon (30 × 30) lands at mid-span.
- 04Results update as you go. The cross-section and the 3D view show where the material is lost.
Method & limits
- The housed dovetail is stepped: 1.5 mm, 12.0 mm and 21.0 mm into the girder, each at a different depth from the top (housing = joist depth, dovetail = d′, tip = d′−30).
- Widths B and C in the machining table run along the girder, so they do not affect the section — only the 3D view.
- Section properties do not depend on where the notches sit horizontally. Rearranging them changes the drawing, not the ratios.
- Ratios are rounded down to two decimals, on the safe side.
- These are the properties of the girder. Checking the joist end itself needs the separate Ae table.
- Shear is not checked. Bending may pass while the width left at the neutral axis governs.