A real-time design tool for stress-graded wood roof trusses. Following JIS Z 2101 E-F grading and the Japanese Building Standards Law allowable-stress approach, it returns bottom-chord tension, top-chord compression, safety factors and midspan deflection as you change species, grade, span and loads.
Parameters
Lumber species
Representative structural species
Stress grade (E-F)
JIS Z 2101 mechanical grading
Truss span L
m
Truss height h
m
Trusses per roof plane
Number used to split an 18.2 m wide building
Dead load DL
kN/m²
Live load LL
kN/m²
Snow load SL
kN/m²
Heavy-snow regions use 2-3 kN/m² or more
Results
—
Equiv. UDL w (kN/m)
—
Reaction R (kN)
—
Bottom-chord tension (kN)
—
Top-chord compression (kN)
—
Safety factor (tension)
—
Deflection (mm / limit)
—
King-post truss diagram — member force visualisation
Bottom chord (red = tension), top chord (blue = compression), king post, roof load w and the two support reactions R. Line thickness scales with member force.
Deflection vs span L
Allowable stress by grade (fb / ft / fc)
Theory & Key Formulas
$$F_{\text{bottom}} = \frac{w L^{2}}{8 h}, \qquad SF = \frac{f_{t}}{F/A}, \qquad \delta = \frac{5 w L^{4}}{384 E I}$$
w: equivalent UDL, L: truss span, h: truss height, F: member force, f_t: allowable tensile stress, A: cross-section area, delta: deflection. The practical serviceability limit is delta/L < 1/250.
DL: dead, LL: live, SL: snow load. The 18.2 m building width is divided into N_trusses, giving the tributary spacing s per truss; that converts the area load to a line load w.
Wood Truss Stress-Graded Design — JIS Z 2101 and Japanese Building Code
🙋
A "wood truss" is the triangular wood framework in a roof, right? How can a bunch of small timber sticks actually span 10 or 20 metres?
🎓
Exactly — think of the king-post or scissors trusses you see in gymnasiums, warehouses and modern Japanese houses. The trick is the triangle: it's a rigid shape, so each member only sees axial force (tension or compression), not bending. Wood is weak in bending but strong axially, so triangulating it uses the material extremely efficiently. That's why small timber sections can span 10-30 m.
🙋
In the left panel I see things like "E70-F225" — what does that mean? Is a higher grade simply better wood?
🎓
Good question. It's the JIS Z 2101 mechanical grading: E is the characteristic modulus of elasticity (E70 = 7.0 GPa) and F is the characteristic bending strength (F225 = 22.5 N/mm^2). Standard housing lumber is E70-F225 (Grade 1); for long spans or snowy roofs you go E110-F315 or higher. Note that changing the grade doesn't change the bottom-chord force itself — but you'll see the safety factor and deflection improve significantly.
🙋
The top and bottom chords are colour-coded. Which one breaks first, the red or the blue?
🎓
Wood typically has lower tensile strength f_t (~18 N/mm^2) than compressive strength f_c (~22 N/mm^2), so purely axially the bottom-chord tension is the first thing to worry about. But the top chord carries compression and can also buckle (long slender member bowing sideways). On long spans with shallow truss height, buckling tends to govern. In practice you check tension chord, compression chord, web members and king post separately — the smallest safety factor wins.
🙋
When I increase snow load from 0.6 to 3.0 the safety factor drops fast. How do designers handle this in snowy regions?
🎓
Nice catch. Heavy-snow regions in Japan (Hokkaido, the Hokuriku coast, etc.) compute snow load as at least 30 N/m^2 per centimetre of design snow depth — easily 4-5 kN/m^2 in the mountains of Niigata. Designers respond by (1) bumping the grade to E110-F315 or above, (2) increasing truss height h to reduce chord force, (3) adding more trusses to shrink the tributary width s, and (4) using larger sections like 120 x 300. That's why traditional snow-country houses have steep roofs and chunky, closely-spaced rafters.
🙋
Truss height h has a huge effect. So bigger h is always better?
🎓
From the formula F_bottom = wL^2/(8h), yes — more h, less chord force. But making h larger means a steeper roof, more roof area, more material and more cost. Rule of thumb: truss height should be about span/5 to span/8, so a 12 m span uses h = 1.5-2.4 m. Scissors trusses or rigid-jointed trusses let you keep h modest while distributing forces. Combine with CLT (cross-laminated timber) or Glulam and you can go to mass timber long spans — Izumo Dome at 142 m is the largest wooden dome in the world, built with Glulam keel arches.
Frequently asked questions
Notations like 'E70-F225' come from the JIS Z 2101 mechanical grading system used in Japan. E is the characteristic value of the modulus of elasticity (E70 = 7.0 GPa) and F is the characteristic bending strength (F225 = 22.5 N/mm^2). Higher E means lower deflection; higher F means higher allowable stress. Standard housing structural lumber is E70-F225, while long-span trusses or heavy roof loads use E110-F315 or higher. This tool lets you toggle four grades (E70 / E90 / E110 / E130) and see the impact instantly.
In a king-post truss the bottom chord carries tension and the top chord carries compression. Wood typically has a higher compressive strength than tensile, but the top chord also has to be checked for buckling. With long spans and shallow truss heights, top-chord buckling dominates; with shorter spans and adequate truss height, bottom-chord tension governs. The tool computes F_bottom = wL^2/(8h) and reports SF_tension and SF_compression separately so you can see which one is critical.
Japanese Building Standards Law Enforcement Order Article 82 prescribes 'dead + live' for long-term and 'dead + live + snow' for short-term (snow case). In heavy-snow regions the snow combination usually governs. The tool simply sums the three components into one equivalent uniform load w. In a real design you also need to check seismic and wind combinations, and allowable stresses are increased for short-term loads (roughly doubled). Treat this tool as long-term / service-load screening.
Typical deflection limits for wood trusses are L/250 to L/300 (40-48 mm for a 12 m span). The Japan Housing Finance Agency's housing performance standard uses L/250, and L/200 is sometimes used when long-term creep is considered. This tool uses L/250 as the pass/fail criterion. The deflection formula is the simplified chord-elongation estimate delta = 2 * F_bottom * L / (E * A_bottom), which omits joint slip and roof-plane stiffness. Real designs should account for creep deformation (about twice the initial deflection under long-term loads).
Real-world applications
Roof framing in Japanese post-and-beam housing: Most traditional Japanese houses use king-post or Howe-truss variants for the roof. Spans of 6-10 m, truss height 1.2-2 m, and either 910 mm (half ken) or 1820 mm (one ken) spacing are typical. E70-F225 lumber at 105 x 270 mm is screened with this kind of tool and verified against the Housing Performance Standard. The 18.2 m (10 ken) building width is a classic modular-design number.
Glulam long-span structures: Gymnasiums, warehouses and large retail roofs span 20-40 m with Glulam (engineered Larch, Hinoki or Douglas Fir). Glulam picks higher grades (E110-F315+) and uses big sections (e.g. 150 x 600 mm). Izumo Dome (142 m span, one of the largest mass-timber roofs ever built) is constructed from Glulam keel arches; while it is not a simple king-post truss, the design philosophy of an axial-force-dominated wood system is shared.
Prefabricated truss-plate construction: The GangNail / MiTek truss-plate system dominates housing in North America and the Nordics, mass-producing wood trusses in a factory with punched steel connector plates. A whole house worth of roof trusses can be assembled in a day. The chord forces and safety factors from this tool can be cross-checked with the truss-plate manufacturer's allowable-load tables (Truswal, Alpine, etc.) to size each joint.
CLT and mid-rise mass timber: The rise of CLT (cross-laminated timber) has opened the door to wood buildings 10 storeys or higher. Hybrid CLT panel + wood truss roofs and Glulam column + steel-plate truss beam systems extend the axial-dominated wood-design philosophy of this tool into the mid-rise category. Demand is growing worldwide for both lifecycle-cost reduction and carbon storage.
Common misconceptions and pitfalls
The biggest pitfall is using the JIS characteristic strength directly as an allowable stress. The f_t = 18 N/mm^2 (E70-F225) that you enter here is a characteristic strength, not an allowable stress. Allowable stress also depends on load-duration, moisture, temperature and size factors. The Japanese Building Standards Law uses long-term = characteristic x 1.1/3 and short-term = long-term x 2. Glulam adds lamina-grade and adhesive corrections. The SF reported here is therefore "margin against characteristic strength" — for real designs aim for SF >= 3. An SF of 2 frequently fails the actual code check.
Next is ignoring joint and connection capacity. Most documented failures of wood trusses happen at the joints, not in the chord members. Tension bolts, hanger straps, gusset plates or truss plates all top out at 50-70% of the strength of the parent member. To resolve a 73.7 kN bottom-chord force at a joint you would need about six M16 tension bolts (~12 kN per bolt in tension). Declaring "the member is fine" without sizing the joint is dangerous.
Finally, overlooking creep and moisture movement. Under sustained loads, wood deflection grows to 1.5-2x its initial value (creep). The 8.9 mm shown here is the instantaneous deflection; long-term it becomes 15-18 mm. The L/250 = 48 mm criterion is fine for the instantaneous check, but L/300 = 40 mm is a safer long-term target. On top of that, wood shrinks and swells ±0.3% with moisture, so over-restraining a joint will eventually split the timber. Glulam moves less than solid sawn lumber, and where you use sawn timber, kiln-dried (KD) lumber is essential.
How to Use
Enter truss span in metres (typical range 6–15 m for residential roof structures) and roof pitch height in metres to define truss geometry.
Specify the number of trusses in the array and dead load in kN/m² (typically 0.5–1.2 kN/m² for timber roof decking plus insulation).
The simulator calculates equivalent uniform distributed load (UDL), support reactions, bottom-chord tension per JIS Z 2101 stress-graded lumber categories, and compares deflection against L/180 serviceability limit.
Review safety factors for tension; if below 2.0, reduce span or increase truss spacing.
Worked Example
Span 10 m, height 2.5 m, 8 trusses at 1.2 m centres, dead load 0.8 kN/m². Tributary load per truss = 0.8 × 1.2 = 0.96 kN/m. Equivalent UDL w = 0.96 kN/m; support reaction R = 4.8 kN. Bottom-chord tension T = (0.96 × 10²)/(8 × 2.5) = 4.8 kN. For E-F grade Karamatsu (Japanese larch, f_t,0,k = 12 MPa, E = 10.5 GPa), safety factor = 12/(4.8/0.002) ≈ 5.0. Deflection = (5 × 0.96 × 10⁴)/(384 × 10500 × 8 × 10⁻⁶) ≈ 18 mm; limit 10000/180 = 55.6 mm, satisfactory.
Practical Notes
JIS Z 2101 stress grades (E-F, E50-F300) vary by species; Karamatsu and Sugi are common; verify moisture content ≤15% for design values.
Truss spacing governs tributary load; closer spacing (0.9 m) reduces member stresses but increases material cost; optimize for 1.2–1.5 m centres in temperate climates.
Snow load (Japan: 0.3–2.0 kN/m² by region) must be added to dead load; check local building code (Building Standard Law Article 88).
Bottom-chord governs tension design; if safety factor <2.5, increase section modulus by doubling cross-section or using laminated veneer lumber (LVL).