Mono Roof Truss Calculator

Inputs Geometry Loads Section

Clear span (m)

Building length along ridge (m)

Pitch (degrees)

Spacing between trusses (m)

Dead load (kN/m²)

Live/Snow load (kN/m²)

Allowable bending stress fb (MPa)

Elastic modulus E (MPa)

Section width b (mm)

Section depth h (mm)

Overhang each end (m) (optional)

Key Results

Rafter length (m)

-

Rise (m)

-

Truss count

-

Uniform line load w (N/mm)

-

Max moment M = wL²/8 (kN·m)

-

Required section modulus S_req (mm³)

-

Provided section modulus S_prov (mm³)

-

Bending utilization M/(fb·S)

-

Max deflection δ = 5wL⁴/(384EI) (mm)

-

Materials & Layout

Member cut lengths

Top chord (rafter): - m
Bottom chord (span): - m
Heel height (rise): - m
Overhang each end: - m

Panelization suggestion

Use 4–6 panels; web angles between 30–60° are typical for mono trusses.

Recommended panels: -
Approx. panel length along top chord: - m
Approx. panel length along bottom chord: - m

Example Data Table

Sample inputs and resulting key outputs for quick reference.

Span (m)	Pitch (°)	Spacing (m)	Dead (kN/m²)	Live (kN/m²)	Rafter (m)	M (kN·m)
6.0	15	0.6	0.50	0.75	6.21	3.62
8.0	12	0.6	0.60	0.75	8.08	6.14
5.0	18	0.4	0.45	0.65	5.24	1.73

Worked Example: Using This Calculator

A complete walk-through with the default values. Click the button to load them, then press Calculate.

Given

Clear span = 6.00 m; length along ridge = 12.00 m
Pitch = 15°; truss spacing = 0.60 m
Dead load = 0.50 kN/m²; live/snow = 0.75 kN/m²
Trial section b×h = 50 × 200 mm, fb = 12 MPa, E = 10,000 MPa
Overhang each end = 0.30 m

Steps

Rise: rise = span·tan(15°) = 1.608 m
Rafter length without overhang: L = √(6²+1.608²) = 6.212 m
Cut length with overhangs: 6.212 + 2·0.30 = 6.812 m
Line load: w = (0.50+0.75)·0.60 = 0.75 N/mm
Max moment: M = wL²/8 = 3.617 kN·m
Required modulus: S_req = M/fb = 301,443 mm³
Provided modulus: S = b·h²/6 = 333,333 mm³
Utilization: M/(fb·S) = 0.90 (OK)
Deflection: δ = 43.6 mm under service load
Truss count: ⌊12/0.6⌋ + 1 = 21

Summary

Rafter cut length	6.812 m
Rise	1.608 m
Uniform line load w	0.750 N/mm
Max moment	3.617 kN·m
S_req vs S	301,443 mm³ vs 333,333 mm³
Utilization	0.90
Deflection	43.6 mm
Truss count	21

These values are for preliminary checks. Verify full combinations and connections.

Formulae Used

For a mono top chord treated as a simply supported member under uniform line load:

Rise: rise = span · tan(θ), where θ is roof pitch in degrees.
Rafter length: L = √(span² + rise²).
Uniform line load: w = (dead + live) · spacing converting kN/m² to kN/m.
Max bending moment: M = w·L²/8.
Section modulus required: S_req = M / f_b using consistent units (N, mm).
Rectangle section: S_prov = b·h²/6, I = b·h³/12.
Deflection: δ_max = 5·w·L⁴ / (384·E·I).

These closed-form checks support preliminary sizing only. Final designs must be reviewed by a licensed engineer and satisfy local codes, load combinations, factors, and connection design.

How to Use

Enter span, pitch, spacing, and loads per area.
Specify material properties and a trial rectangular section.
Click Calculate to compute geometry, loads, bending, and deflection.
Target utilization ≤ 1.00 and check deflection against your limit.
Use Download CSV for records and Download PDF to print.

Recommended Deflection Limits (Typical)

Common serviceability ratios used in many practices. Confirm with your governing code.

Member / Case	Limit	Notes
Top chord under live/snow	L/240	Service load, instantaneous
Top chord total load	L/180	Service load, long-term
Ceiling finishes	L/360	To reduce cracking
Overhang cantilever	L/150	Check vibration/visual

Typical Timber Sections (mm) with Properties

Rectangular sections with section modulus S and second moment I for quick trials.

b × h (mm)	S = b·h²/6 (mm³)	I = b·h³/12 (mm⁴)
38 × 140	124,133	8,689,333
50 × 150	187,500	14,062,500
50 × 200	333,333	33,333,333
63 × 225	531,563	59,800,781

Dead Load Components Guide (kN/m²)

Indicative surface loads for rapid estimates. Replace with project-specific weights.

Component	Typical Range	Example Value
Metal sheet roofing	0.05 – 0.15	0.10
Sheathing / decking	0.10 – 0.30	0.20
Insulation	0.05 – 0.30	0.15
Ceiling + battens	0.10 – 0.25	0.15
Miscellaneous services	0.05 – 0.15	0.10

FAQs

Which loads should I enter?

Enter unfactored service loads per area. Include dead items like roofing, sheathing, ceiling, and services. Add live or snow per your code. For wind uplift, this tool is not applicable.

Does this design a complete truss?

No. It gives preliminary sizing for the top chord using simple formulas. It does not design joints, plates, webs, connections, bracing, bearings, or global stability. Engage a licensed engineer.

Can I switch to imperial units?

Inputs are metric: m, mm, kN/m², MPa. You can convert and enter equivalent numbers. I can add a toggle for feet, inches, psf, and ksi on request.

What spacing should I choose?

Spacing depends on purlins, sheathing, and local practice. Many light roofs use 0.6–1.2 m. Closer spacing reduces load per truss and deflection. Confirm against manufacturer guidance and code.

What deflection limit should I check?

Common limits: L/240 for live, L/180 total, and L/360 when finishes are crack-sensitive. Your jurisdiction may differ. Compare reported deflection with the selected limit to judge acceptability.

Notes & Assumptions

Mono truss modeled as simply supported with uniform load on top chord.
Loads are service-level inputs; adapt to required combinations as needed.
Units: inputs in m, kN/m², MPa, mm; internal conversions handled automatically.
Overhang excluded from structural span for bending and deflection.