Calculations › Timber Rafter
Timber Rafter
EN 1995-1-1
Checks a timber roof rafter in bending, shear and deflection to EN 1995-1-1.
Diagram
Example inputs
Rafter length (along slope)4000 mm
Roof pitch30 °
Rafter spacing600 mm
Permanent load (on plan)0.75 kN/m²
Snow load (on plan)0.5 kN/m²
Wind load (perp. to slope)0.3 kN/m²
Width b47 mm
Depth h175 mm
Timber gradeC24
Service class1
National annexUK
Results
Timber Rafter — 47×175mm
C24 · SC1 · 30° pitch · EN 1995-1-1
Results
✓ Bending PASS
util 0.456.61EN 1995-1-1 §6.1.6
| kmod (modification factor) | 0.8 | — | EN 1995-1-1 Table 3.1 |
| Design bending strength fm,d = fm,k × kmod / γM | 14.77 | N/mm² | EN 1995-1-1 §2.4.1 |
| Horizontal span = rafterLength × cos(pitch) | 3464 | mm | |
| Load per rafter wEd = (1.35·gk + 1.5·sk) × spacing | 1.058 | kN/m | |
| Design moment MEd = wEd × L² / 8 | 1.59 | kNm | EN 1995-1-1 §6.1.6 |
| Section modulus Wel = b × h² / 6 | 239896 | mm³ | |
| Design bending stress σm,d = MEd / Wel | 6.61 | N/mm² | EN 1995-1-1 §6.1.6 |
✓ Shear PASS
util 0.140.33EN 1995-1-1 §6.1.7
| Design shear strength fv,d = fv,k × kmod / γM | 2.46 | N/mm² | EN 1995-1-1 §2.4.1 |
| Design shear force VEd = wEd × L / 2 | 1.83 | kN | EN 1995-1-1 §6.1.7 |
| Design shear stress τd = 1.5 × VEd / (b × h) | 0.33 | N/mm² | EN 1995-1-1 §6.1.7 |
✓ Deflection PASS
util 0.536.10EN 1995-1-1 §7.2
| Second moment of area I = b × h³ / 12 | 20990885 | mm⁴ | |
| Characteristic load per rafter wk = (gk + sk) × spacing | 0.75 | kN/m | |
| Instantaneous deflection wInst = 5wkL⁴ / (384 × E × I) | 6.1 | mm | EN 1995-1-1 §7.2 |
| Deflection limit = L / 300 | 11.5 | mm | EN 1995-1-1 Table 7.2 |
WARNINGS
Vibration check recommended — EN 1995-1-1 §7.3. Slender rafter; dynamic response may govern.
Try it yourself
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