1. Design Basis and Code Reference
Approved Document A (England): Structural safety and loading.
Eurocode basis adopted in this note: BS EN 1990 for basis of design and combinations, and BS EN
1995-1-1 for timber member design.
Material grade: C24 timber.
Stud spacing: 406 mm centres.
Header beam to be built up from: (2) 2" x 6" C24 members, acting together, overall section 76 x
140 mm.
2. Geometry Taken from Sketch
Item Value
Longer roof zone 3.973 m
Shorter roof zone 2.236 m
Wall height 2.451 m
Wall width 2.250 m
Small opening 0.650 m
Large opening 1.700 m
Common stud size 38 x 140 mm (2 x 6 nominal)
Header beam size 76 x 140 mm built-up from (2) 2" x 6"
3. Adopted Loading
Roof dead load, Gk = 0.60 kN/m2
Roof variable load, Qk = 1.00 kN/m2
Wall self-weight = 0.30 kN/m2 of wall face
Wall strip above header used for header check = 0.45 m
4. Load Combinations
ULS roof design load:
qd = 1.35Gk + 1.50Qk
qd = 1.35(0.60) + 1.50(1.00)
qd = 0.81 + 1.50 = 2.31 kN/m2
Wall line load above header:
wwall,above = 0.30 x 0.45 = 0.135 kN/m
Adopt: wwall,above = 0.14 kN/m
5. C24 Material Properties and Design Values Used in This Note
Adopted characteristic properties for C24 used for preliminary sizing:
fm,k = 24 N/mm2 (bending)
fc,0,k = 21 N/mm2 (compression parallel to grain)
fv,k = 4.0 N/mm2 (shear)
E0,mean = 11,000 N/mm2
Adopted modification / safety factors for this preliminary note:
kmod = 0.80
γM = 1.30
Design strengths used for comparison:
fm,d = kmod x fm,k / γM = 0.80 x 24 / 1.30 = 14.77 N/mm2
fc,0,d = kmod x fc,0,k / γM = 0.80 x 21 / 1.30 = 12.92 N/mm2
fv,d = kmod x fv,k / γM = 0.80 x 4.0 / 1.30 = 2.46 N/mm2
6. Roof Reaction Line Loads to Supporting Walls
Longer roof zone reaction:
Rlong = qd x L / 2 = 2.31 x 3.973 / 2 = 4.59 kN/m
Shorter roof zone reaction:
Rshort = qd x L / 2 = 2.31 x 2.236 / 2 = 2.58 kN/m
7. Common Stud Checks
Stud section area: A = 38 x 140 = 5,320 mm2
ULS wall self-weight per metre of wall: 1.35 x (0.30 x 2.451) = 0.99 kN/m
ULS wall self-weight per stud: 0.99 x 0.406 = 0.40 kN
7.1 Front Wall Common Stud
Roof load per stud = Rshort x spacing = 2.58 x 0.406 = 1.05 kN
Total axial load per stud = 1.05 + 0.40 = 1.45 kN
Compression stress, σc = N / A = 1.45 x 1000 / 5320 = 0.27 N/mm2
Code comparison: 0.27 N/mm2 < fc,0,d = 12.92 N/mm2 -> ADEQUATE
7.2 Cheek Wall Common Stud
Roof load per stud = Rlong x spacing = 4.59 x 0.406 = 1.86 kN
Total axial load per stud = 1.86 + 0.40 = 2.26 kN
Compression stress, σc = N / A = 2.26 x 1000 / 5320 = 0.42 N/mm2
Code comparison: 0.42 N/mm2 < fc,0,d = 12.92 N/mm2 -> ADEQUATE
8. Header Beam Check
Header beam adopted: (2) 2" x 6" C24 members acting compositely. Overall built-up section = 76 x
140 mm.
Section properties: Z = b d2 / 6 = 76 x 1402 / 6 = 248,267 mm3
I = b d3 / 12 = 76 x 1403 / 12 = 17.38 x 10^6 mm^4
Conservative header line load used for both openings: w = Rlong + wwall,above = 4.59 + 0.14 =
4.73 kN/m
8.1 Large Opening Header, L = 1.70 m
Bending moment, M = wL2 / 8 = 4.73 x 1.702 / 8 = 1.71 kNm
Shear, V = wL / 2 = 4.73 x 1.70 / 2 = 4.02 kN
Bending stress, fb = M / Z = 1.71 x 10^6 / 248,267 = 6.88 N/mm2
Code comparison: 6.88 N/mm2 < fm,d = 14.77 N/mm2 -> ADEQUATE
Shear stress, τ = 1.5V / bd = 1.5 x 4.02 x 1000 / (76 x 140) = 0.57 N/mm2
Code comparison: 0.57 N/mm2 < fv,d = 2.46 N/mm2 -> ADEQUATE
Service line load for deflection = 3.18 + 0.14 = 3.32 kN/m
Deflection, δ = 5wL^4 / 384EI = 1.89 mm
Allowable check used: L/360 = 1700/360 = 4.72 mm
Code comparison: 1.89 mm < 4.72 mm -> ADEQUATE
8.2 Small Opening Header, L = 0.65 m
Bending moment, M = wL2 / 8 = 4.73 x 0.652 / 8 = 0.25 kNm
Shear, V = wL / 2 = 4.73 x 0.65 / 2 = 1.54 kN
Bending stress, fb = M / Z = 0.25 x 10^6 / 248,267 = 1.01 N/mm2
Code comparison: 1.01 N/mm2 < fm,d = 14.77 N/mm2 -> ADEQUATE
Shear stress, τ = 1.5V / bd = 1.5 x 1.54 x 1000 / (76 x 140) = 0.22 N/mm2
Code comparison: 0.22 N/mm2 < fv,d = 2.46 N/mm2 -> ADEQUATE
9. Jamb / Trimmer Stud Check Under 1700 mm Header
Header end reaction per side = wL / 2 = 4.73 x 1.70 / 2 = 4.02 kN
Take one 2 x 6 jack / trimmer stud: A = 38 x 140 = 5,320 mm2
Compression stress in one trimmer = N / A = 4.02 x 1000 / 5320 = 0.76 N/mm2
Code comparison: 0.76 N/mm2 < fc,0,d = 12.92 N/mm2 -> ADEQUATE
10. Summary
Member Adopted Size Governing Check Result
Front wall common
studs
38 x 140 C24 @ 406
mm c/c
σc = 0.27 N/mm2 <
12.92 N/mm2
Adequate
Cheek wall common
studs
38 x 140 C24 @ 406
mm c/c
σc = 0.42 N/mm2 <
12.92 N/mm2
Adequate
Header over 1700
opening
(2) 2" x 6" C24 built-
up
fb = 6.88 < 14.77, τ =
0.57 < 2.46
Adequate
Header over 650
opening
(2) 2" x 6" C24 built-
up
fb = 1.01 < 14.77, τ =
0.22 < 2.46
Adequate
Jamb / trimmer under
1700 header
38 x 140 C24 σc = 0.76 N/mm2 <
12.92 N/mm2
Adequate
Conclusion: On the adopted preliminary loading basis, the common 2 x 6 C24 studs at 406 mm
centres are adequate, the header beam shall be formed from (2) 2" x 6" C24 members, and the jamb /
trimmer studs under the 1700 mm header are adequate.