Structural Engineering Justification
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1 Structural Engineering Justification Project Type: Side Extension General Comments: Client Name: - Address: - Revision: v1 Section Summary Section Size Material Grade Connection Floor Joists 1 No. 225 x 50mm Timber Grade C16 Approved flooring to be spiked to every floor joist. Timber Rafters 1 No. 150 x 50mm Timber Grade C16 Spiked to wall plate & ridge board. Beam A 305 x 165 x 54 kg/m UB Grade S275 UB Sliced connection - see detail. Beam B 356 x 171 x 51 kg/m UB Grade S275 UB Sliced connection - see detail. Roof Trimmer 3 No. 225 x 50mm Timber Grade C16 50 mm DS toothed plate connector with M10 bolts at 400 mm c/c s. Imposed loadings are in accordance with BS6399-1:1996 Loading for buildings. Roof Dead Load Imposed Load Ceiling Dead Load Imposed Load Floor Dead Load Imposed Load Walls Partitions Blockwork (100) Brickwork (112.5) 0.85 kn/m² 0.85 kn/m² 0.25 kn/m² 0.25 kn/m² 0.50 kn/m² 1.50 kn/m² 0.50 kn/m² 1.80 kn/m² 2.50 kn/m² Page 1 of 11
2 Floor Joist Design (BS5268-2:2002) Max opening span L = 4.2 m Floor Dead Load DL DL = 0.50 kn/m Floor Live Load LL LL = 1.50 kn/m 2 Joist spacing S S = 0.40 m Joist Dead Load wd Joist Live Load w l = S x DL = 0.20 kn/m = S x LL = 0.60 kn/m Joist self weight Fj = 0.15 kn/m Total Service Load = 0.95 kn/m Ra = Rb = W / 2 = 0.95 x L / 2 = 2.00 kn BM max = W L / 8 = 2.09 kn/m Consider long term uniformly distributed load Load duration factor K 3 = 1.00 Modification factors Section depth factor K 7 = (300 / h) 0.11 = 1.03 Load sharing factor K 8 = 1.10 Bending stress Bending stress σ m = 5.30 N/mm 2 (Class C16 BS5268:Part2:2002) Permissible bending stress σ m_adm = σ m K 3 K 7 K 8 = 6.00 N/mm 2 Z required Z = BM max / σ m_adm = 349 cm 3 Page 2 of 11
3 Specified Joist details Joist breadth; b = 50 mm (Class C16 BS5268:Part2:2002) Joist depth h = 225 mm Joist spacing s = 400 mm Joist span L = 5300 mm Modulus of elasticity E mean = 8800 N/mm 2 SEPB P128 Strength Class C16 Timber (BS5268:Pt 2:2002) Section properties Second moment of area I = b h 3 / 12 = mm 4 Section modulus Z = b h 2 / 6 = mm 3 Applied bending stress σ m_max = BM / Z = 4.97 N/mm 2 OK - Applied bending stress within permissible limits of: 6.00 N/mm 2 Check shear stress Shear stress τ = 0.67 N/mm 2 SEPB P128 (Class C16 BS5268:Part2:2002) Permissible shear stress τ adm = τ K 3 K 8 = N/mm 2 Applied shear stress τ max = 3 W L / (4 b h) = 0.34 N/mm 2 OK - Applied shear stress within permissible limits of: N/mm2 Check deflection Permissible deflection δ adm = min(0.003 x L) = 15.9 (should not be greater than 14 mm) = 14 mm Maximum deflection δ max = 5 W L 3 / 384 E mean I = 4.41 mm OK - Actual deflection within permissible limits of: 14 mm Therefore use 225mm x 50mm C16 400c/c s Page 3 of 11
4 Timber Rafters (BS5268-2:2002) Roof Dead Load DL DL = 0.85 kn/m Roof Live Load LL LL = 0.85 kn/m 2 Ceiling Dead Load DL = 0.25 kn/m 2 Ceiling Live Load LL = 0.25 kn/m 2 Rafter spacing S S = 0.40 m Roof pitch PR = 33.0 Deg 1 Length RLR = 3.20 m Roof Dead Load = 0.85/ cos (PR) = 1.01 kn/m Roof Live Load = 0.85 kn/m Joist self weight Fj = 0.15 kn/m Ceiling Dead Load Ceiling Live Load = S x DL = 0.10 kn/m = S x LL = 0.10 kn/m UDL Total Service Load = 2.21 kn/m Ra = Rb = W / 2 = 1.42 kn BMmax = W L / 8 = 1.81 knm Consider long term uniformly distributed load Load duration factor K 3 = 1.00 Modification factors Section depth factor K 7 = (300 / h) 0.11 = 1.03 Load sharing factor K 8 = 1.10 Bending stress Bending stress σ m = 5.30 N/mm 2 SEPB P128 (Class C16 BS5268:Part2:2002) Permissible bending stress σ m_adm = σ m K 3 K 7 K 8 = 6.00 N/mm 2 Z required Z = BM max / σ m_adm = 302 cm 3 Page 4 of 11
5 Specified Joist details Joist breadth; b = 50 mm (Class C16 BS5268:Part2:2002) Joist depth h = 150 mm Joist spacing s = 400 mm Joist span L = 3200 mm Modulus of elasticity E mean = 8800 N/mm 2 SEPB P128 Strength Class C16 Timber (BS5268:Pt 2:2002) Section properties Second moment of area I = b h 3 / 12 = mm 4 Section modulus Z = b h 2 / 6 = mm 3 Applied bending stress σ m_max = BM / Z = 9.67 N/mm 2 OK - Applied bending stress within permissible limits of: 6.00 N/mm 2 Check shear stress Shear stress τ = 0.67 N/mm 2 SEPB P128 (Class C16 BS5268:Part2:2002) Permissible shear stress τ adm = τ K 3 K 8 = N/mm 2 Applied shear stress τ max = 3 W L / (4 b h) = 0.71 N/mm 2 OK - Applied shear stress within permissible limits of: N/mm2 Check deflection Permissible deflection δ adm = min(0.003 x L) = 9.6 mm (maximum of 14 mm) Maximum deflection δ max = 5 W L 3 / 384 E mean I = 7.63 mm OK - Actual deflection within permissible limits of: 9.6 mm Therefore use 50mm x 150mm C16 timbers. 2 No. Rafters either side of Velux window locations. Page 5 of 11
6 P Beam A (BS5950 Part 1: 2000) a b with UDL & Point Load from Trimmer c Max opening span L = 7.00 m Spacing S = 4.00 m Floor Dead Load DL DL = 0.50 kn/m Floor Live Load LL LL = 1.50 kn/m 2 Wall Dead Load DL DL = 2.50 kn/m 2 Wall Height H = 3.20 m Roof pitch PR = 32.5 Deg 1 Length - wall to ridge RLR = 3.00 m Length - wall to eave RLE = 1.00 m Floor Dead Load wd Floor Live Load w l Wall Dead Load = 0.5 x L x DL = 1.75 kn/m = 0.5 x L x LL = 5.25 kn/m = DL x Wall Height = 8.00 Beam self weight Fj = 0.25 kn/m UDL Total Service Load = kn/m UDL - Design Load (w) = 1.5 x UDL = kn/m Point Load from Trimmer = 2.00 kn Point Design Load - (P) = 1.5 x P = 3.00 kn Distance a = 3.50 m Distance b = 2.50 m Rb = (Pb + wl x L/2) / 4 = kn W Total (Ra + Rb) Ra BM under point load P = wl + P = kn = W - Rb = kn = Pab / L = 3.75 kn BM due to UDL = W L / 8 = knm BM Total = knm Py = 275 N/mm² (BS5950 Part 1:2000 Table 9 for Grade S275 steel) Page 6 of 11
7 Sx Required = BM / Py = cm 3 I required = S x W x L 3 = cm 3 Max Deflection = L / 360 = mm Le = 1.0 x L = 7000 mm Try 305 x 165 x 54 kg/m UB (SEPB P214) Section Depth = mm Flange Thickness (t) = 7.9 mm Beam Sx = Second moment of area OK - Actual beam greater = Ix = cm 4 than require limit of: cm 3 Minor axis slendernesss (h) = Le/ry = 201 x = Depth / Thickness = h / x = 5.12 Slenderness factor (V) = 0.79 BS5950:Table 14 Slenderness correction factor (n) = 1.0 Buckling parameter (u) = 0.89 Lateral torsional buckling (hlt) = n x u x V x h = Pb = N/mm² BS5950:Table 11 Buckling resistance moment (Mb) = Sx x Pb = 91.1 knm OK - Actual beam greater than require limit of: knm Therefore use 305 x 165 x 54 kg/m UB as Beam A. Page 7 of 11
8 P Beam B (BS5950 Part 1: 2000) a b with UDL & Point Load from Beam A c Max opening span L = 4.50 m Spacing S = 6.00 m Floor Dead Load DL DL = 0.50 kn/m Floor Live Load LL LL = 1.50 kn/m 2 Wall Dead Load DL DL = 2.50 kn/m 2 Wall Height H = 3.20 m Roof pitch PR = 32.5 Deg 1 Length - wall to ridge RLR = 3.00 m Length - wall to eave RLE = 1.00 m Roof Dead Load Roof Live Load Wall Dead Load = ((0.85 / cos(rp) x (RLR + RLE/2)) = 3.53 kn/m = (0.85 x (RLR + RLE/2)) = 5.31 kn/m = DL x Wall Height = 8.00 Beam self weight Fj = 0.25 kn/m UDL Total Service Load = kn/m UDL - Design Load (w) = 1.5 x UDL = kn/m Point Load from Beam A = kn Point Design Load - (P) = kn Distance a = 4.00 m Distance b = 0.50 m Rb = (Pb + wl x L/2) / 4 = kn W Total (Ra + Rb) Ra BM under point load P = wl + P = kn = W - Rb = kn = Pab / L = kn BM due to UDL = W L / 8 = knm BM Total = knm Py = 275 N/mm² (BS5950 Part 1:2000 Table 9 for Grade S275 steel) Page 8 of 11
9 Sx Required = BM / Py = cm 3 I required = S x W x L 3 = cm 3 Max Deflection = L / 360 = mm Le = 1.0 x L = 4500 mm Try 356 x 171 x 51 kg/m UB (SEPB P214) Section Depth = mm Flange Thickness (t) = 7.4 mm Beam Sx = Second moment of area OK - Actual beam greater = Ix = cm 4 than require limit of: cm 3 Minor axis slendernesss (h) = Le/ry = 129 x = Depth / Thickness = h / x = 2.70 Slenderness factor (V) = 0.79 BS5950:Table 14 Slenderness correction factor (n) = 1.0 Buckling parameter (u) = 0.89 Lateral torsional buckling (hlt) = n x u x V x h = Pb = N/mm² BS5950:Table 11 Buckling resistance moment (Mb) = Sx x Pb = 96.5 knm OK - Actual beam greater than require limit of: knm Therefore use 356 x 171 x 51 kg/m UB as Beam B. Page 9 of 11
10 Roof Trimmer (BS5268-2:2002) Max opening span L = 4.00 m Joist spacing S S = 3.00 m Roof pitch PR = 33.0 Deg 1 Length - wall to ridge RLR = 3.00 m Roof Dead Load = ((0.85 / cos(rp) x (RLR + RLE/2)) x 0.4 = 1.22 kn/m Roof Live Load = (0.85 x (RLR + RLE/2)) x 0.4 = 1.02 kn/m Joist self weight Fj = 0.15 kn/m Total Service Load = 2.39 kn/m Ra = Rb = W / 2 = 2.39 x L / 2 = 4.77 kn BM max = W L / 8 = 4.77 kn/m Consider long term uniformly distributed load Load duration factor K 3 = 1.00 Modification factors Section depth factor K 7 = (300 / h) 0.11 = 1.03 Load sharing factor K 8 = 1.10 Bending stress Bending stress σ m = 5.30 N/mm 2 (Class C16 BS5268:Part2:2002) Permissible bending stress σ m_adm = σ m K 3 K 7 K 8 = 6.00 N/mm 2 Z required Z = BM max / σ m_adm = 795 cm 3 Page 10 of 11
11 Specified Joist details Joist breadth; b = 150 mm (Class C16 BS5268:Part2:2002) Joist depth h = 225 mm Joist spacing s = 400 mm Joist span L = 4800 mm Modulus of elasticity E mean = 8800 N/mm 2 SEPB P128 Strength Class C16 Timber (BS5268:Pt 2:2002) Section properties Second moment of area I = b h 3 / 12 = ###### mm 4 Section modulus Z = b h 2 / 6 = mm 3 Applied bending stress σ m_max = BM / Z = 3.77 N/mm 2 OK - Applied bending stress within permissible limits of: 6.00 N/mm 2 Check shear stress Shear stress τ = 0.67 N/mm 2 SEPB P128 (Class C16 BS5268:Part2:2002) Permissible shear stress τ adm = τ K 3 K 8 = N/mm 2 Applied shear stress τ max = 3 W L / (4 b h) = 0.25 N/mm 2 OK - Applied shear stress within permissible limits of: N/mm2 Check deflection Permissible deflection δ adm = min(0.003 x L) = 14.4 (should not be greater than 14 mm) = 14 mm Maximum deflection δ max = 5 W L 3 / 384 E mean I = 2.74 mm OK - Actual deflection within permissible limits of: 14 mm Therefore use 3no. 225 x 50mm C16 timbers Sections to be connected together using 50 mm DS toothed plate connector with M10 bolts at 400 mm c/c s. Page 11 of 11
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