Structural Calculations for Timber Canopy with Gable Roof

8/3/2019 Structural Calculations for Timber Canopy with Gable Roof

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GABLE CANOPY: TIMBER

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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

1.01: Dimension & Geometry

Canopy Width = L = 6.000 m Rise 1.2426 m

Canopy Pitch 22.5 degrees 0.393 radians 1/3 Rise 0.4142 m

Rafter Length = L1 = 3.247 m d = 2/3 Rise 0.8284 m

Load Width = Rafter Spacing = 1.200 m Gable End Area 3.7279 m²

Collar-Tie Length = 4.000 m

1.02: Estimate Moments to Rafters for Collar-Tied Roof Trusses (Dead Loading)

kPa kN/m LF LF

SWT 0.03

DL (cladding) 0.04

DL(battens) 0.02

DL+SWT 0.09 0.11 0.9 1.2

along projected length = Fy = DL cos (alpha) = 0.10 kN/m

W1 = wL/2 = 0.299 kN

W2 = wL/2 = 0.299 kN

W = 2 *W1 = 0.599 kN

Reaction A = 0.299 kN

Reaction B = 0.299 kN

Maximum = R1 = 0.299 kN

Span Moment M1=w.L^2/8 = 0.449 kNm

Collar-Tie Force F =(Ra.L/2 - W1.L/4)/d = 0.542 kN

Rafter Moment - udl M1=w.L1^2/8 = 0.132 kNm

Rafter Moment from Collar-Tie M2=(2/9)Fsin(α).L1 = 0.150 kNm

Resultant Rafter Moment (Est.) M1+M2 = 0.281 kNm

Ridge Reactions Bx = -F = -0.542 kN By = W1-Ra = 0.000 kN

1.03: Live LoadLL = 0.37 kPa adopt 0.25 kPa and also check directly for point load of 1.8kN

factored

kPa kN/m LF kN/m

1 LL 0.25 0.30 1.5 0.45

1.04: Moments to Rafters for Collar-Tied Roof Trusses (Live Loading)

Considering Uniformly Distributed Loading(UDL)

W1 = wL/2 = 0.900 kN

W2 = wL/2 = 0.900 kN

W = 2 *W1 = 1.800 kN



Maximum = R1 = 0.900 kN

Span Moment - UDL M1=w.L^2/8 = 1.35 kNm

Collar-Tie Force F =(Ra.L/2 - W1.L/4)/d = 1.63 kN

Rafter Moment - udl M1=w.L1^2/8 = 0.395 kNm

Rafter Moment from Collar-Tie M2=(2/9)Fsin(α).L1 = 0.450 kNm

Resultant Rafter Moment (Est.) M1+M2 = 0.845 kNm ...

Ridge Reactions Bx = -F = -1.630 kN By = W1-Ra = 0.000 kN

Considering Point Load at Ridge

Point Load P1 = 1.80 kN



Span Moment - Point Load M=P1.L/4 = 2.700 kNm span moment - point load at apex

Collar-Tie Force - Point Load F = Ra.L/(2.d) = 3.259 kN

Rafter Moment - Point Load M2=(2/9)Fsin(α).L1 = 0.900 kNm max

Max: 0.900 kNm < WindLoadRidge Reactions Bx = -F = -3.259 kN By = P1-Ra = 0.900 kN

(C)Roy Harrison Associates schGableCanopyTimber.xls Calcs



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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

1.05: Wind Class Pressures (theta=0) /1

(-ve, uplift)

Windward Slope Cpn1= -0.3 p1 = -0.29 kPa w1= 0.346 kN/m

Leeward Slope Cpn2 = -0.6 p2 = -0.58 kPa w2= 0.691 kN/m

wx wy

w1 0.13 0.32 kN/m wx,wy are components of w1,w2 distributed along length of rafter

w2 0.26 0.64 kN/m vertical and horizontal loads distributed across projected lengths equal w1,w2

W Wx Wy Directions

w1 1.122 -0.43 -1.04 kN/m -1 -1 {+ve, vertical down, horizontal push to right}

w2 2.244 -0.86 -2.07 kN/m -1 -1

sum -1.29 -3.11 kN/m

1.06: Reactions

Ra Rb checksum

Load 1 -0.73 -0.30 kN -1.04

Load 2 -0.61 -1.47 kN -2.07

(-ve, tiedown) Resultant -1.34 -1.77 kN -3.11

Nett Horizontal Reaction -0.43 kN <<--

1.07: Collar-Tie Force

Collar-T ie Force F =(-W1y.L/4 - W1x.h/2 + Ra.L/2 )/d = -2.65 kN -ve, Compression

Ridge Reactions Bx = W1x - F = 3.08 kN By = W1y-Ra = 0.30 kN

1.08: Estimate of Maximum Moment Simply Supported Beams (Wind Loading)

Rafter1 Rafter2

Rafter Moment - udl M1=w.L1^2/8 = 0.46 0.91 kNm

Rafter Moment from Collar-Tie M2=(2/9)Fsin(α).L1 = 0.73 0.73 kNm

Resultant Rafter Moment (Est.) M1+M2 = -1.19 -1.64 kNm -1 -1 max -1.64

NB: The maximum moment in the span is less than the sum of the maximum resulting from the LH and RH loads, for these two maxima

do not occur at the same location in the span. It is therefore a conservative estimate.

1.09: Wind Class Pressures (theta=0) /2

(-ve, uplift)

Windward Slope Cpn1= 0 p1 = 0.00 kPa w1= 0.000 kN/m

Leeward Slope Cpn2 = 0.6 p2 = 0.58 kPa w2= 0.691 kN/m

wx wy



W Wx Wy Directions

w1 0.000 0.00 0.00 kN/m 1 1w2 2.244 0.86 2.07 kN/m 1 1

sum 0.86 2.07 kN/m

1.10: Reactions roller pin

Ra Rb checksum

Load 1 0.00 0.00 kN 0.00

Load 2 0.61 1.47 kN 2.07

(-ve, tiedown) Resultant 0.61 1.47 kN 2.07

Nett Horizontal Reaction 0.86 kN


Collar-Tie Force F =(-W1y.L/4 - W1x.h/2 + Ra.L/2 )/d = 2.20 kN +ve, Tension

Ridge Reactions Bx = W1x - F = -2.20 kN By = W1y-Ra = -0.61 kN

1.12: Estimate of Maximum Moment Simply Supported Beams (Wind Loading)Rafter1 Rafter2






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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

Resultant Rafter Moment (Est.) M1+M2 = 0.61 1.52 kNm 1 1 max 1.52

1.13: Wind Class Pressures (Theta=90) \1

(-ve, uplift)

Windward Slope Cpn1= -0.3 p1 = -0.29 kPa w1= 0.346 kN/m

Leeward Slope Cpn2 = -0.3 p2 = -0.29 kPa w2= 0.346 kN/m

wx wy



W Wx Wy Directions

w1 1.122 -0.43 -1.04 kN/m -1 -1

w2 1.122 -0.43 -1.04 kN/m -1 -1

sum -0.86 -2.07 kN/m

1.14: Reactions

Ra Rb checksum

Load 1 -0.73 -0.30 kN -1.04

Load 2 -0.30 -0.73 kN -1.04

(-ve, tiedown) Resultant -1.04 -1.04 kN -2.07



Collar-T ie Force F =(-W1y.L/4 - W1x.h/2 + Ra.L/2 )/d = -1.56 kN -ve, Compression

Ridge Reactions Bx = W1x - F = 1.98 kN By = W1y-Ra = 0.00 kN


Rafter1 Rafter2



Resultant Rafter Moment (Est.) M1+M2 = -0.88 -0.88 kNm -1 -1 max -0.88

NB: The maximum moment in the span is less than the sum of the maximum resulting from the LH and RH loads, for these two maxima

do not occur at the same location in the span. It is therefore a conservative estimate.

1.17: Wind Class Pressures (Theta=90) \2

(-ve, uplift)

Windward Slope Cpn1= 0.4 p1 = 0.38 kPa w1= 0.461 kN/m

Leeward Slope Cpn2 = 0.4 p2 = 0.38 kPa w2= 0.461 kN/m

wx wy



W Wx Wy Directionsw1 1.496 0.57 1.38 kN/m 1 1

w2 1.496 0.57 1.38 kN/m 1 1

sum 1.15 2.76 kN/m

1.18: Reactions

Ra Rb checksum

Load 1 0.98 0.40 kN 1.38

Load 2 0.40 0.98 kN 1.38

(-ve, tiedown) Resultant 1.38 1.38 kN 2.76



Collar-Tie Force F =(-W1y.L/4 - W1x.h/2 + Ra.L/2 )/d = 2.07 kN +ve, Tension

Ridge Reactions Bx = W1x - F = -2.65 kN By = W1y-Ra = 0.00 kN


Rafter1 Rafter2





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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa


Resultant Rafter Moment (Est.) M1+M2 = 1.18 1.18 kNm 1 1 max 1.18

1.21: LoadCase Combinations

LF = 0.9 1.20 1.50

Ridge

Collar-Tie Force Rafter Moment Ra Rb Rbx Bx By

kN kNm kN kN kN kN

G = SWT + DL 0.54 T 0.281 0.30 0.30 0.00 -0.54 0.00

LL 1.63 T 0.845 0.90 0.90 0.00 -1.63 0.00

PL 3.26 T 0.900 0.90 0.90 0.00 -3.26 0.90

WL (theta=0) /1 -2.65 C -1.64 -1.34 -1.77 -0.43 3.08 0.30

WL (theta=0) /2 2.20 T 1.52 0.61 1.47 0.86 -2.20 -0.61

WL (theta=90) /1 -1.56 C -0.88 -1.04 -1.04 0.00 1.98 0.00WL (theta=90) /2 2.07 T 1.18 1.38 1.38 0.00 -2.65 0.00

0.9G 0.49 T 0.25 0.27 0.27 0.00 -0.49 0.00

1.2G 0.65 T 0.34 0.36 0.36 0.00 -0.65 0.00

1.2G + 1.5LL 3.09 T 1.61 1.71 1.71 0.00 -3.09 0.00

1.2G + 1.5PL 5.54 T 1.69 1.71 1.71 0.00 -5.54 1.35

0.9G + WL0/1 -2.17 C -1.39 -1.07 -1.50 -0.43 2.60 0.30

1.2G + WL0/2 2.85 T 1.86 0.97 1.83 0.86 -2.85 -0.61

0.9G + WL90/1 -1.07 C -0.63 -0.77 -0.77 0.00 1.50 0.00

1.2G + WL90/2 2.72 T 1.52 1.74 1.74 0.00 -3.30 0.00

min -2.17 C -1.39 -1.07 -1.50 -0.43 -5.54 -0.61

max 5.54 T 1.86 1.74 1.83 0.86 2.60 1.35

abs(max) 5.54 1.86 1.74 1.83 0.86 5.54 1.35(+ve sagging moment)

(-ve hogging moment)

(-ve, tie-down reaction)

(-ve compression)

Consider Point Load Centre of Collar-Tie

P = 1.1 kN M= PL/4 = 1.10 kNm

Consider Point Load on Collar-Tie Located Near Ends (similar to TDA pergola guide)

P = 1.1 kN M=Pab/L = 0.31 kNm a = 0.300 m b= 3.700 m

RIDGE BOARD

None load bearing connection board: size to AS1684.2

T = thickness of rafter = 45 mm Grade Same as Rafter: F7

D = Depth of rafter + 50mm = 190 mm

ADOPT: RIDGE BOARD 190 x 45 F7




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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

RAFTER

M*[LL] = 1.69 kNm V*[LL]= 1.83 kN M*[WL]= 1.86 kNm V*[WL]= 1.83 kN

Material

TIMBER F7 E = 7900 MPa f'by = 20.0 MPa=N/mm² EI = 8.13E+10 Nmm²

Timber Density = 550 kg/m³ rho_b 0.91 f's 2.10 MPa

SD6 f'p = 12.00 MPa f'l = 35.00 MPa

Section & Member Design AS1720

D = 140 mm B = 45 mm Axx = 6300 mm²

Ixx = 10290000 mm4

Zxx = 147000 mm³ ø = 0.85

k_1[LL] 0.94 Medium-Term 5.0 days k_1[wind] 1.00 Instantaneous 5.0 sec

k_4[moisture] 1.00 k_7[Length,Position of bearing] 1.00

k_6[temperature] 1.00 k_11[size,bending] 1.00k_9[strength sharing] 1.00 k_11[size,shear] 1.00

Lay = 1.624 m DesignCase 1 Slenderness Coefficient S1 13.24

{have battens max. 900 c/c} rho_b.S1 12.02 k_12 0.899

Bearing Length 45.00 mm Bearing Width 45.00 mm Bearing Area 2025 mm²

Theta 90.00 {90=perpendicular to grain} øNp 19.4 kN ok! (for option rafters top of fascia)

øMs = 2.35 kNm LL:ok! øMb = 2.11 kNm LL:ok! øV = 10.57 kN LL:ok!

øMs = 2.50 kNm WL:ok! øMb = 2.25 kNm WL:ok! øV = 11.25 kN WL:ok!

ADOPT: RAFTER 140 x 45 F7

COLLAR-TIE

M*[LL] = 0.31 kNm V*[LL]= 1.10 kN N*c[WL] = 2.17 kN N*t[LL] = 5.54 kN

Material

TIMBER F7 E = 7900 MPa f'by = 20.0 MPa=N/mm² EI = 1.02E+11 Nmm²Timber Density = 550 kg/m³ rho_b 0.91 rho_c 0.98 f's 2.10 MPa

SD6 f'p = 12.00 MPa f'l = 35.00 MPa f'c 15.00 MPa f't 10.00


D = 120 mm B = 90 mm Axx = 10800 mm²

Ixx = 12960000 mm4

Zxx = 216000 mm³ ø = 0.85


k_4[moisture] 1.00 k_7[Length,Position of bearing] 1.00 k_11[compression] 1.000

k_6[temperature] 1.00 k_11[size,bending] 1.00 k_11[tension] 1.000

k_9[strength sharing] 1.00 k_11[size,shear] 1.00


Lax = 4.000 m rho_b.S1 8.73 k_12 1.000

øMs = 3.45 kNm LL:ok! øMb = 3.45 kNm LL:ok! øV = 18.12 kN LL:ok!

g13 1.000 S3= 33.3 K_12 = 0.19 S4= 44.4 K_12 = 0.106

øNcxx 25.87 øNcyy 14.55

øNc = 14.55 kN WL:ok! øNt 86.3 kN LL:ok!ADOPT: COLLAR-TIE 2\120 x 45 F7

RIDGE COLLAR

M*[LL] = kN V*[LL]= kN N*c[LL] = 5.54 kN N*t[WL] = 2.60 kN

Material


Timber Density = 550 kg/m³ rho_b 0.91 rho_c 0.98 f's 2.10 MPa



D = 70 mm B = 45 mm Axx = 3150 mm²

Ixx = 1286250 mm4

Zxx = 36750 mm³ ø = 0.85



k_6[temperature] 1.00 k_11[size,bending] 1.00 k_11[tension] 1.000k_9[strength sharing] 1.00 k_11[size,shear] 1.00


Lax = 1.400 m L = 1.400 m rho_b.S1 7.89 k_12 1.000




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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

g13 1.000 S3= 20.0 K_12 = 0.52 S4= 31.1 K_12 = 0.216


øNc = 8.14 kN LL:ok! øNt 26.8 kN WL:ok!

ADOPT: RIDGE COLLAR 70 x 45 F7

CONNECTIONS

Collar-Tie to Rafter

V*[LL] = 5.54 kN V*[WL]= 2.17 kN N*[LL] = #N/A kN N*[WL] = #N/A kN

ø 0.85 JD4 isSeasoned 1 k1[LL] = 0.77 k13= 1

k14 = 1 k16 = 1 table column 3 k1[WL] = 1.14

Nail Diam 2.8 mm

Shear Axial Minimum Timber Thickness = t1 = 10D 28 mm

n[rows] = 5 5 Minimum Nail Penetration = tp = 10D 28 mm

n[cols] = 3 3 Required Edge Distance = 5D 14 mm

n[shear] = 15 15 Required End Distance = 20D 56 mmk17 = 0.9 Required Spacing Across Grain = 10D 28 mm

Qk 665 N 9.3 N/mm Required Spacing Along the Grain = 20D 56 mm

Timber Thickness t1 = 45.00 mm Maximum penetration 40 mm Length of Penetration 28 mm

Proportional Reduction of Shear Capacity 1.00

Due to reduced Penetration 1.00 Due to Reduced Timber Thickness 1.00

NAIL: øNj[shear] 5.9 kN LL:ok! øNj[axial] 3.3 kN #N/A

NAIL: øNj[shear] 8.7 kN WL:ok! øNj[axial] 3.3 kN #N/A

ADOPT: Collar-Tie to Rafter (5 rows x 3 Cols) Diam: 2.8 Nails OPTION 1

Screw Diam. 4.17 mm No8. 4

Shear Axial Minimum Timber Thickness = t1 = 10D 41.7 mm

n[rows] = 3 3 Minimum Nail Penetration = tp = 7D 29.19 mmn[cols] = 2 2 Required Edge Distance = 5D 20.85 mm

n[shear] = 6 6 Required End Distance = 10D 41.7 mm

k17 = 1 Required Spacing Across Grain = 3D 12.51 mm

Qk 1520 N 56 N/mm Required Spacing Along the Grain = 10D 41.7 mm

Timber Thickness t1 = 45.00 mm Maximum penetration 40 mm Length of Penetration 29.19 mm


Due to reduced Penetration 1.00 Due to Reduced Timber Thickness 1.00 Capable of Load Bearing!

SCREW øNj[shear] 5.97 kN LL:ok! øNj[axial] 8.34 kN #N/A

SCREW øNj[shear] 8.84 kN WL:ok! øNj[axial] 8.34 kN #N/A

ADOPT: Collar-Tie to Rafter (3 rows x 2 Cols) No.8 TYPE 17 Screws OPTION 2

Bolt Diam. 10 mm M10 øVfn = 10.37 øNtb= 18.59

ß° = 22.50 degrees {at zero degrees members parallel}

t1 = 45 mm t2 = 45 mm ø 0.75

f'pj = 12.5 MPa f'cj = 35.5 MPa k7= 1 k16 = 1

Shear Axial Perpendicular Loading Edge Dist' 4D 40

n[rows] = 3 3 Parallel Loading Edge Distance 2D 20

n[cols] = 1 1 Required End Distance = 8D 80

n[shear] = 3 3 Required Spacing Across Grain = 5D 50

k17 = 1 Required Spacing Along the Grain = 5D 50

b/D 4.5

beff[parallel to grain] 45 mm Qskl 7100 N

beff[perpendicular to grain] = 2t1 90 mm Qskp 5625.0 N

Qsk [Hankinson] 6837.4 N

Washer Thickness 2.5 Req' Washer Diameter 45 Square Washer Side Length 40Aw = 570 mm² Actual Washer Diam. 22.5 Proportional Reduction Capacity

Proportional Reduction of Shear Capacity Due to washer Size 0.5

BOLT øNj[shear] 5.92 kN LL:ok! øNj[axial] 12.34 kN #N/A




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???,????:SUBURB

Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

BOLT øNj[shear] 8.77 kN WL:ok! øNj[axial] 18.28 kN #N/A

ADOPT: Collar-Tie to Rafter (3 rows x 1 Cols) M10 (Property Class 4.6 Bolts)+22.5 washers OPTION 3

CONNECTIONS

Ridge Collar




Nail Diam 2.8 mm


n[rows] = 20 20 Minimum Nail Penetration = tp = 10D 28 mm

n[cols] = 2 2 Required Edge Distance = 5D 14 mmn[shear] = 40 40 Required End Distance = 20D 56 mm

k17 = 0.75 Required Spacing Across Grain = 10D 28 mm







Length>300mm,NOT practical Length of fastening 1120 W idth of Fastening : 56

ADOPT: Ridge Collar (20 rows x 2 Cols) Diam: 2.8 Nails OPTION 1


Shear Axial Minimum Timber Thickness = t1 = 10D 41.7 mmn[rows] = 3 3 Minimum Nail Penetration = tp = 7D 29.19 mm

n[cols] = 2 2 Required Edge Distance = 5D 20.85 mm









Space: ok! Length of fastening 125.1 Width of Fastening : 54.21

ADOPT: Ridge Collar (3 rows x 2 Cols) No.8 TYPE 17 Screws OPTION 2



t1 = 45 mm t2 = 45 mm ø 0.75

f'pj = 12.5 MPa f'cj = 35.5 MPa k7= 1 k16 = 1


n[rows] = 2 2 Parallel Loading Edge Distance 2D 20 40




b/D 4.5


beff[perpendicular to grain] = 2t1 90 mm Qskp 5625 N

Qsk [Hankinson] 7100 NWasher Thickness 2.5 Req' Washer Diameter 45 Square Washer Side Length 40

Aw = 570 mm² Actual Washer Diam. 45 Proportional Reduction Capacity

Proportional Reduction of Shear Capacity Due to washer Size 1




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???,????:SUBURB

Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa



Space: ok! Length of fastening 130 Width of Fastening : 40

ADOPT: Ridge Collar (2 rows x 1 Cols) M10 (Property Class 4.6 Bolts)+45.0 washers OPTION 3

CONNECTIONS

Rafter to Ridgeboard




Nail Diam 2.8 mm


n[rows] = 4 4 Minimum Nail Penetration = tp = 10D 28 mmn[cols] = 1 1 Required Edge Distance = 5D 14 mm

n[shear] = 4 4 Required End Distance = 20D 56 mm









ADOPT: Rafter to Ridgeboard (4 rows x 1 Cols) Diam: 2.8 Nails OPTION 1

Screw Diam. 4.17 mm No8. 4Shear Axial Minimum Timber Thickness = t1 = 10D 41.7 mm

n[rows] = 2 2 Minimum Nail Penetration = tp = 7D 29.19 mm











ADOPT: Rafter to Ridgeboard (2 rows x 1 Cols) No.8 TYPE 17 Screws OPTION 2



t1 = 45 mm t2 = 45 mm ø 0.75

f'pj = 12.5 MPa f'cj = 35.5 MPa k7= 1 k16 = 1






b/D 4.5


beff[perpendicular to grain] = 2t1 90 mm Qskp 5625.0 NQsk [Hankinson] 5625.0 N

Washer Thickness 2.5 Req' Washer Diameter 45 Square Washer Side Length 40





9/18

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???,????:SUBURB

Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

Proportional Reduction of Shear Capacity Due to washer Size 1




ADOPT: Rafter to Ridgeboard (1 rows x 1 Cols) M10 (Property Class 4.6 Bolts)+45.0 washers OPTION 3

CONNECTIONS

Rafter to Perimeter Frame (Fascia Beams)

V*[LL] = 1.83 kN V*[WL]= 1.50 kN N*[LL] = #N/A kN N*[WL] = 0.86 kN



Nail Diam 2.8 mm

Shear Axial Minimum Timber Thickness = t1 = 10D 28 mmn[rows] = 5 5 Minimum Nail Penetration = tp = 10D 28 mm

n[cols] = 1 1 Required Edge Distance = 5D 14 mm

n[shear] = 5 5 Required End Distance = 20D 56 mm







NAIL: øNj[shear] 2.9 kN WL:ok! øNj[axial] 1.1 kN WL:ok!


ADOPT: Rafter to Perimeter Frame (5 rows x 1 Cols) Diam: 2.8 Nails OPTION 1


Shear Axial Minimum Timber Thickness = t1 = 10D 41.7 mm

n[rows] = 2 2 Minimum Nail Penetration = tp = 7D 29.19 mm









SCREW øNj[shear] 2.95 kN WL:ok! øNj[axial] 2.78 kN WL:ok!


ADOPT: Rafter to Perimeter Frame (2 rows x 1 Cols) No.8 TYPE 17 Screws OPTION 2


ß° = 90.00 degrees {at zero degrees members parallel} {90 equals bolt to fascia, 22.5deg's = bolt to rafter}

t1 = 45 mm t2 = 45 mm ø 0.75

f'pj = 12.5 MPa f'cj = 35.5 MPa k7= 1 k16 = 1






b/D 4.5

beff[parallel to grain] 45 mm Qskl 7100 Nbeff[perpendicular to grain] = 2t1 90 mm Qskp 5625 N

Qsk [Hankinson] 5625 N





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???,????:SUBURB

Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

Aw = 570 mm² Actual Washer Diam. 22.5 Proportional Reduction Capacity



BOLT øNj[shear] 4.81 kN WL:ok! øNj[axial] 12.18 kN WL:ok!


ADOPT: Rafter to Perimeter Frame (2 rows x 1 Cols) M10 (Property Class 4.6 Bolts)+22.5 washers OPTION 3

Maximum Bending Moment Fascia Beams

NB: For canopies attached to an existing building only. Only bending in a vertical plane considered {strong axis bending}.

Rafter Spacing 1.200 m

Fascia Beam Span 3.000 m

Number of Rafter Spacings in Span 2.500 =n isOdd 0.50 {=0(zero) Odd else Even}

Number of Raf ters in Span 1.500Bay Width 3.000 m

Minimum Number of Bays 1

Minimum Total Columns 4

From Rafter end reactions Simplified from Udl wind udl = (3/8)p2 + (1/8)p1

Action Moment Reaction Action Moment

kN kNm kN kPa kN/m kNm

Wind -1.50 -1.18 -1.13 Wind -0.252 -0.756 -0.85

Liveload 1.83 1.44 1.37 Liveload 0.250 0.750 0.84

For point loading of fascia M = (n^2-1)PL/8n , n is odd M = nPL/8 , n is even M=PL/3 for n=3, forces=2

Ra=Rb=(n-1)P/2

FASCIA BEAMS

M*[LL] = 1.44 kNm V*[LL]= 1.37 kN M*[WL]= 1.18 kNm V*[WL]= 1.13 kNMaterial



SD6 f'p = 12.00 MPa f'l = 35.00 MPa


D = 190 mm B = 45 mm Axx = 8550 mm²

Ixx = 2.572E+07 mm4

Zxx = 270750 mm³ ø = 0.85



k_6[temperature] 1.00 k_11[size,bending] 1.00



{have rafters max. 900 c/c} rho_b.S1 12.04 k_12 0.898


Theta 90.00 {90=perpendicular to grain} øNp 25.9 kN ok! (for option rafters top of fascia)øMs = 4.33 kNm LL:ok! øMb = 3.89 kNm LL:ok! øV = 14.35 kN LL:ok!


ADOPT: FASCIA BEAMS 190 x 45 F7

CONNECTIONS

Fascia Beam to Posts



k14 = 1 k16 = 1 k1[WL] = 1.14


ß° = 90.00 degrees {at zero degrees members parallel} {90 equals bolt to fascia, 22.5deg's = bolt to rafter}t1 = 45 mm t2 = 45 mm ø 0.75

f'pj = 12.5 MPa f'cj = 35.5 MPa k7= 1 k16 = 1




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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa






b/D 4.5


beff[perpendicular to grain] = 2t1 90 mm Qskp 5625 N

Qsk [Hankinson] 5625 N







ADOPT: Fascia Beam to Posts (2 rows x 1 Cols) M10 (Property Class 4.6 Bolts)+45.0 washers OPTION 3

Allowing for 3 Rafters: 5.48 kN ok!

Table 1.11:

Frictional Drag on RoofF0 = 0.010 Drag on Roof: 1 Bay 0.346 kN

F1 =F0 bd qz Nett Longitudinal Pressure Coefficient Cpn = 1.20

F1 = smooth/parallel to ribs Nett Gable End Load = qz.A.Cpn = 4.3 kN

2F1 = across corrugations

4F1 = across ribs

Magnifier 2.000

Drag ForcesDrag on rafters assumed shielded by gable end infill. If gable end infill not present then magnitude of rafter drag assumed

similar order of magnitude to the gable end loading. Drag on upper surface of cladding only considered.

Table 1.12:

Minimum Total Columns 10 Minimum Columns per Bay 2 Minimum Number of Bays 1

Maximum Column Height 2.400 m

Column Drag

Assume Maximum Column Width 90 mm Fd = Cf ig1. Cdyn. qz. Az Cfig = Cfig1 + sum(Ksh Cfig.1)

Kar = 1 Ki = 1 Cd = 1.2 Cfig1 = Kar Ki Cd = 1.2 Cdyn= 1

Az = 0.216 m²

Lever Arm m kNm kNm

Column Drag Fd = 0.249 kN Mid Height of Column 1.200 0.30 0.30

Nett Gable End Load / Column 0.429 kN Centroid of Gable end 2.814 1.21 1.03 h2=h

Nett Roof Drag / Column 0.173 kN Mid Height of Roof 3.021 0.52 0.41 h3=h

Nett Horizontal per Column 0.85 kN Column Base Moment 2.03 1.74 kNm

POST

N*[LL] = 1.37 kNm N*[WL]= 1.13 kN M*[WL]= 2.03 kNm V*[WL]= 0.85 kN

Material





D = 90 mm B = 90 mm Axx = 8100 mm²

Ixx = 5.47E+06 mm4

Zxx = 121500 mm³ ø = 0.85




k_9[strength sharing] 1.00 k_11[size,shear] 1.00Lay = 2.400 m DesignCase 1 Slenderness Coefficient S1 6.45

Lax = 2.400 m L = 2.400 m rho_b.S1 5.86 k_12 1.000





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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

Theta 0.00 {90=perpendicular to grain} øNp 75.5 kN ok! (for option rafters top of fascia)


g13 1.000 S3= 26.7 K_12 = 0.29 S4= 26.7 K_12 = 0.294


øNc = 28.50 kN LL:ok! øNt 68.9 kN WL:ok!

ADOPT: POST 1/90 x 90 F7

GABLE END FASCIA BEAM

With no gable end infill, just a decorative finish across end of canopy. With infill becomes beam bent about weak axis.

Gable End Load to Fascia = W = 2.15 kN FullSpan = 6.000 m M=W.L/6 = 2.15 kNm

Span = 3.000 m M=W.L/6 = 1.07 kNmGABLE END FACIA

M*[LL] = #N/A kNm V*[LL]= #N/A kN M*[WL]= 1.07 kNm V*[WL]= 1.07 kN

Material



SD6 f'p = 12.00 MPa f'l = 35.00 MPa


D = 45 mm B = 190 mm Axx = 8550 mm²

Iyy = 1.443E+06 mm4

Zyy = 64125 mm³ ø = 0.85



k_6[temperature] 1.00 k_11[size,bending] 1.00


Lay = 3.000 m DesignCase 1 Slenderness Coefficient S1 2.42{have rafters max. 900 c/c} rho_b.S1 2.19 k_12 1.000

øMs = 1.02 kNm #N/A øMb = 1.02 kNm #N/A øV = 14.35 kN #N/A


ADOPT: GABLE END FACIA 45 x 190 F7

STRUT If Gable end fascia to be braced/supported back to the purlins at 1000 c/c

N*c[WL] = 2.15 kN

Material





D = 70 mm B = 45 mm Axx = 3150 mm²Ixx = 1286250 mm

4Zxx = 36750 mm³ ø = 0.85






Lax = 2.800 m L = 2.800 m rho_b.S1 11.16 k_12 0.942

g13 1.000 S3= 40.0 K_12 = 0.13 S4= 62.2 K_12 = 0.054


øNc = 2.17 kN WL:ok!

ADOPT: STRUT 70 x 45 F7




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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

PIERS FOR COLUMNS

Density kg/m³ kN/m³ Limit State 1 L = 450 mm

Soil 1937.00 19.00 DL load factor 0.90 Area[squar 202500 mm²

Concrete 2400.00 23.54 Overturning Factor 1.00 Eq. Diam = 507.8 mm

D = 507.8 mm

Assume Soil to be : CLAYEY Check Up Lift Area[circ le] 202500 mm²

bearing allo p max = 150.00 kPa N u * = 1.13 Eq. L = 450.0 mm

Diamete d = 0.508 Volumes Soil 0.31 m³

Trial Depth D = 0.600 Concrete 0.12 m³

Adopt Depth : 0.600 m Forces Soil 5.93 kN

φ = 35 0.61 radians Concrete 2.86 kNγ = 1900 kN/m³ cohes 0.00 kN

c = 0.00 kPa DL N d N d = 0.00

active 0.27 Σ F= 8.79 kNpassive 3.69 FoS = 7.03soil cone {e} 0.42 > 1.00 okapex length {x} 0.36

diameter {f} 1.35 Check Over Turning Total cone height { 0.96

Cone Vol {V_tot} 0.46 P = H o 0.85

Apex vol {v2} 0.02 M o 2.03

Cylinder vol {v_cyl} 0.12 h = M o / H o = 2.38 m

Q2 =P(10h+3.4D)/(5.6 D ) 6.56

Q 1 = Q 2 + P 7.41 kN

S 1 = Q 1 / (0.68 d D) 35.75

⇒ p average

p u = 1.5 x S 1 53.63

< pmax ok

Bearing Force 1.37 kN

Bearing Area 0.20 m^2 6.8 kPa ok!

φ




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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

Assessment of Additional loads Applied to Existing House. Structure by Attached Canopy

NB: Assessment of the house structure is for the strength limit state only. Therefore can expect some diminished performance

for the serviceability limit state. Recommend use of props and other temporary supports during construction and maintenance operations.

Assumptions about existing house used for general assessment 1) Eaves width 500 mm

2) 240 mm Brick veneer, with 150 mm from face of brick to studwork

3) Rafters at 1200 mm c/c

4) Roof Pitch 20 degrees and steel sheet roof

5) Maximum Opening 2700 mm

Actions From Canopy at Connection Bracket 1.2

Actions on Fascia 1.2 m Actions House Rafters

LoadCase Fx Fy Fx Fy Fx Fy

kN kN kN/m kN/m kN kN

1.2 G 0.27 0.00 0.22 0.00 0.27

1.2 DL + 1.5 PL 1.71 0.00 1.42 0.00 1.71

1.2 DL + 1.5 LL 1.71 0.00 1.42 0.00 1.71

0.9G + WL0/1 -0.43 -1.50 -0.36 -1.25 -0.43 -1.50

1.2G + WL0/2 0.86 1.83 0.72 1.52 0.86 1.830.9G + WL90/1 0.00 -0.77 0.00 -0.64 0.00 -0.77

1.2G + WL90/2 0.00 1.74 0.00 1.45 0.00 1.74

MAX 0.86 1.83 MAX 0.86 1.83

Action : Fascia Board

Span = 1.200 m

Fy = 1.83 kN a= 0.6 m b = 0.600 m Mx = 0.55 kNm

Fx = 0.86 kN a= 0.6 m b = 0.600 m My = 0.26 kNm

Action : Rafter cumulative

Fascia to External Face of brick 0.500 0.500 m

External Face of Brick to Wall Stud 0.150 0.650 m

Lever arm of Connection Bracket 0.150 0.800 m

Vertical Distance from support to wall stud 0.237 m

Moment in Rafter

Due Fx Due Fy Resultant

1.2 G 0.22 0.22 kNm1.2 DL + 1.5 LL 1.37 1.37 kNm

0.9G + WL0/1 -0.10 -1.20 -1.30 kNm

1.2G + WL0/2 0.20 1.46 1.66 kNm

Max 1.66 kNm

Action: Rafter Connection

Magnification factor due to backspan 1.5 {NB: For backspans greater than twice overhang this reduces}

Force in Connection

Due Fx Due Fy

1.2 G 0.40 kN

1.2 DL + 1.5 LL 2.56 kN

0.9G + WL0/1 -0.43 -2.25 kN tie-down

1.2G + WL0/2 0.86 2.74 kN

Max 0.86 2.74 kN

Stud and bottom plate anchorages are generally impractical to strengthen, due to inaccessibility.

In brick veneer construction, external brickwork is none loadbearing, and is therefore available to provide resistance to uplift forces.

Density 22 kN/m³ LF = 0.9 Resistance 19.80 kN/m³




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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

Brick Width 0.110 m Brick Depth + mortar 0.086 m Brick Resistance 2.18 kN/m²

Max. Height of Wall Available 2.400 m

less 2 of brick work = 2.228 m Centres of anchorages = 1.200 m

to allow for fact that anchorage cannot be achieved below 1 brick rebate in ground slab from inside of wall cavity.

Area Resistance

Max. Height of Triangle = 1.039 m 0.624 m² 1.36 kN Additional Straight Required

Max. Straight Available Above = 1.189 m 1.427 m² 3.11 kN

total 4.47 kN Full Height Anchorage Adequate

3.72 kN/m

Tie-Down Force (P) = 2.25 kN

Min. Straight Required = 0.342 m 0.410 m² 0.89 kN

Minimum Height of Brickwork Required: 1.381 m 16 courses of brickwork 58% of height

Action: Tie-Down Beam / Lintel

Multiple Rafters Attached to beam to span opening. Max. W idth = 2.700 mAction [uplift] 2.25 kN M= 1.71 kNm R = 1.41 R2 = 3.66 kN

Action[gravity] 2.74 kN M= 2.08 kNm R = 1.71 R2 = 4.45 kN

Rafter Spacings in Span = n = 2.25 isOdd 0.25 {=0(zero) Odd else Even}

M = (n^2-1)PL/8n , n is odd M = nPL/8 , n is even Ra=Rb=(n-1)P/2 M=PL/3 for n=3, forces=2

R = Reaction from rafters between supports, R2 allows reaction allowing for rafter immediately over support

Tie Down OptionsLower Anchorage

M10 dowel : epoxy grouted into wall. Tie-downs hidden in wall cavity

M10-4.6 phi.Vf 10.4 kN/bolt if provide means to prevent bending

D = 10 mm Z = 98.17 mm³ phi = 0.9

fy = 300 MPa phi.Ms = 0.027 kNm

allow 10mm lever arm for bending F(max.) = 2.65 kN if cannot prevent bending

prevent bending of bolt by attaching 40mm wide SHS or timber to bottom of tie-down to fill gap between brick and bottom plate

and so preventing development of cantilever action on anchor dowel.

M10 Dynabolt to side of footing beam. Tie-Downs taken down external face of wall

phiVu= 11.1 kN Xsc = 0.82 Xse= 1 Xsa= 1

phi.Vur = 9.1 kN/bolt

Upper Anchorage

House Timbers

Rafter Pitch ß° = 20.00 degrees

JD4 t1 = 35 mm t2 = 35 mm

M10 bolt direct to rafter

beff = 35 mm D = 10 mm

f'cj 35.5 MPa f'pj 12.5 MPa

Qskl 6213 N Qskp 2188 N Qsk [Hankinson] 5112 N

ø 0.75 k1 1.15 wind k16 1

k17 1 n 1 øNj = 4.41 kN

Required Edge Distance = 4 x D = 40 mm

4/ 2.8 Diam. Nail direct to rafter

Qk 665 N Qk 9.3 N Table Column 3

ø 0.85 k1 = 1.15 k13= 1 k14 = 1 k16 = 1

k17 = 1 na = 4 na[axial] = 1

øNj[shear] = 2.60 kN/joint øNj[axial] = 0.22 kN/joint

Minimum Nail Length = 10 x D = 28 mm

Required Edge Distance = 5 x D = 14.0 mm

Required End Distance = 20 x D = 56 mm

Required Spacing Across Grain = 1 28 mmRequired Spacing Along the Grain 56 mm

2/ No. 14 Type 17 Hexhead Self-Drilling Screw direct to rafter




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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

Qk 3130 N Qk 85 N Table Column 7

ø 0.85 k1 = 1.15 k13= 1 k14 = 1 k16 = 1

k17 = 1 na = 2 na[axial] = 1 D = 6.3 mm

øNj[shear] = 6.12 kN/joint øNj[axial] = 3.75 kN/joint

Minimum Screw Length = 7 x D = 44.1 mm

Required Edge Distance = 5 x D = 31.5 mm

Required End Distance = 10 x D = 63 mm

Required Spacing Across Grain = 18.9 mm

Required Spacing Along the Grain 63 mm

Tie Down OptionsMain BodyM10-4.6 øNf = 18.6 kN/bolt

30x0.8 Steel Strap G300 øNt = 6.48 kN

Duragal 30x30x2.5 CA welded 1 le øNt = 43.7 kN

Duragal 30x30x2.5 CA Bolted(M10) øNt = 36.36 kN

20x20x1.6 SHS G350 øNt = 34.96 kN øNc = 1.17 kN (@ 3m)

40x40x1.6 SHS G350 øNt = 75.29 kN øNc = 10.85 kN (@ 3m)

13.5x2.3 CHS G250 øNt = 18.93 kN

17.2x2.3 CHS G250 øNt = 25.27 kN

21.3x2.6 CHS G250 øNt = 34.43 kN øNc = 1.32 kN (@ 3m)

26.9x2.0CHS G350 øNt = 51.32 kN øNc = 2.34 kN (@ 3m)

70 x 35 MGP10 øNt = 20.06 kN{wind} øNc = 2.27 kN {LL} (@ 3m)

70 x 35 F5 øNt = 18.48 kN{wind} øNc = 1.21 kN {LL} (@ 3m)

Abel TieDown øNt = 3.6 kN (Nominal)

Reductions in Capacity for Fasteners30x0.8 Steel Strap G300

Strap G300 fu = 340 MPa fy = 300 MPa

Width 30 mm Thickness 0.8 mm rea = Ag = 24 mm²

phi.Nt = phi Ag fy = 6.48 kN phi = 0.9

Strap Capacity with Nail kt = 1

Hole Diameter 3 mm Ah = 2.4 mm² An = 21.6 mm²

phi.Nt = phi 0.85 kt An 5.62 kN øNt = 5.62 kN

Strap Capacity with Screw kt = 1

Hole Diameter 6.3 mm Ah = 5.04 mm² An = 18.96 mm²


Strap Capacity with Bolt kt = 1



Looped Strap anchorage => 4.8m of strapping per tie-down if require anchorage at wall base, therefore try alternative tie-down

Duragal 30x30x2.5 CA welded 1 l phi.Nt = 43.7 kN

3 mm cfw phi.Vw = 0.313 kN/mm Length of W eld (2 lines 25 mm

øRwj = 15.65 kN Adopt : 25 mm weld each side of angle.

To use welded angle require cleat for attachment to anchor dowel in wall

Cleat Plate

Width 50 mm Thickness 5 mm fy = 250 MPa

Area = 250 mm² ole Diam = 12 mm Ah = 60 An = 190

phi.Nt = 42.75 kN Adopt: 50 x 5FL Cleat

Duragal 30x30x2.5 CA Bolted(M10) 1 leg

Do not require full capacity of angle, and do not require bolt size adopted in duragal tables, therefore check capacity for smaller hole.

Angle C450LO/C400LO fu = 450 MPa fy = 500 MPa

Width 30 mm Thickness 2.4 mm ri = 2.5 mm

Area = Ag = 134.4 mm²





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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

phi = 0.9 kt = 1

phi.Nt = phi Ag fy = 60.49 kN phi.Nt = phi 0.85 kt An 36.36 kN

phi.Nt = 36.36 kN Therefore can bolt angle top and bottom without need for cleat.

70 x 35 F5

H = 70 B = 35 Area = Ag = 2450.0 mm²

Hole Diameter 14 mm Ah = 490 mm² An = 1960.0 mm²

ø 0.85 k1 = 1 k4 = 1 k6 = 1 k11 = 1

ft' = 8.2 MPa

øNt = 13.7 kN Therefore can bolt timber at base

Table TN18/1.12 Rafter Strengthening Plates {stiffeners}C-SECTIONS (Fielders)

75LC10 øMs = 1.72 kNm x 2.00 = 3.44 kNm

75LC12 øMs = 2.08 kNm x 2.00 = 4.16 kNm

75LC15 øMs = 2.56 kNm x 2.00 = 5.11 kNm

TIMBERS

90x35 F7 øMs = 0.80 kNm x 2.00 = 1.60 kNm wind {1800 long}

øMs = 0.76 kNm x 2.00 = 1.52 kNm liveload {1800 long}

90x45 MGP10 øMs = 0.98 kNm x 2.00 = 1.96 kNm wind {1800 long}






Table TN18/1.13 Tie-Down Beams Over Openings

Prydabeams

PB1.4 øMb = 2.22 kNm (@2.4m)

PB1.6 øMb = 2.88 kNm (@3m)

PB1.8 øMb = 3.68 kNm (@3.6m)

PB2.0 øMb = 5.65 kNm (@3.6m)

PB3.0 øMb = 8.80 kNm (@3.6m)

C-SECTIONS (Fielders) (@2.7m) (@3.6m) Flange

75LC10 øMs = 1.72 kNm øMb = 0.49 kNm øMb = 0.29 kNm 44



F100LC10 øMs = 2.63 kNm øMb = 0.71 kNm øMb = 0.42 kNm 44




F100LC24 øMs = 6.48 kNm øMb = 1.83 kNm øMb = -- kNm 46









F250LC24 øMs = 28.00 kNm øMb = 18.13 kNm øMb = 10.50 kNm 71NB: Typically wider than 40mm cavity, and therefore only suitable if space available above cavity in eaves space.

SHS/RHS (Tubeline C350LO) (@2.7m) (@3.6m)




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Wind Class

N2 Vu = 40 m/s qz= 0.96 kPa

Vp = 33 m/s qz= 0.65 kPa

35x35x1.6SHS øMs = 0.81 kNm øMb = 0.78 kNm øMb = 0.76 kNm









50x20x2.5RHS øMs = 1.42 kNm øMb = 1.22 kNm øMb = 1.15 kNm

50x20x3.0RHS øMs = 1.63 kNm øMb = 1.39 kNm øMb = 1.31 kNm


Structural Calculations for Timber Canopy with Gable Roof

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