GF1_Tudor Arch for Arena

COLUMN _POINT 4 TO 5

Liner Section Column

Axial Resistance Parallel Clause 6.5.8

To The Grain (Column Capacity)

Pr=phi*Fc*A*Kzcg*Kc

Fc=fc(Kd*Kh*Ksc*Kt)

Kzc=0.68(Z)^-0.13 < 1.0

Kc=[1.0+(FcKzcgCc^3/35E05KseKt)]^-1

phi= 0.8

Fc:

fc= 30.2 Mpa Table 6.3

Ksc= 1.00 Service condition factor, See Table 6.4.2

Kt= 1.0 Treatment factor, See Table 5.4.3

Kd= 1.0 Duration factor, See Clause 4.3.2.2

Kh= 1.0 System factor, See Clause 6.4.3

Fc= 30.2 Mpa

A = 261820 mm^2

Kzc= see below

Kc = see below

Pr = 2884.3 kN

Column Lengths

Weak Axis = Lx = 2200 mm

Strong Axis = Ly = 17000 mm

Column Size

Weak Axis = dx = 265 mm

Strong Axis = dy = 988 mm

Kzcg

Kzcg = 0.6

Z = 4.45094 m3 Member volumn

Kc

Kc = 0.81 Clause 6.5.8.5

E = 12400 Table 6.3 - Modulus of Elasticity

E05=0.87E = 10788 Mpa Table 5.3.1 A-D

Kse = 1.0 Table 6.4.2 service condition factor

Cc = 17.2

Cc<=50, slenderness is within limitation

Bending Moment Resistance Reference

Mr1 = ϕ*Fb*S*Kx*Kzbg Clause 6.5.6.5.1

Mr2 = ϕ*Fb*S*Kx*Kl

Mr = Min(Mr1,Mr2)

ϕ = 0.9 Clause 6.5.6.5.1

Fb:

Fb = fb(Kd*Kh*Ksb*Kt) Clause 6.5.6.5.1

fb = 25.60 Mpa Bending at extreme fibre, See Table 6.3

Kd = 1.00 Duration factor, See Clause 6.4.1

Kh = 1.00 System factor, See Clause 6.4.2.2

Ksb = 1.00 Service condition factor, See table 6.4.2

Kt = 1.0 Treatment factor, See Clause 6.4.4

Fb= 25.6 Mpa

S:

S = b*h2/6

b = 265 mm Width of beam

h = 988 mm Height of beam

S = 43113027 mm^3 Section modulus

KX:

KX = 1-2000*(t/R)2

Clause 6.5.6.5.2

t = 19 mm Lamination thickness, see table 8.2 page 374

R = 2800 mm Radius of curvature of the innermost lamination

KX = 0.91 Curvature Factor

Kzbg:

Kzbg = 1.03*(B*L)-0.18

Clause 6.5.6.5.1

B = 0.265 m Either the beam width (for single piece

laminations) or the width of the widest piece

(for multi piece laminations)

L = 9 m Length of beam frome point of zero moment

to point of zero moment

Kzbg = 0.88

Mr1 = 794.37 kN*m

KL:

CB = (Le*d/b2)^0.5

Le = 4224 mm Effective length, See table 6.5.6.4.3

CB = 7.7

KL = 1 Clause 6.5.6.4.4

Mr2 = 901.85 kN*m

Mr = 901.85 kN*m

Resistance to combined bending and axial load

Pf = 282 kN

Pr = 2884.3 kN

Mf = 201 kN*m

Mr = 901.85 kN*m

0.32

Check Resistance to combined bending and axial load : OK

Vr1 = Φ*Fv*2Ag/3*KN Clause 6.5.7.2.1

Fv=fv(Kd*Kh*Ksv*Kt)

Φ = 0.9

Fv:

fv = 2.0 Mpa Bending at extreme fibre, See Table 6.3



Ksv = 1.00 Service condition factor, See table 6.4.2


Fv= 2 Mpa

Ag:

Ag = b*h Gross cross section areac of member



Ag = 261820 mm2

KN :

KN = 1 Notch factor, See clause 6.5.7.2.2

Vr1 = 314.18 kN

Vr2 = Φ*Fv*0.48*Ag*KN*Cv*Z-0.18

Clause 6.5.7.2.1

Cv = 3.69 Shear load coefficient, see clause 6.5.7.4

and table 6.5.7.4

l = 17 m Length of beam

Shear Resistance (Gross Section)

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Z = 4.45 m3

Beam volume

Vr2 = 638.0 kN

If Z > 2m3 then Vr = Vr1 else Vr =Vr2

Vr = 314.2 kN

Vf = 220

0.70

Check shear Resistance : OK

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TURDOR ARCH @ POINT 4

Bending Moment Resistance (Based on bending strength)

Mrb1 = M'r*KL*Kx*KM Section 8.2

Mrb2 = M'r*KZbg*KX*KM Section 8.2

Mrb = Min(Mrb1,Mrb2) Section 8.2

M'rb = φ*Fb*S Section 2.5

φ = 0.9 Clause 6.5.6.5.1

Fb:







Fb= 25.6 Mpa

S:

S = b*h2/6




M'rb = 993.3241 kN*m

KX:

KX = 1-2000*(t/R)2

Clause 6.5.6.5.2

t = 19 mm Lamination thickness, See table 8.2 page 374

wood design manual

R = 2800 mm Radius of curvature of the innermost

KX = 0.91 lamination Curvature Factor

Kzbg:

Kzbg = 1.03*(B*L)-0.18

Clause 6.5.6.5.1






Kzbg = 0.880824

KL:

CB = (Le*d/b2)^0.5


CB = 7.7

KL = 1 Clause 6.5.6.4.4

KM:

KM = 1/(1+2.7*tan α) Section 8.4

α = 0.645444 radian

Location : Not apex of curved

KM = 1

Mrb1 = 901.85 kN*m

Mrb2 = 794.37 kN*m

Mrb = 794.37 kN*m

Bending Moment Resistance (Based on radial tension strength)

Mrt1= φ*Ftp*S*KZtp*KR Clause 6.5.6.6.2

Mrt2 = φ*Ftp*2*A/3*R*KZtp Clause 6.5.6.6.1

φ = 0.9 Clause 6.5.6.6.1

Ftp:

Ftp = ftp(Kd*Kh*Kstp*Kt) Clause 6.5.6.6.1

ftp = 0.83 Mpa Specified strength intension perpendicular

to grain, see table 6.3



Kstp = 1.00 Service condition factor, See table 6.4.2


Ftp= 0.83 Mpa

S:

S = b*h2/6




KZtp:

A = 261820 mm2

Maximum cross sectional area of member

R = 3294 mm Radius of curvature at centerline of member

β = 1.2 rad Enclosed angle in radian

Loading : Uniformly distributed

Member : Double tapered curved

KZtp = 0.55383

KR:

α = 0.65 radian

A = 0.16 Constants given in table 6.5.6.6.3

B = 0.06 Constants given in table 6.5.6.6.3

C = 0.11 Constants given in table 6.5.6.6.3

KR = [A+B*(d/R)+C*(d/R)2]

-1

KR = 5.322196


Mrt1= 94.93 kN*m

Mrt2 = 237.87 kN*m

Mrt = FALSE kN*m

Mr = 794.37 kN*m



Pr=phi*Fc*A*Kzcg*Kc

Fc=fc(Kd*Kh*Ksc*Kt)

Kzc=0.68(Z)^-0.13 < 1.0


phi= 0.8

Fc:


Ksc= 1.00 Table 6.4.2 service condition factor

Kt= 1.0 Table 5.4.3 treatment factor

Kd= 1.0 Duration factor see Clause 4.3.2.2

Kh= 1.0 System factor see Clause 6.4.3

Fc= 30.2 Mpa

A = 210370.3 mm^2

Kzc= see below

Kc = see below

Pr = 2016.1 kN

2016.1 kN Calculated with equivalent section

2411.5 kN Calculated with smaller section and Cc=1

Column Lengths



Column Size

Equivalent Smaller end Larger end

Weak Axis = dx = 265 mm 265 mm 265 mm

Strong Axis = dy = 793.85 mm 635 mm 988 mm

Kzcg

Kzcg = 0.6


Kzcg = 0.6 For member with constant section

Z = 2.860675 m3 of smaller one

Kc

Kc = 0.69 Clause 6.5.8.5


0.87E = 10788 Table 5.3.1 A-D


Cc = 21.4



Pf = 282 kN

Pr = 2016.1 kN

Mf = 201 kN*m

Mr = 794.37 kN*m

0.39



Fv=fv(Kd*Kh*Ksv*Kt)

Φ = 0.9

Fv:






Fv= 2 Mpa

Ag:




Ag = 261820 mm2

KN :


Vr1 = 314.18 kN


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Vr2 = Φ*Fv*0.48*Ag*KN*Cv*Z-0.18

Clause 6.5.7.2.1


and table 6.5.7.4


Z = 4.45 m3

Beam volume

Vr2 = 638.0 kN


Vr = 314.2 kN

Vf = 220

0.70


� =��

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φ = 0.9 Clause 6.5.6.5.1

Fb:







Fb= 25.6 Mpa

S:

S = b*h2/6



S = 1.67E+08 mm^3 Section modulus

M'rb = 3857.527 kN*m

KX:

KX = 1-2000*(t/R)2

Clause 6.5.6.5.2


wood design manual



Kzbg:

Kzbg = 1.03*(B*L)-0.18

Clause 6.5.6.5.1






Kzbg = 0.880824

KL:

CB = (Le*d/b2)^0.5


CB = 10.8

KL = 1 Clause 6.5.6.4.4

KM:


α = 0.645444 radian

Location : Apex of curved

KM = 0.329684

Mrb1 = 1154.64 kN*m

Mrb2 = 1017.04 kN*m

Mrb = 1017.04 kN*m




φ = 0.9 Clause 6.5.6.6.1

Ftp:








Ftp= 0.83 Mpa

S:

S = b*h2/6



S = 1.67E+08 mm^3 Section modulus

KZtp:

A = 515955 mm2


R = 3773.5 mm Radius of curvature at centerline of member




KZtp = 0.469206

KR:

α = 0.645444 radian




KR = [A+B*(d/R)+C*(d/R)2]

-1

KR = 4.540452


Mrt1= 266.45 kN*m

Mrt2 = 454.93 kN*m

Mrt = FALSE kN*m

Mr = 1017.04 kN*m



Pr=phi*Fc*A*Kzcg*Kc

Fc=fc(Kd*Kh*Ksc*Kt)

Kzc=0.68(Z)^-0.13 < 1.0


phi= 0.8

Fc:






Fc= 30.2 Mpa

A = 324731 mm^2

Kzc= see below

Kc = see below

Pr = 2411.5 kN



Column Lengths



Column Size




Kzcg

Kzcg = 0.5




Kc

Kc = 0.90 Clause 6.5.8.5


0.87E = 10788 Table 5.3.1 A-D


Cc = 13.9



Pf = 304 kN

Pr = 2411.5 kN

Mf = 710 kN*m

Mr = 1017.04 kN*m

0.82



Fv=fv(Kd*Kh*Ksv*Kt)

Φ = 0.9

Fv:






Fv= 2 Mpa

Ag:




Ag = 515955 mm2

KN :


Vr1 = 619.15 kN


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Vr2 = Φ*Fv*0.48*Ag*KN*Cv*Z-0.18

Clause 6.5.7.2.1


and table 6.5.7.4


Z = 8.77 m3

Beam volume

Vr2 = 1112.8 kN


Vr = 619.1 kN

Vf = 220

0.36


� =��

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φ = 0.9 Clause 6.5.6.5.1

Fb:







Fb= 25.6 Mpa

S:

S = b*h2/6




M'rb = 1480.034 kN*m

KX:

KX = 1-2000*(t/R)2

Clause 6.5.6.5.2


wood design manual



Kzbg:

Kzbg = 1.03*(B*L)-0.18

Clause 6.5.6.5.1






Kzbg = 0.880824

KL:

CB = (Le*d/b2)^0.5


CB = 8.5

KL = 1 Clause 6.5.6.4.4

KM:


α = 0.645444 radian


KM = 1

Mrb1 = 1343.74 kN*m

Mrb2 = 1183.59 kN*m

Mrb = 1183.59 kN*m




φ = 0.9 Clause 6.5.6.6.1

Ftp:








Ftp= 0.83 Mpa

S:

S = b*h2/6




KZtp:

A = 319590 mm2


R = 3403 mm Radius of curvature at centerline of member




KZtp = 0.528254

KR:

α = 0.65 radian




KR = [A+B*(d/R)+C*(d/R)2]

-1

KR = 5.126129


Mrt1= 129.94 kN*m

Mrt2 = 286.11 kN*m

Mrt = FALSE kN*m

Mr = 1183.59 kN*m



Pr=phi*Fc*A*Kzcg*Kc

Fc=fc(Kd*Kh*Ksc*Kt)

Kzc=0.68(Z)^-0.13 < 1.0


phi= 0.8

Fc:






Fc= 30.2 Mpa

A = 236366.8 mm^2

Kzc= see below

Kc = see below

Pr = 2411.5 kN



Column Lengths



Column Size




Kzcg

Kzcg = 0.6




Kc

Kc = 0.76 Clause 6.5.8.5


0.87E = 10788 Table 5.3.1 A-D


Cc = 19.1



Pf = 289 kN

Pr = 2411.5 kN

Mf = 374 kN*m

Mr = 1183.59 kN*m

0.44



Fv=fv(Kd*Kh*Ksv*Kt)

Φ = 0.9

Fv:






Fv= 2 Mpa

Ag:




Ag = 319590 mm2

KN :


Vr1 = 383.51 kN


� =��

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Vr2 = Φ*Fv*0.48*Ag*KN*Cv*Z-0.18

Clause 6.5.7.2.1


and table 6.5.7.4


Z = 5.43 m3

Beam volume

Vr2 = 751.3 kN


Vr = 383.5 kN

Vf = 137

0.36


� =��

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φ = 0.9 Clause 6.5.6.5.1

Fb:







Fb= 25.6 Mpa

S:

S = b*h2/6


h = 920.5 mm Height of beam


M'rb = 862.2331 kN*m

KX:

KX = 1-2000*(t/R)2

Clause 6.5.6.5.2


wood design manual



Kzbg:

Kzbg = 1.03*(B*L)-0.18

Clause 6.5.6.5.1






Kzbg = 0.880824

KL:

CB = (Le*d/b2)^0.5


CB = 7.4

KL = 1 Clause 6.5.6.4.4

KM:


α = 0.645444 radian


KM = 1

Mrb1 = 782.83 kN*m

Mrb2 = 689.53 kN*m

Mrb = 689.53 kN*m




φ = 0.9 Clause 6.5.6.6.1

Ftp:








Ftp= 0.83 Mpa

S:

S = b*h2/6




KZtp:

A = 243932.5 mm2





Member : Const Depth curved

KZtp = 0.383947

KR:

α = 0.65 radian




KR = [A+B*(d/R)+C*(d/R)2]

-1

KR = 5.384763


Mrt1= 57.80 kN*m

Mrt2 = 152.06 kN*m

Mrt = FALSE kN*m

Mr = 689.53 kN*m



Pr=phi*Fc*A*Kzcg*Kc

Fc=fc(Kd*Kh*Ksc*Kt)

Kzc=0.68(Z)^-0.13 < 1.0


phi= 0.8

Fc:






Fc= 30.2 Mpa

A = 202320.9 mm^2

Kzc= see below

Kc = see below

Pr = 1873.0 kN



Column Lengths



Column Size



Strong Axis = dy = 763.475 mm 635 mm 920.5 mm

Kzcg

Kzcg = 0.6




Kc

Kc = 0.66 Clause 6.5.8.5


0.87E = 10788 Table 5.3.1 A-D


Cc = 22.3



Pf = 245 kN

Pr = 1873.0 kN

Mf = 277 kN*m

Mr = 689.53 kN*m

0.53



Fv=fv(Kd*Kh*Ksv*Kt)

Φ = 0.9

Fv:






Fv= 2 Mpa

Ag:




Ag = 243932.5 mm2

KN :


Vr1 = 292.72 kN


� =��

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Vr2 = Φ*Fv*0.48*Ag*KN*Cv*Z-0.18

Clause 6.5.7.2.1


and table 6.5.7.4


Z = 4.15 m3

Beam volume

Vr2 = 602.0 kN


Vr = 292.7 kN

Vf = 29

0.10


� =��

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φ = 0.9 Clause 6.5.6.5.1

Fb:







Fb= 25.6 Mpa

S:

S = b*h2/6




M'rb = 410.3218 kN*m

KX:

KX = 1-2000*(t/R)2

Clause 6.5.6.5.2


wood design manual



Kzbg:

Kzbg = 1.03*(B*L)-0.18

Clause 6.5.6.5.1






Kzbg = 0.880824

KL:

CB = (Le*d/b2)^0.5


CB = 6.2

KL = 1 Clause 6.5.6.4.4

KM:


α = 0.645444 radian


KM = 1

Mrb1 = 372.53 kN*m

Mrb2 = 328.14 kN*m

Mrb = 328.14 kN*m




φ = 0.9 Clause 6.5.6.6.1

Ftp:








Ftp= 0.83 Mpa

S:

S = b*h2/6




KZtp:

A = 168275 mm2






KZtp = 0.608508

KR:

α = 0.65 radian




KR = [A+B*(d/R)+C*(d/R)2]

-1

KR = 5.656584


Mrt1= 45.79 kN*m

Mrt2 = 158.97 kN*m

Mrt = FALSE kN*m

Mr = 328.14 kN*m



Pr=phi*Fc*A*Kzcg*Kc

Fc=fc(Kd*Kh*Ksc*Kt)

Kzc=0.68(Z)^-0.13 < 1.0


phi= 0.8

Fc:






Fc= 30.2 Mpa

A = 168275 mm^2

Kzc= see below

Kc = see below

Pr = 1262.3 kN



Column Lengths



Column Size



Strong Axis = dy = 635 mm 635 mm 635 mm

Kzcg

Kzcg = 0.6




Kc

Kc = 0.52 Clause 6.5.8.5


0.87E = 10788 Table 5.3.1 A-D


Cc = 26.8



Pf = 218 kN

Pr = 1262.3 kN

Mf = 0 kN*m

Mr = 328.14 kN*m

0.17



Fv=fv(Kd*Kh*Ksv*Kt)

Φ = 0.9

Fv:






Fv= 2 Mpa

Ag:




Ag = 168275 mm2

KN :


Vr1 = 201.93 kN


� =��

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Vr2 = Φ*Fv*0.48*Ag*KN*Cv*Z-0.18

Clause 6.5.7.2.1


and table 6.5.7.4


Z = 2.86 m3

Beam volume

Vr2 = 444.0 kN


Vr = 201.9 kN

Vf = 94

0.47


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GF1_Tudor Arch for Arena