GF4_Tudor Arch for Hall Way - Exterior

Bending Moment Resistance Reference

Clause 6.5.6.5.1

0.9 Clause 6.5.6.5.1

Clause 6.5.6.5.1

30.60 Mpa Bending at extreme fibre, See Table 6.3

1.00 Duration factor, See Clause 6.4.1

1.00 System factor, See Clause 6.4.2.2

1.00 Service condition factor, See table 6.4.2

1.0 Treatment factor, See Clause 6.4.4

30.6 MpaS:

b = 80 mm Width of beamh = 570 mm Height of beam

S = 4332000 mm^3 Section modulus

Clause 6.5.6.5.2t = 10 mm Lamination thicknessR = 100000 mm Radius of curvature of the innermost lamination

1.00 Curvature Factor

Clause 6.5.6.5.1B = 1 m Either the beam width (for single piece laminations)

or the width of the widest piece(for multi piece laminations)

L = 1 m Length of beam frome point of zero moment to point of zero moment

1

119.30 kN*m

1000 mm Effective length, See table 6.5.6.4.3

9.4

Mr1 = j*Fb*S*Kx*Kzbg

Mr2 = j*Fb*S*Kx*Kl

Mr = Min(Mr1,Mr2)

j =

Fb:

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

fb =

Kd =

Kh =

Ksb =

Kt =

Fb=

S = b*h2/6

KX:

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

KX =

Kzbg:

Kzbg = 1.03*(B*L)-0.18

Kzbg =

Mr1 =

KL:

CB = (Le*d/b2)^0.5

Le =

CB =

1 Clause 6.5.6.4.4

119.30 kN*m

119.30 kN*m

KL =

Mr2 =

Mr =

Shear Resistance (Gross Section)

Clause 6.5.7.2.1

0.9






2 Mpa

Gross cross section areac of memberb = 315 mm Width of beamh = 540 mm Height of beam

170100

1 Notch factor, See clause 6.5.7.2.2

204.12 kN

Clause 6.5.7.2.1

3.69 Shear load coefficient, see clause 6.5.7.4 and table 6.5.7.4l = 32 m Length of beam

Z = 5.44 Beam volume

399.8 kN

399.752 kN

Vr1 = F*Fv*2Ag/3*KN

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

F =

Fv:

fv =

Kd =

Kh =

Ksv =

Kt =

Fv=

Ag:

Ag = b*h

Ag = mm2

KN :

KN =

Vr1 =

Vr2 = F*Fv*0.48*Ag*KN*Cv*Z-0.18

Cv =

m3

Vr2 =

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

Vr =

Bending Moment Resistance (Based on bending strength)

Section 8.2

Section 8.2

Section 8.2

Section 2.5

0.9 Clause 6.5.6.5.1

Clause 6.5.6.5.1






30.6 MpaS:



119.30328 kN*m

Clause 6.5.6.5.2t = 19 mm Lamination thickness, See table 8.2 page 374 wood design manualR = 100000 mm Radius of curvature of the innermost lamination


Clause 6.5.6.5.1B = 1 m Either the beam width (for single piece laminations)

or the width of the widest piece(for multi piece laminations)

L = 1 m Length of beam frome point of zero moment

to point of zero moment

1


Mrb1 = M'r*KL*Kx*KM

Mrb2 = M'r*KZbg*KX*KM

Mrb = Min(Mrb1,Mrb2)

M'rb = f*Fb*S

f =

Fb:


fb =

Kd =

Kh =

Ksb =

Kt =

Fb=

S = b*h2/6

M'rb =

KX:

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

KX =

Kzbg:

Kzbg = 1.03*(B*L)-0.18

Kzbg =

KL:

CB = (Le*d/b2)^0.5

Le =

9.4

1 Clause 6.5.6.4.4

Section 8.40.0436 radian

Location : Apex of curved

0.8946187

106.72 kN*m

106.72 kN*m

106.72 kN*m

CB =

KL =

KM:

KM = 1/(1+2.7*tan a) a =

KM =

Mrb1 =

Mrb2 =

Mrb =

COLUMN _POINT 4 TO 5Liner Section Column

Axial Resistance Parallel Clause 6.5.8To The Grain (Column Capacity)

Pr=phi*Fc*A*Kzcg*KcFc=fc(Kd*Kh*Ksc*Kt)Kzc=0.68(Z)^-0.13 < 1.0Kc=[1.0+(FcKzcgCc^3/35E05KseKt)]^-1

phi= 0.8Fc:

fc= 30.2 Mpa Table 6.3Ksc= 1.00 Service condition factor, See Table 6.4.2 Kt= 1.0 Treatment factor, See Table 5.4.3Kd= 1.0 Duration factor, See Clause 4.3.2.2Kh= 1.0 System factor, See Clause 6.4.3

Fc= 30.2 MpaA = 106400 mm^2

Kzc= see belowKc = see below

Pr = 1431.2 kN

Column Lengths

Weak Axis = Lx = 3000 mmStrong Axis = Ly = 6200 mm

Column Size

Weak Axis = dx = 175 mmStrong Axis = dy = 608 mm

Kzcg

Kzcg = 0.7Z = 0.65968 m3 Member volumn

Kc

Kc = 0.78 Clause 6.5.8.5E = 12400 Table 6.3 - Modulus of Elasticity

E05=0.87E = 10788 Mpa Table 5.3.1 A-DKse = 1.0 Table 6.4.2 service condition factorCc = 17.1

Cc<=50, slenderness is within limitation

Bending Moment Resistance Reference

Clause 6.5.6.5.1

0.9 Clause 6.5.6.5.1

Clause 6.5.6.5.1






25.6 MpaS:



Clause 6.5.6.5.2t = 19 mm Lamination thickness, see table 8.2 page 374R = 2800 mm Radius of curvature of the innermost lamination


Clause 6.5.6.5.1B = 0.175 m Either the beam width (for single piece

laminations) or the width of the widest piece(for multi piece laminations)


1.00

225.54 kN*m


10.7

Mr1 = j*Fb*S*Kx*Kzbg

Mr2 = j*Fb*S*Kx*Kl

Mr = Min(Mr1,Mr2)

j =

Fb:


fb =

Kd =

Kh =

Ksb =

Kt =

Fb=

S = b*h2/6

KX:

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

KX =

Kzbg:

Kzbg = 1.03*(B*L)-0.18

Kzbg =

Mr1 =

KL:

CB = (Le*d/b2)^0.5

Le =

CB =

1 Clause 6.5.6.4.4

225.54 kN*m

225.54 kN*m

Resistance to combined bending and axial load Pf = 38 kNPr = 1431.2 kNMf = 14.1 kN*mMr = 225.54 kN*m

0.09

Check Resistance to combined bending and axial load : OK


Clause 6.5.7.2.1

0.9






2 Mpa

Gross cross section areac of memberb = 175 mm Width of beamh = 608 mm Height of beam

106400


127.68 kN

Clause 6.5.7.2.1

KL =

Mr2 =

Mr =

Vr1 = F*Fv*2Ag/3*KN

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

F =

Fv:

fv =

Kd =

Kh =

Ksv =

Kt =

Fv=

Ag:

Ag = b*h

Ag = mm2

KN :

KN =

Vr1 =

Vr2 = F*Fv*0.48*Ag*KN*Cv*Z-0.18

𝑘=𝑃_𝑓/𝑃_𝑟 +𝑀_𝑓/𝑀_𝑟 =

3.69 Shear load coefficient, see clause 6.5.7.4 and table 6.5.7.4

l = 6200 mm Length of beam


365.6 kN

127.7 kN

10

0.08

Check shear Resistance : OK

Cv =

m3

Vr2 =


Vr =

Vf =𝑘=𝑉_𝑓/𝑉_𝑟 =

TURDOR ARCH @ POINT 4Bending Moment Resistance (Based on bending strength)

Section 8.2

Section 8.2

Section 8.2

Section 2.5

0.9 Clause 6.5.6.5.1

Clause 6.5.6.5.1






25.6 MpaS:



248.41421 kN*m

Clause 6.5.6.5.2t = 19 mm Lamination thickness, See table 8.2 page 374

wood design manualR = 2800 mm Radius of curvature of the innermost

0.91 lamination Curvature Factor




1

Mrb1 = M'r*KL*Kx*KM



M'rb = f*Fb*S

f =

Fb:


fb =

Kd =

Kh =

Ksb =

Kt =

Fb=

S = b*h2/6

M'rb =

KX:

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

KX =

Kzbg:

Kzbg = 1.03*(B*L)-0.18

Kzbg =

KL:

CB = (Le*d/b2)^0.5


10.7

1 Clause 6.5.6.4.4


Location : Not apex of curved

1

225.54 kN*m

225.54 kN*m

225.54 kN*m

Bending Moment Resistance (Based on radial tension strength)

Clause 6.5.6.6.2

Clause 6.5.6.6.1

0.9 Clause 6.5.6.6.1

Clause 6.5.6.6.1

0.83 Mpa Specified strength intension perpendicular to grain, see table 6.3





0.83 Mpa

S:



A = 106400 Maximum cross sectional area of memberR = 3104 mm Radius of curvature at centerline of member

0.9 rad Enclosed angle in radian Loading : Uniformly distributedMember : Double tapered curved

Le =

CB =

KL =

KM:

KM = 1/(1+2.7*tan a) a =

KM =

Mrb1 =

Mrb2 =

Mrb =

Mrt1= f*Ftp*S*KZtp*KR

Mrt2 = f*Ftp*2*A/3*R*KZtp

f =

Ftp:

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

ftp =

Kd =

Kh =

Kstp =

Kt =

Ftp=

S = b*h2/6

KZtp:

mm2

b =

0.6995909

0.55 radianA = 0.16 Constants given in table 6.5.6.6.3B = 0.06 Constants given in table 6.5.6.6.3C = 0.11 Constants given in table 6.5.6.6.3

5.6826898Location : Not apex of curved

32.02 kN*m

115.06 kN*m

0.00 kN*m

Mr = 225.54 kN*m



phi= 0.8Fc:

fc= 30.2 Mpa Table 6.3Ksc= 1.00 Table 6.4.2 service condition factorKt= 1.0 Table 5.4.3 treatment factorKd= 1.0 Duration factor see Clause 4.3.2.2Kh= 1.0 System factor see Clause 6.4.3

Fc= 30.2 MpaA = 84455 mm^2


Pr = 1162.7 kN

1162.7 kN Calculated with equivalent section

1225.9 kN Calculated with smaller section and Cc=1

Column Lengths


KZtp =

KR: a =

KR = [A+B*(d/R)+C*(d/R)2]-1

KR =

Mrt1=

Mrt2 =

Mrt =

Column Size

Equivalent Smaller end Larger end

Weak Axis = dx = 175 mm 175 mm 175 mm

Strong Axis = dy = 482.6 mm 380 mm 608 mm

Kzcg


Kzcg = 0.8 For member with constant section

Z = 0.4123 m3 of smaller one

Kc


0.87E = 10788 Table 5.3.1 A-DKse = 1.0 Table 6.4.2 service condition factorCc = 17.1


Resistance to combined bending and axial load Pf = 38 kNPr = 1162.7 kNMf = 14.1 kN*mMr = 225.54 kN*m

0.10



Clause 6.5.7.2.1

0.9






2 Mpa

Gross cross section areac of member

Vr1 = F*Fv*2Ag/3*KN

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

F =

Fv:

fv =

Kd =

Kh =

Ksv =

Kt =

Fv=

Ag:

Ag = b*h

𝑘=𝑉_𝑓/𝑉_𝑟 =



106400


127.68 kN

Clause 6.5.7.2.1


l = 6.2 m Length of beam


365.6 kN

127.7 kN

10

0.08


Ag = mm2

KN :

KN =

Vr1 =

Vr2 = F*Fv*0.48*Ag*KN*Cv*Z-0.18

Cv =

m3

Vr2 =


Vr =



Section 8.2

Section 8.2

Section 8.2

Section 2.5

0.9 Clause 6.5.6.5.1

Clause 6.5.6.5.1






25.6 MpaS:



954.82061 kN*m







1

Mrb1 = M'r*KL*Kx*KM



M'rb = f*Fb*S

f =

Fb:


fb =

Kd =

Kh =

Ksb =

Kt =

Fb=

S = b*h2/6

M'rb =

KX:

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

KX =

Kzbg:

Kzbg = 1.03*(B*L)-0.18

Kzbg =

KL:

CB = (Le*d/b2)^0.5


15.0

1 Clause 6.5.6.4.4


Location : Apex of curved

0.3750223

325.10 kN*m

325.10 kN*m

325.10 kN*m


Clause 6.5.6.6.2

Clause 6.5.6.6.1

0.9 Clause 6.5.6.6.1

Clause 6.5.6.6.1






0.83 Mpa

S:





Le =

CB =

KL =

KM:

KM = 1/(1+2.7*tan a) a =

KM =

Mrb1 =

Mrb2 =

Mrb =



f =

Ftp:


ftp =

Kd =

Kh =

Kstp =

Kt =

Ftp=

S = b*h2/6

KZtp:

mm2

b =

0.6005656



95.53 kN*m

211.87 kN*m

0.00 kN*m

Mr = 325.10 kN*m



phi= 0.8Fc:


Fc= 30.2 MpaA = 130445 mm^2


Pr = 1225.9 kN



Column Lengths


KZtp =

KR: a =

KR = [A+B*(d/R)+C*(d/R)2]-1

KR =

Mrt1=

Mrt2 =

Mrt =

Column Size




Kzcg




Kc




Resistance to combined bending and axial load Pf = 25.2 kNPr = 1225.9 kNMf = 32.1 kN*mMr = 325.10 kN*m

0.12



Clause 6.5.7.2.1

0.9






2 Mpa


Vr1 = F*Fv*2Ag/3*KN

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

F =

Fv:

fv =

Kd =

Kh =

Ksv =

Kt =

Fv=

Ag:

Ag = b*h




137550


165.06 kN

Clause 6.5.7.2.1




451.3 kN

165.1 kN

25

0.15


Ag = mm2

KN :

KN =

Vr1 =

Vr2 = F*Fv*0.48*Ag*KN*Cv*Z-0.18

Cv =

m3

Vr2 =


Vr =



Section 8.2

Section 8.2

Section 8.2

Section 2.5

0.9 Clause 6.5.6.5.1

Clause 6.5.6.5.1






25.6 MpaS:



255.82301 kN*m







1

Mrb1 = M'r*KL*Kx*KM



M'rb = f*Fb*S

f =

Fb:


fb =

Kd =

Kh =

Ksb =

Kt =

Fb=

S = b*h2/6

M'rb =

KX:

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

KX =

Kzbg:

Kzbg = 1.03*(B*L)-0.18

Kzbg =

KL:

CB = (Le*d/b2)^0.5


10.8

1 Clause 6.5.6.4.4



1

232.26 kN*m

232.26 kN*m

232.26 kN*m


Clause 6.5.6.6.2

Clause 6.5.6.6.1

0.9 Clause 6.5.6.6.1

Clause 6.5.6.6.1






0.83 Mpa

S:



A = 107975 Maximum cross sectional area of memberR = 3108.5 mm Radius of curvature at centerline of member


Le =

CB =

KL =

KM:

KM = 1/(1+2.7*tan a) a =

KM =

Mrb1 =

Mrb2 =

Mrb =



f =

Ftp:


ftp =

Kd =

Kh =

Kstp =

Kt =

Ftp=

S = b*h2/6

KZtp:

mm2

b =

0.6973359



32.82 kN*m

116.56 kN*m

0.00 kN*m

Mr = 232.26 kN*m



phi= 0.8Fc:


Fc= 30.2 MpaA = 85163.75 mm^2


Pr = 1171.5 kN



Column Lengths


KZtp =

KR: a =

KR = [A+B*(d/R)+C*(d/R)2]-1

KR =

Mrt1=

Mrt2 =

Mrt =

Column Size




Kzcg




Kc





0.05



Clause 6.5.7.2.1

0.9






2 Mpa


Vr1 = F*Fv*2Ag/3*KN

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

F =

Fv:

fv =

Kd =

Kh =

Ksv =

Kt =

Fv=

Ag:

Ag = b*h




107975


129.57 kN

Clause 6.5.7.2.1




370.0 kN

129.6 kN

10.8

0.08


Ag = mm2

KN :

KN =

Vr1 =

Vr2 = F*Fv*0.48*Ag*KN*Cv*Z-0.18

Cv =

m3

Vr2 =


Vr =



Section 8.2

Section 8.2

Section 8.2

Section 2.5

0.9 Clause 6.5.6.5.1

Clause 6.5.6.5.1






25.6 MpaS:

b = 175 mm Width of beamh = 498.5 mm Height of beam


166.99351 kN*m







1

Mrb1 = M'r*KL*Kx*KM



M'rb = f*Fb*S

f =

Fb:


fb =

Kd =

Kh =

Ksb =

Kt =

Fb=

S = b*h2/6

M'rb =

KX:

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

KX =

Kzbg:

Kzbg = 1.03*(B*L)-0.18

Kzbg =

KL:

CB = (Le*d/b2)^0.5


9.7

1 Clause 6.5.6.4.4



1

151.61 kN*m

151.61 kN*m

151.61 kN*m


Clause 6.5.6.6.2

Clause 6.5.6.6.1

0.9 Clause 6.5.6.6.1

Clause 6.5.6.6.1






0.83 Mpa

S:



A = 87237.5 Maximum cross sectional area of memberR = 3049.25 mm Radius of curvature at centerline of member

0.9 rad Enclosed angle in radian Loading : Uniformly distributedMember : Const Depth curved

Le =

CB =

KL =

KM:

KM = 1/(1+2.7*tan a) a =

KM =

Mrb1 =

Mrb2 =

Mrb =



f =

Ftp:


ftp =

Kd =

Kh =

Kstp =

Kt =

Ftp=

S = b*h2/6

KZtp:

mm2

b =

0.5009343



15.70 kN*m

66.36 kN*m

0.00 kN*m

Mr = 151.61 kN*m



phi= 0.8Fc:


Fc= 30.2 MpaA = 75831.875 mm^2


Pr = 1055.3 kN



Column Lengths


KZtp =

KR: a =

KR = [A+B*(d/R)+C*(d/R)2]-1

KR =

Mrt1=

Mrt2 =

Mrt =

Column Size



Strong Axis = dy = 433.325 mm 380 mm 498.5 mm

Kzcg




Kc





0.03



Clause 6.5.7.2.1

0.9






2 Mpa


Vr1 = F*Fv*2Ag/3*KN

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

F =

Fv:

fv =

Kd =

Kh =

Ksv =

Kt =

Fv=

Ag:

Ag = b*h




87237.5


104.69 kN

Clause 6.5.7.2.1




310.7 kN

104.7 kN

9

0.09


Ag = mm2

KN :

KN =

Vr1 =

Vr2 = F*Fv*0.48*Ag*KN*Cv*Z-0.18

Cv =

m3

Vr2 =


Vr =



Section 8.2

Section 8.2

Section 8.2

Section 2.5

0.9 Clause 6.5.6.5.1

Clause 6.5.6.5.1






25.6 MpaS:



97.0368 kN*m







1

Mrb1 = M'r*KL*Kx*KM



M'rb = f*Fb*S

f =

Fb:


fb =

Kd =

Kh =

Ksb =

Kt =

Fb=

S = b*h2/6

M'rb =

KX:

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

KX =

Kzbg:

Kzbg = 1.03*(B*L)-0.18

Kzbg =

KL:

CB = (Le*d/b2)^0.5


8.5

1 Clause 6.5.6.4.4



1

88.10 kN*m

88.10 kN*m

88.10 kN*m


Clause 6.5.6.6.2

Clause 6.5.6.6.1

0.9 Clause 6.5.6.6.1

Clause 6.5.6.6.1






0.83 Mpa

S:





Le =

CB =

KL =

KM:

KM = 1/(1+2.7*tan a) a =

KM =

Mrb1 =

Mrb2 =

Mrb =



f =

Ftp:


ftp =

Kd =

Kh =

Kstp =

Kt =

Ftp=

S = b*h2/6

KZtp:

mm2

b =

0.7743161



14.38 kN*m

76.67 kN*m

0.00 kN*m

Mr = 88.10 kN*m



phi= 0.8Fc:


Fc= 30.2 MpaA = 66500 mm^2


Pr = 937.6 kN



Column Lengths


KZtp =

KR: a =

KR = [A+B*(d/R)+C*(d/R)2]-1

KR =

Mrt1=

Mrt2 =

Mrt =

Column Size



Strong Axis = dy = 380 mm 380 mm 380 mm

Kzcg




Kc




Resistance to combined bending and axial load Pf = 1.9 kNPr = 937.6 kNMf = 0 kN*mMr = 88.10 kN*m

0.00



Clause 6.5.7.2.1

0.9






2 Mpa


Vr1 = F*Fv*2Ag/3*KN

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

F =

Fv:

fv =

Kd =

Kh =

Ksv =

Kt =

Fv=

Ag:

Ag = b*h




66500


79.80 kN

Clause 6.5.7.2.1




248.7 kN

79.8 kN

7.7

0.10


Ag = mm2

KN :

KN =

Vr1 =

Vr2 = F*Fv*0.48*Ag*KN*Cv*Z-0.18

Cv =

m3

Vr2 =


Vr =


Documents

GF4_Tudor Arch for Hall Way - Exterior