Laterally unsupported length of mul lion lion Note: Anti-buckling clips are located at every 1/5 points
a := 170.00mm
Location Location of support from expansion joint
tl := 1300.00mm
Panel width at left of mullion
tr := 1300.00mm
Panel width at right of mullion
tw := 0.5 tl + 0.5 tr = 1300.0 1300.000 mm
Tributary width of mullion
C-1.2 PROPERTIES OF O F ALUMINUM MULLION MULLION Reference: Design criteria Alloy "6063"
Aluminum Aluminum alloy
Temper "T6"
Aluminum Aluminum temper
Ea := 70000MPa
Modulus of elasticity
f o = 160.00 160.00 MPa MPa
Characteristic value of 0.2% proof strength
f u = 195.00 195.00 MPa MPa
Characteristic value of ultimate tensile strength
Reference: Section 3.2.5 of BS EN 1999-1-1: 2007
Reference: Table 3.2b of B S EN 1999-1-1:2007
Reference: Table 3.2b of BS EN 1999-1-1: 2007
C-1.3 SECTION PROPERT P ROPERTIES IES OF O F MALE MULLION
Area: 1427.69 Perimeter: 1035.77 Bounding box: X: -51.87 -- 16.53 Y: -89.05 -- 85.95 Centroid: X: 0.00 Y: 0.00 Moments of inertia: X: 4982134.26 Y: 391441.08 Product of inertia: XY: 126106.68 Radii of gyration: X: 59.07 Y: 16.56 Principal moments and X-Y directions about centroid: I: 4985595.81 along [1.00 0.03] J: 387979.53 along [-0.03 1.00]
Am := 1427.69mm Ixm := 498.21cm
2
Cross section area
4
Moment of inertia about the strong axis
4
Iym := 39.14cm
Moment of inertia about the weak axis
cym := 89.05mm
Distance Distance of extreme extreme fiber fr om strong axis
cxm := 51.87mm
Distance Distance of extreme extreme fiber fr om weak axis
Ixm
3
= 55.9 Wel.xm := 55.955 cm cym Iym
3
Elastic section modulus about the strong axis
Wel.ym := 7.55 cm = 7.55 cxm
Elastic section modulus about the weak axis
r ym := 16.56mm
Radius of gyration about the weak axis
Area: 713.85
Plastic neutral axis Area: 713.85
cy1m := 44.38mm
Lower region centroid distance from plastic neutral axis
cy2m := 60.47mm
Upper region centroid distance from plastic neutral axis 2
0.50 Am = 713.85 mm
(
Half cross section area of mullion
)
3
Wpl.xm := 0.5 Am cy1m + cy2m = 74.85 cm
Plastic section modulus about the strong axis
C-1.4 SECTION PROPERTIES OF FEMALE MULLION
Area: 1476.54 Perimeter: 981.46 Bounding box: X: -14.08 -- 28.42 Y: -88.11 -- 86.89 Centroid: X: 0.00 Y: 0.00 Moments of inertia: X: 5260626.70 Y: 214517.33 Product of inertia: XY: 50211.71 Radii of gyration: X: 59.69 Y: 12.05 Principal moments and X-Y directions about centroid: I: 5261126.28 along [1.00 0.01] J: 214017.74 along [-0.01 1.00]
Af := 1476.54mm Ixf := 526.06cm
2
Cross section area
4
Moment of inertia about the strong axis
4
Iyf := 21.45cm
Moment of inertia about the weak axis
cyf := 88.11mm
Distance of extreme fiber fr om strong axis
cxf := 28.42mm
Distance of extreme fiber fr om weak axis
Ixf
3
Wel.xf := = 59.70 cm cyf
Elastic section modulus about the strong axis
Iyf 3 = 7.55 cm Wel.yf := cxf
Elastic section modulus about the weak axis
r yf := 12.05mm
Radius of gyration about the weak axis
Area: 738.27 Area: 738.27
cy1f := 62.13mm
Lower region centroid distance from plastic neutral axis
cy2f := 44.24mm
Upper region centroid distance from plastic neutral axis 2
0.50 Af = 738.27 mm
(
Half cross section area of mullion
)
3
Wpl.xf := 0.5 Af cy1f + cy2f = 78.53 cm
Plastic section modulus
C-1.5 COMBINED SECTION PROPERTIES OF UNITIZED MULLION 2
At := Am + Af = 2904.23 mm
4
Itx := Ixm + Ixf = 1024.27 cm 4
Total cross section area Total moment of inertia about the strong axis
Ity := Iym + Iyf = 60.59 cm
Total moment of inertia about the weak axis
Ixm = 0.49 LSxm := Itx
Load share factor for mal e mullion
Ixf
= 0.51 LSxf := Itx
Load share factor for female mullion
C-1.6 MOMENT RESISTANCE FOR LOCAL BUCKLING εm :=
250MPa f o
= 1.25
Slenderness limit coefficient for moment resistance Reference: Table 6.2 of BS EN 1999-1-1:2007
γM1 := 1.10
Partial safety factor for ultimate limit state
γM2 := 1.25
Partial safety factor for ultimate limit state
Reference: Table 6.1 of BS EN 1999-1-1:2007
Reference: Table 6.1 of BS EN 1999-1-1:2007
Limiting Slenderness Ratio Reference: Table 6.2 of BS EN 1999-1-1:2007 (see Appendix B-3)
β1i := 11ε m = 13.75
Limit for internal element class 1 section
β2i := 16ε m = 20.00
Limit for internal element class 2 section
β3i := 22 ε m = 27.50
Limit for internal element class 3 section
β1o := 3ε m = 3.75
Limit for outstand element class 1 section
β2o := 4.5ε m = 5.63
Limit for outstand element class 2 section
β3o := 6ε m = 7.50
Limit for outstand element class 3 section
C-1.6.1 Local Buckling Resistance of Male Mullion about the Strong Axis NOTE: No. = element number Type = "O" for outstand, "I" for internal Stress = "C" for uniform compression, "F" for stress gradient b = length of element t = thickness of element yc = extreme fiber of element under compression (for element under stress gradient) yo = other extreme fiber of element ( for element under stress gradient) η = stress gradient coefficient (Figure 6.2 of BS EN 1999-1-1:2007) β = slenderness ratio of element (ηb/t)
Slenderness Ratio of Male Mullion Elements (Strong Axis Bending) Reference: Section 6.1.4.3 of BS EN 1999-1-1:2007 (see Appendix B-3)
No.
Type
Stress
b
t
yo
yc
yo / yc
η
β
1
O
C
25.70
2.50
N/A
N/A
N/A
1.00
10.28
2
O
C
21.40
3.90
N/A
N/A
N/A
1.00
5.49
3
I
C
11.40
3.90
N/A
N/A
N/A
1.00
2.92
4
O
C
33.00
2.00
N/A
N/A
N/A
1.00
16.50
5
I
C
12.80
2.00
N/A
N/A
N/A
1.00
6.40
6
I
C
11.40
2.00
N/A
N/A
N/A
1.00
5.70
7
I
C
22.80
5.00
N/A
N/A
N/A
1.00
4.56
8
I
F
111.30
3.00
29.25
-82.05
-0.36
0.59
21.89
9
I
F
107.30
2.20
27.25
-80.05
-0.34
0.59
28.78
10
I
F
43.00
3.00
-31.25
-74.25
0.42
0.83
11.90
11
I
F
41.00
2.00
-33.25
-74.75
0.44
0.83
17.02
Element's Designation 2 1
8
3
9
4
5 6
10 11 7
Male Mullion Elements Classification (Strong Axis Bending) Reference: Section 6.1.4.1 of BS EN 1999-1-1:2007 (see Appendix B-3)
No.
Type
β
β1
β2
β3
Class
1
O
10.28
3.75
5.63
7.50
4
2
O
5.49
3.75
5.63
7.50
2
3
I
2.92
13.75
20.00
27.50
1
4
O
16.50
3.75
5.63
7.50
4
5
I
6.40
13.75
20.00
27.50
1
6
I
5.70
13.75
20.00
27.50
1
7
I
4.56
13.75
20.00
27.50
1
8
I
21.89
13.75
20.00
27.50
3
9
I
28.78
13.75
20.00
27.50
4
10
I
11.90
13.75
20.00
27.50
1
11
I
17.02
13.75
20.00
27.50
2
Male Mullion Class 4 Elements Effective Thickness (Strong Axis Bending) Reference: Section 6.1.5 of BS EN 1 999-1-1:2007 (see Appendix B-3)
No.
Type
t
β
Class
C1
C2
ρc
teff
1
O
2.50
10.28
4
10
24
0.86
2.15
2
O
3.90
5.49
2
10
24
1.00
3.90
3
I
3.90
2.92
1
32
220
1.00
3.90
4
O
2.00
16.50
4
10
24
0.62
1.24
5
I
2.00
6.40
1
32
220
1.00
2.00
6
I
2.00
5.70
1
32
220
1.00
2.00
7
I
5.00
4.56
1
32
220
1.00
5.00
8
I
3.00
21.89
3
32
220
1.00
3.00
9
I
2.20
28.78
4
32
220
0.97
2.14
10
I
3.00
11.90
1
32
220
1.00
3.00
11
I
2.00
17.02
2
32
220
1.00
2.00
Effective Section Properties of Male Mullion
Area: 1385.35 Perimeter: 1035.89 Bounding box: X: -52.77 -- 15.63 Y: -89.01 -- 85.99 Centroid: X: 0.00 Y: 0.00 Moments of inertia: X: 4890366.65 Y: 341906.45 Product of inertia: XY: 127215.78 Radii of gyration: X: 59.41 Y: 15.71 Principal moments and X-Y directions about centroid: I: 4893921.97 along [1.00 0.03] J: 338351.13 along [-0.03 1.00]
Ixm.eff := 489.04cm
4
Moment of inertia about strong axis of effective section
4
Iym.eff := 34.16cm
Moment of inertia about weak axis of effective section
cym.eff := 89.01mm
Extreme fiber distance of effective section
Ixm.eff
3
= 54.94 cm Weff.xm := cym.eff
Effective elastic section modulus about strong axis
Moment Resistance of Male Mullion due to Local buckling (Strong Axis Bending)
Mu.Rdm :=
Weff.xm f o
γM1
= 7.99 kN m
Moment resistance for local buckling
C-1.6.2 Local Buckling Resistance of Female Mullion about the Strong Axis NOTE: No. = element number Type = "O" for outstand, "I" for internal Stress = "C" for uniform compression, "F" for stress gradient b = length of element t = thickness of element yc = extreme fiber of element under compression (for element under stress gradient) yo = other extreme fiber of element ( for element under stress gradient) η = stress gradient coefficient (Figure 6.2 of BS EN 1999-1-1:2007) β = slenderness ratio of element (ηb/t)
Slenderness Ratio of Female Mullion Elements (Strong Axis Bending) Reference: Section 6.1.4.3 of BS EN 1999-1-1:2007 (see Appendix B-3)
No.
Type
Stress
b
t
yo
yc
yo / yc
η
β
1
I
C
11.40
5.90
N/A
N/A
N/A
1.00
1.93
2
O
C
25.40
5.90
N/A
N/A
N/A
1.00
4.31
3
I
C
11.40
2.00
N/A
N/A
N/A
1.00
5.70
4
I
C
14.30
2.00
N/A
N/A
N/A
1.00
7.15
5
I
C
22.80
5.00
N/A
N/A
N/A
1.00
4.56
6
I
F
112.30
3.00
32.36
-79.94
-0.40
0.58
21.71
7
I
F
111.30
2.20
31.86
-79.44
-0.40
0.58
29.34
8
I
F
40.00
3.00
-34.36
-74.36
0.46
0.83
11.07
9
I
F
37.30
2.00
-37.06
-74.36
0.50
0.85
15.85
Element's Designation
2
1
6
7
3
4
8
9
5
Male Mullion Elements Classification (Strong Axis Bending) Reference: Section 6.1.4.1 of BS EN 1999-1-1:2007 (see Appendix B-3)
Male Mullion Class 4 Elements Effective Thickness (Strong Axis Bending) Reference: Section 6.1.5 of BS EN 1 999-1-1:2007 (see Appendix B-3)
No.
Type
t
β
Class
C1
C2
ρc
teff
1
I
5.90
1.93
1
32
220
1.00
5.90
2
O
5.90
4.31
2
10
24
1.00
5.90
3
I
2.00
5.70
1
32
220
1.00
2.00
4
I
2.00
7.15
1
32
220
1.00
2.00
5
I
5.00
4.56
1
32
220
1.00
5.00
6
I
3.00
21.71
3
32
220
1.00
3.00
7
I
2.20
29.34
4
32
220
0.96
2.12
8
I
3.00
11.07
1
32
220
1.00
3.00
9
I
2.00
15.85
2
32
220
1.00
2.00
Effective Section Properties of Female Mullion
Area: 1372.24 Perimeter: 947.43 Bounding box: X: -13.48 -- 32.52 Y: -89.00 -- 85.99 Centroid: X: 0.00 Y: 0.00 Moments of inertia: X: 4931840.91 Y: 206371.18 Product of inertia: XY: 16648.15 Radii of gyration: X: 59.95 Y: 12.26 Principal moments and X-Y directions about centroid: I: 4931899.56 along [1.00 0.00] J: 206312.53 along [0.00 1.00]
Ixf.eff := 493.18cm
4
4
Moment of inertia about strong axis of effective section
Iyf.eff := 20.64cm
Moment of inertia about weak axis of effective section
cyf.eff := 89.00mm
Extreme fiber distance of effective section
Ixf.eff
3
= 55.41 cm Weff.xf := cyf.eff
Effective elastic section modulus about strong axis
Moment Resistance of Female Mullion due to Local buckling (Strong Axis Bending) Weff.xf f o
Mu.Rdf :=
= 8.06 kN m
γM1
Moment resistance for local buckling
C-1.7 MOMENT RESISTANCE FOR LATERAL TORSIONAL BUCKLING Reference: Section 4.5.6 of BS 8118-1:1991 Note: BS EN 1999-1-1:2007 has no provision for elastic critical moment of unsymmetrical section which is necessary for lateral-torsional buckling analysis. Thus, conservative approach of BS 8118-1:1991 was used (not applying elastic critical moment), see Appendix B-5
C-1.7.1 Lateral Torsional Buckling Resistance of Male Mullion γm := 1.20
Material factor for aluminum
Lem = 38.22 λ sm := r ym
Lateral torsional buc kling slenderness
p1m :=
λ am :=
Reference: Table 3.3 of BS8118-1:1991
γm Mu.Rdm Wel.xm
λ sm π
p1m Ea
= 171.41 MPa
Intercept stress
= 0.60
Buckling stress parameters Reference: Appendix K of BS8118-1:1991
λ 1s := 0.60 cas := 0.10
cas 1 - cas λ 1s φm := 0.50 1 + + = 1.88 λ am 2 λ am
Nam := φm 1 -
1-
1
2
2
λ am φm
psm := Nam p1m = 171.35 MPa
Mb.Rdm :=
Wel.xm psm
γm
= 1.00
= 7.99 kN m
Buckling stress
Factored moment resistance to lateral torsional buckling
