The 2010 Specification for Aluminum Structures is the first unified allowable strength design and load and resistance factor design aluminum Specification. It provides rules for determining the str...
The 2010 Specification for Aluminum Structures is the first unified allowable strength design and load and resistance factor design aluminum Specification. It provides rules for determining …Descripción completa
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SECTION C-1 UNITIZED SYSTEM MULLION AT TYPICAL ZONE
BS EN 1999 - 1 - 1 : 2007 Eurocode 9 - Design of Aluminum Structures : General Structural Rules
C-1.1 DESIGN PARAMETERS P ARAMETERS
Drawing Num N umber: ber: MBH-FIB-AR-DDR-00-FA-8013 Lm := 3800.00mm
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
