Facade Structural Design & Analysis Avinash Vijayakumar Nair Masters in Facade Design Technische Hochschule Ostwestfalen Lippe avinash.nair@stud.th-owl.de Guided by Prof J. Schulz and Prof T. Vierra
Abstract - The façade technology can be characterized by the detachment of the massive brick wall into a separation of structure and façade. In this facade has an important role considering overall asthetics and the sustainability of the entire building. The double-skin facade system is a system that consists of two building skins separated by a ventilated cavity. The main purpose of the double skin facade in this project is to adapt to ambient conditions and balance out the lighting inside the building using automated triangular louvers which is adjusted after studying the effect of sun-path on the entire building through-out the year.
Curtain walls separate the interior from the exterior, but only support their own weight and the loads imposed on them (such as wind loads, dead loads, and so on) which they transfer back to the primary structure of the building. This is in contrast to many forms of traditional construction in which the external walls are a fundamental part of the primary structure of the building.
The project of office building in Herford is a refurbishment project for which the facade design was developed after studying the requirements as per the site location. The windload and the dead-load calculations are carried out as per the EN norms on basis of which the profiles and reinforcements selected for the building. This facade structure was also created on the Rhinoceres software for which the structural deformation and utilization was calculated using Karamba 3D plugin. The result is compared for the critical condition for which the considered profiles specification are under permissible deflection limits.
The double-skin façade is a system that consists of two building skins separated by a ventilated cavity. The main aim of the cavity is to vary the physical properties of the façade throughout the year, improving the building’s performance. Between the heat-insulated inner façade and the outer skin is an unheated thermal buffer zone, which is ventilated if required and can incorporate movable solar shading devices. Double-skin façades are designed to adapt to ambient conditions and balance out seasonal climate fluctuations. Thus heat, coldness, light and wind are regulated to attain optimum comfort without any complex technology or use of energy. Sometimes the heat energy that builds up in the cavity is used not just passively but also actively.
Keywords: Double-Skin Facade, Mullion, Transom, Louvers, Reinforcement, Deflection, Moment of Inertia. A. INTRODUCTION Curtain wall systems are non-structural cladding systems for the external walls of buildings. They are generally associated with large, multi-storey buildings.
Typically curtain wall systems comprise a lightweight aluminium frame onto which glazed or opaque infill panels can be fixed. These infill panels are often described as ‘glazing’ whether or not they are made of glass.
The requirement of this project is to create a facade concept for the refurbishment of the Herford Office building considering the surrounding conditions and the climatic conditions on the building. The type of facade created is a double-skin facade with automated louvers mounted on the second skin. The main objective is to carry out the structural calculations for the main structure manually and also on the software to have a safety assement of the facade design on the structure.
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B. METHODOLOGY The building is located in Herforder Strasse 80, Hiddenhausen. The global co-ordinates are Longitude: 8.66 E and Latitude: 52.169 N. The main building has a gross floor space of 575,6 m2. The wind direction and the sun path is shown in the fig where the wind is acting on the south and west faces of the building. To begin with design analysis the South, West and East Facade are the main facades dealing with the maximun radiation throughout the year which was calculated using Solumbra. Therefore, Second Skin was designed to reduced the radiation & glare effect using active louvers. The glass and insulation material are selected after considering the overall U-value requirements for the design using the Flixo software. The width of panels were considered as 1.8m to have a larger open views of the surroundings and also to optimize the number of active louvers used on the Second skin. Therefore, 1.8m width is used further in the design structural check. The main approach followed here is to calculate the deflections and moments induced on the facade due to the Windload acting on the structure using the manual calculation methods where the deflections are calculated using the formulas of Uniformly distributed load, point load & dead load on the beams. The permissible deflections are calculated in respect to the EN-14351-1 norm for windows and facade by account the all types of load acting on the structure.
Fig 2. Actual site map analysed using google street view. During the manual calculations three different cases are considerd to calculate the overall deflections. These three cases are considered by selecting the three types of panel dimensions which are of different sizes in width and height. In the first step, the required Ixx for the mullion and required Iyy for the transoms are calculated. Based on this calculation the type of facade mullion design is selected from the Schueco catalogue. The required Ixx for mullions are different as per the panel height. To reduced the deflection of larger panels, steel reinforcements are considered of adequate thickness. Similarly, the Iyy is calculated considering the deadload transferred on the transom by the glass and the self-weight load acting on the transom. After, this the transom is selected from the catalogue with higher Iyy than the required. Thereafter, the deflection calculations are made after using the Ixx and Iyy values obtained from the selection. The vertical deflection of the mullion is calculated considering the deflection caused on the left and the right side of the mullion. This deflection is added and compared with the permissible deflection as per the EN norms. Similarly, the dead load deflection is calculated for the transom which is also compared with the permissible dead load deflection from the EN norms. These values are compared and concluded safe for design. In the last part, the model of this panel is created in Rhinoceros 6 software using Grasshopper. This model is used to calculate the deflections on the mullions and transoms elements after applying all the loads and supports conditions. These values are presented for comparison with the manual calculations.
Fig 1. Rendered view of the final concept. Page 2
C. SOUTH ELEVATION & SECTION VIEWS: In the South Elevation, different panels are highlighted in red with the respective case name which is used in the further strucutral calculations.
CASE A
CASE C CASE B
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D. SELECTION OF THE PROFILES COMBINATION FOR THE FACADE MODULE: a) Types of Mullions combination for selection from Schueco catalogue:
As per the structural calculation results, the best possible combination for the mullion is of 125mm depth with Aluminium insert for the 3.63m height and box steel reinforcement of 6mm thickness for 3.97m & 4.23m. As, this combination is also the most cost effective considering the longer span is reinforced with steel which is almost 52 percent of the total facade area and the rest of the part is reinforced using Aluminium Insert.
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b) Types of Transom combination for selection from Schueco catalogue:
c) Selection of Glass thickness from Interpane catalogue : The glass of 38mm (6/12/4/12/4) is selected from Interpane catalogue as per the system requirements for which the weight density is 35 Kg/m2 and Ug is 0,723 W/m2K. The air gap in-between the glass is filled by Argon Gas for which the g-value is 51. Delivery programme for 3-fold ipaphone sound insulating glass with increased thermal insulation Technical data: Combined thermal and sound insulation ipaphon with iplus 1.1 coating
33 36 37 39 43
-2 -2 -1 -2 -2
-6 -6 -6 -5 -4
-1 -1 -1 -1 -1
53 52 52
74 73 73
97 97 97
33 36 38
-2 -1 -2
-5 -5 -6
-1 0 -1
-5 -5 -6
36 38 40 42 47 36 34 38
max. Aspect ratio
97 97 96 96 95
max. area
74 73 73 72 70
max. size
53 52 51 51 51
mm
Weight
dB
Ctr 100-5000
dB
C dB
RW
C100-5000
General color rendering index Review
dB
Total thickness
ipaphon 33/36 ipaphon 36/34 ipaphon 38/38
–
d B -6 -6 -6 -5 -4
mm
ipaphon 33/36 ipaphon 36/38 ipaphon 37/40 ipaphon 39/42 ipaphon 43/47 V
Ctr
W(m2 K) 4:/12/4/12/:4 Ar 0,7 6:/12/4/12/:4 Ar 0,7 8:/12/4/12/:4 Ar 0,7 8:/12/4/12/:6 Ar 0,7 8:/12/4/10/:12 VSG 0,8 Ar 4:/12/4/12/:4 Kr 0,5 6:/10/4/10/:4 Kr 0,6 6:/12/4/12/:4 Kr 0,5
g-Value Transperncy
Thickness Outside/SZR/Inside Ug- Value EN 673
Product Description
Nominal sound insulation values EN ISO 717-1
photometric and radiometric physical nominal values EN 410
g/m2
cm
m2
–
30 35 40 45 61
141 x 240 141 x 240 141 x 240 141 x 240 141 x 240
3,40 3,40 3,40 3,40 3,40
1:6 1:6 1:6 1:6 1:6
30 35 35
141 x 240 141 x 240 141 x 240
3,40 3,40 3,40
1:6 1:6 1:6
: indicates the position of the layers; Ar = argon gas filling; Kr = krypton gas filling. Standard version ipaphon is always iplus 1.1 - almost all low-E and sun protection coatings can be combined. x The purchaser of our products is solely responsible for ensuring that the glass thickness is correct in accordance with the applicable technical regulations. x Please note that the inherent colour of the insulating glass element increases with greater glass thickness in the form of a green/yellow tint. x The stated nominal values refer to the test conditions and the application range of the respective standard. Deviations from the vertical lead to changes in values. x The technical data are subject to tolerances in accordance with the AGC INTERPANE Tolerances Manual. x With an aspect ratio of ³ 1 : 3, we recommend using the thinner pane of toughened safety glass. Larger dimensions are possible - please enquire!
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E. FORMULATIONS: The maximum deflection of a transom due to the weight of the glazing is given by the formula:
The deflection caused due to the self-weight of the transom and glass weight is derived as shown below: a. The deflection caused due to the self-weight
....(1.1) Where the following terms are as mentioned below: G - weight of the glass pane in kg. a - distance of the glazing blocks from the mullion in mm. E - modulus of Elasticity of Aluminium in N/mm2 L - length of the Transom in mm Iyy - moment of Inertia of transom in mm4 The maximum transom deflection by dead load: ....(1.2) whichever is less ( as per the EN-14351-1) The formula for the deflection due to windload acting on the transom is derived as shown below:
The formula for calculating the deflection due to the self-weight of transom in mm is as follows: As per the deflection formula we can state that:
.....(1.4) .....(1.3) The following terms are as mentioned below:
The following terms are as mentioned below:
W1 - windload of the transom due to upper field. W2- windload of the transom due to lower field. E - modulus of elasticity of Aluminium in N/mm2 L - length of the transom in mm Ixx - moment of Inertia of transom in mm4
W - self-weight of the transom in N. L - length of the transom in mm. Iyy- moment of inertia of transom in mm4 E - 69500 N/mm2 (modulus of elasticity of aluminium in N/mm2)
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b. The deflection caused due to glass weight resting on the transom transferred through the glazing blocks.
Therefore, the total dead load deflection formula is given as shown below:
.....(1.6) The maximum mullion and transom deflection by windload:
whichever is less ( as per the EN14351-1)
......(1.7)
The formula for calculating the deflection due to the self-weight of glass on transom in mm is as follows:
.....(1.5) P - Glass weight in kg E - modulus of elasticity of Aluminium in N/mm2 a - distance of the glazing blocks from the mullion in mm. L - length of the transom in mm. Iyy- moment of inertia of transom in mm4. The overall deflection due to dead-load is calculated by adding the equation 1.4 and 1.5.
.....(1.8) .....(1.9) The above formula 1.8 and 1.9 is used for calculating the deflection and bending moment for the mullions. Page 7
Building dimension b - 40130mm , d - 14160mm , H - 15350mm
The formulas to be used for the calculations are: .....(1.1)
Velocity pressure as per wind zone 10 < h < 18
.....(1.2) .....(1.3)
......(1.4)
qp - 0.80 KN/m2 H/D = 0.382 e = b or 2h, whichever is smaller b: crosswind dimension H<=b Wind pressures on wall surface for conditions e>=d
.......(1.5) External pressure co-efficients for vertical walls of rectangular buildings
...(1.7)
As H/D is less then 1, As per section 7 ....(1.8)
....(1.9)
F. WIND LOAD CALCULATION Site Location: Herforder Straße 80, Hiddenhausen
For wind pressure we= qp (ze) x cpe For area A
This location comes under wind zone -1 category.
We = 0.80 x (-1.4) = - 1.12 KN/m2
vb,0 = 22.5 (time-averaged wind speeds)
For area B
qb,0 = 0.32 (associated speed pressures)
We = 0.80 x (-1.1) = -0.88 KN/m2
As per the surrounding condition the building comes under Terrain category- 2
Area A is under suction wind pressure. Hence, the design windload of 1.2KPa is used for further structural calculation. Page 8
F. PANEL SPECIFICATION: CASE A: Floor: Third Floor Number of panels: 62 Largest Glass weight: 125.31 Kg Mullion Type: Type D Transom Type: Type H Total Area: 472.07 m2
CASE B: Floor: First & Second Floor Number of panels: 124 Largest Glass weight: 127.18 Kg Mullion Type: Type C Transom Type: Type H Total Area: 810.216 m2
CASE C: Floor: Ground Floor Number of panels: 62 Largest Glass weight: 184 Kg Mullion Type: Type D Transom Type: Type H Total Area: 443.052 m2
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G. CALCULATIONS ON DIFFERENT CASES: CASE 1: The top module of the facade with 4.23m height is used for the windload and deadload calculations. G.1.1 Required Ixx and Iyy: The required Ixx for the mullion is calculated using the formula mentioned below:
G.1.2 Actual vertical Mullion Deflection due to Windload: Span of member L=4230mm Field width s1=1800mm s2=1800mm Allowable deflection δmax= L/200 or 15mm = 21.15mm Design Wind Pressure Wl = 1.2 kN/m2 L=4230mm ar=900mm al=900mm
Where: ( as per fig a) L = Span of the mullion ( in mm) Eal= Modulus of Elasticity for Aluminium = 69500 N/mm2 δmax= Max. Allowable deflection (in mm) = L/200 a = Half of the transom span (in mm)
Max Load Right
Max Load Left
wr= Wl x ar = 0.0012 x 900 = 1.080 N/mm
wl= Wl x al = 0.0012 x 900 = 1.080 N/mm
Total Load Right
Total Load Left
Wr= wr x (L-ar) = 1.08 x (4230-900) = 3596.4N
Wl= wl x (L-al) = 1.08 x (4230-900) =3596.4N
= 5004397 mm4 Ixx= 500.4397 cm4 Hence, Type D mullion profile combination should be used for safe design. The required Iyy for the transom is calculated using the formula mentioned below: Where: (as per fig b) Glass weight =125.31 Kg Transom Length = 1750 mm Block Spacing = 150 mm δmax= Max. Allowable deflection (in mm) = L/500 Iyy= Moment of Inertia of Transom in y-direction
δMax R = 10.35 mm
= 14.65 cm4 Hence, Type H transom should be used for safe design.
δMax L = 10.35 mm
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Total Deflection δTotal= δMax R+ δMax L = 20.70 mm = L/204 The total deflection is less than the deflection limit. Therefore, the mullion design with the steel insert of 6mm thickness is SAFE. Max Bending Moment MMax R= 1.08 x ( 3 x 42302 - 4 x 9002 )/24 = 2269741.5 Nmm = 2.270 kNm MMax L= 1.08 x ( 3 x 42302 - 4 x 9002 )/24 = 2269741.5 Nmm = 2.270 kNm MMax Total= MMax R + MMax L = 4.540 kNm
G.1.3 Transom Deflection due to Windload.
G.1.4 Transom Deflection due to deadload. Transom Self Weight (Sw) = 4.42 Kg
The deflection limit is
Transom Length (L) = 1750mm
= 3.5 mm Influence area from upper field wwl1= 0.8736 m
2
Influence area from lower field wwl2= 0.8010 m2 Lx= 1800mm Ixx= 215cm4
Glass weight = 125.31 Kg ( Glass density 35 Kg/m2) Block Spacing = 150mm Glass height = 2040mm
Windload on transom due to upper field W1= wwl1 x 1200 = 1048.32 N Windload on transom due to lower field W2= wwl2 x 1200 = 961.20 N
δ under dead load = 1.75 mm δ under windlaod = 1.50 mm
As Windload and deadload deflection are less than the deflection limit. The transom design is SAFE.
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CASE 2: The top module of the facade with 4.23m height is used for the windload and deadload calculations. G.2.1 Required Ixx and Iyy: The required Ixx for the mullion is calculated using the formula mentioned below:
G.2.2 Actual vertical Mullion Deflection due to Windload: Span of member L=3630mm Field width s1=1800mm s2=1800mm Allowable deflection δmax= L/200 or 19 mm = 18.15 mm Design Wind Pressure Wl = 1.2 kN/m2 L=3630mm ar=900mm al=900mm
Where: ( as per fig c) L = Span of the mullion ( in mm) Eal= Modulus of Elasticity for Aluminium = 69500 Kg/m2 δmax= Max. Allowable deflection (in mm) = L/200 a = Half of the transom span (in mm)
Max Load Right
Max Load Left
wr= Wl x ar = 0.0012 x 900 = 1.080 N/mm
wl= Wl x al = 0.0012 x 900 = 1.080 N/mm
Total Load Right
Total Load Left
Wr= wr x (L-ar) = 1.08 x (3630-900) = 2948.4N
Wl= wl x (L-al) = 1.08 x (3630-900) =2948.4N
= 3481186 mm4 Ixx= 348.1186 cm4 Hence, Type C mullion profile combination should be used for safe design. The required Iyy for the transom is calculated using the formula mentioned below: Where: (as per fig d) Glass weight =127.18 Kg Transom Length = 1750 mm Block Spacing = 150 mm δmax= Max. Allowable deflection (in mm) = L/500 Iyy= Moment of Inertia of Transom in y-direction
δMax R = 7.95 mm
= 14.86 cm4 Hence, Type H transom should be used for safe design.
δMax L = 7.95 mm Page 12
Total Deflection δTotal= δMax R+ δMax L = 15.90mm = L/228 The total deflection is less than the deflection limit. Therefore, the mullion with the Alu Insert is SAFE. Max Bending Moment MMax R= 1.08 x ( 3 x 36302 - 4 x 9002 )/24 = 1633081.50 Nmm = 1.633 kNm MMax L= 1.08 x ( 3 x 36302 - 4 x 9002 )/24 = 1633081.50 Nmm = 1.633 kNm MMax Total= MMax R + MMax L = 3.266 kNm G.2.4 Transom Deflection due to deadload. G.2.3 Transom Deflection due to Windload. The deflection limit is
Transom Self Weight (Sw) = 4.42 Kg Transom Length (L) = 1750mm
= 3.5 mm Influence area from upper field wwl1= 0.8736 m2 Influence area from lower field wwl2= 0.8010 m
Glass weight = 127.18 Kg ( Glass density 35 Kg/m2) Block Spacing = 150mm
2
Lx= 1800mm Ixx= 215cm
Glass height = 2070mm
4
Windload on transom due to upper field W1= wwl1 x 1200 = 1048.32 N Windload on transom due to lower field W2= wwl2 x 1200 = 961.20 N
δ under windlaod = 1.50 mm
δ under dead load = 1.77 mm As Windload and deadload deflection are less than the deflection limit. The transom design is SAFE.
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CASE 3: The top module of the facade with 4.23m height is used for the windload and deadload calculations. G.3.1 Required Ixx and Iyy: The required Ixx for the mullion is calculated using the formula mentioned below:
G.3.2 Actual vertical Mullion Deflection due to Windload: Span of member L=3970mm Field width s1=1800mm s2=1800mm Allowable deflection δmax= L/200 or 19 mm = 19.85 mm Design Wind Pressure Wl = 1.2 kN/m2 L=3630mm ar=900mm al=900mm
Where: ( as per fig e) L = Span of the mullion ( in mm) Eal= Modulus of Elasticity for Aluminium = 69500 Kg/m2 δmax= Max. Allowable deflection (in mm) = L/200 a = Half of the transom span (in mm)
Max Load Right
Max Load Left
wr= Wl x ar = 0.0012 x 900 = 1.080 N/mm
wl= Wl x al = 0.0012 x 900 = 1.080 N/mm
Total Load Right
Total Load Left
Wr= wr x (L-ar) = 1.08 x (3970-900) = 3315.6N
Wl= wl x (L-al) = 1.08 x (3970-900) =3315.6N
= 4639199 mm4 Ixx= 463.9199 cm4 Hence, Type D mullion profile combination should be used for safe design. The required Iyy for the transom is calculated using the formula mentioned below: Where: (as per fig f) Glass weight =184 Kg Transom Length = 1750 mm Block Spacing = 150 mm δmax= Max. Allowable deflection (in mm) = L/500 Iyy= Moment of Inertia of Transom in y-direction
δMax R = 7.95 mm
= 21.50cm4 Hence, Type H transom should be used for safe design.
δMax L = 7.95 mm Page 14
Total Deflection δTotal= δMax R+ δMax L = 15.90mm = L/228 The total deflection is less than the deflection limit. Therefore, the mullion design with the steel insert of 6mm thickness is SAFE. Max Bending Moment MMax R= 1.08 x ( 3 x 39702 - 4 x 9002 )/24 = 1981921.50 Nmm = 1.982 kNm MMax L= 1.08 x ( 3 x 39702 - 4 x 9002 )/24 = 1981921.50 Nmm = 1.982 kNm MMax Total= MMax R + MMax L = 3.964 kNm G.3.3 Transom Deflection due to Windload.
G.3.4 Transom Deflection due to deadload. Transom Self Weight (Sw) = 4.42 Kg
The deflection limit is = 3.5 mm Influence area from upper field wwl1= 0.7952 m2 Influence area from lower field wwl2= 0.8010 m2 Lx= 1800mm Ixx= 215cm4
Transom Length (L) = 1750mm Glass weight = 184 Kg ( Glass density 35 Kg/m2) Block Spacing = 150mm Glass height = 2070mm
Windload on transom due to upper field W1= wwl1 x 1200 = 954.24 N Windload on transom due to lower field W2= wwl2 x 1200 = 961.20 N
δ under windlaod = 1.43 mm
δ under dead load = 2.46 mm As Windload and deadload deflection are less than the deflection limit. The transom design is SAFE.
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H. SNOW LOAD CALCULATION: Snow load is a vertical load which acts on roof of a structure. For snow load calculations we have to determine the following conditions: a) For the persistent / transient design conditions:
d) Sk value: The characteristic value of snow load is related to the geographical location. For Herford the Sk is 0,85 KN/m2.
µi : The snow load shape co-efficient Sk : The characteristic value of snow load on the tile ground. Sad: The design value of exceptional snow load on the ground for a given location. Ce : The exposure co-efficient. Ct : The thermal co-efficient. b) Ce - value:
e) µi value:
As the building situated in a suburban area, there would not be much snow removal due to the occupation of the terrain by surrounding constructions. For this reason, we take Ce value corresponding to ‘Normal Topograpghy.’ Ce=1.0
The structure has a flat roof.
As the angle is zero, the value of µi is 0,8 f) Snow load calculations:
µi = 0,8; Sk= 0,85; Ce= 1,0; Ct= 1,0 S = (0,80) x (1,0) x (1,0) x (0,85) c) Ct -value: As the building is considered to have good thermal isolation, the thermal co-efficient value is 1.0 ; Ct=1,0
S = 0,68 KN/m2 g) Area of the roof: Building Dimensions: b - 40130mm , d - 14160mm , H - 15350mm Area of roof = (Length) x (Depth) = 40,13 x 15,35 = 616 m2 Therefore, the total snow load on the roof of the building is: Total Snow Load = 0,68 x 616 = 419KN
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I. GRASSHOPPER DEFINITIONS: The overall layout of the definitins are divided into sub-parts as mentioned below: 1. Basic Structure Layout. 2. Defining Mullions and Transoms. 3. Defining Supports and Material. 4. Loads acting on the structure. 5. Defining the Cross-Sections. 6. Generating and Analysing model. 7. Final Results.
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Grasshopper Illustrations: a. Facade module creation
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b. Assigning Support & Cross-section properties
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c. Analysing model and Final results:
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d. Final Output :
Fig a. Total Utilization diagram. (Scale 1:50)
Fig b. Total Displacement diagram. (Scale 1:50)
The displacement results are for two separate points for each element. The displacements are shown in the table below for each elements: Element Name/Nr Mullion / 4
X - axis
Y - axis
Z - axis
0.00mm
-0.01mm
-7.03mm
Transom / 9
0.00mm
-0.01mm
-4.08mm
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J. CONCLUSION: The facade profiles are selected as per the structural calculation carried on three different cases which are considered as critical cases in the overall building elevation. The windload for the structure is derived from the EN 1991 wind actions on the building. Thereafter, deflection calculation on each case is carried as per the EN 14351-1. The profiles are selected as per the maximum Ixx and Iyy requirement for each case. Later on, which total deflection and bending moment is shown for each case. Also, total snow load is calculated on the roof of the buildings as per the EN 1991 snow loads. In the second part, the deflections and profile utilizations are calculated on Rhinoceros using Karamba 3D. The deflection and utilization diagrams are also generated showing the percentage and data points on the 3D diagram. The overall values are later used for comparison of manual and software calculations. Both the calculations conclude that the design is structurally safe for further use.
K. ACKNOWLEDGEMENT: I appreciate Prof J.Schulz and Prof T.Vieria for there guidance through-out the C2 module which was beneficial for the analysing and creating this technical paper. L. REFERENCES: 1. EN 1991-1-4 (2005) (English): Eurocode 1: Actions on structures - Part 14: General actions - Wind actions [Authority: The European Union Per Regulation 305/2011, Directive 98/34/EC, Directive 2004/18/EC] 2. Aluminium Design Manual 2010 by The Aluminum Association, Inc. 3. Alfred Böge · Wolfgang Böge Handbuch Maschinenbau. 4. Vismann Wendehorst Bautechnische Zahlentafeln, 2012. 5. Schueco FWS 50 Order manual and system components catalogue.
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