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International Journal of
Advanced Structures and Geotechnical Engineering
ISSN 2319-5347, Vol. 04, No. 03, July 2015
IJASGE 040301 Copyright © 2015 BASHA RESEARCH CENTRE. All rights reserved
Structural Design of Pergola with Airfoil Louvers
MUHAMMAD TAYYAB NAQASH Aluminium TechnologyAauxiliary Industries w.l.l. P.o box 40625, Doha, Qatar,
Email: [email protected]
Abstract: The here presented paper deals with the structural calculation for a Pergola consists of Airfoil
Louvers and its supporting beams that are connected to the wall. The overall height of the pergola is about 5.0m,
subjected to a wind load of 1.2 Kpa, calculated for a mean hourly basic wind speed of 25m/sec [1]. Therefore
the pergola is checked for the prescribed wind load. Stresses and deflection checks obtained from the numerical
model [2] have been carried out for louvers and the supporting beams and found SAFE according to different
acceptance criterion. [3, 4]. The louvers are attached to the Aluminum plate when then is connected to a steel
tube. The paper gives complete design procedure for the design of a pergola using SAP 2000 software.
Keywords: Airfoil Louvers, Structural design, Aluminum, Steel, Numerical models
Introduction:
Figure 1: Sectional view of the louvers
Materials:
The materials and its properties used in the pergola are
mentioned here. All structural steel shall have fy
nominal yield strength of as specified below and
having similar chemical composition and mechanical
properties to those specified in BS 4360 [5] for the
specified grade of steel. Grade 43 (BS 5950) [6, 7],
Modulus of Elasticity E= 210000 MPa
Allowable stresses: Strength Py = 275 Mpa (for t ≤
16mm), Poisson Ratio µ=0.3, Shear Modulus G=E/
(2(1+ µ)), Coefficient of thermal expansion
α=12x10-6
/0C
Aluminum extrusions used 52i54 alloy to Structural
Use of Aluminum BS 8118 Part 1: 1991 [8, 9]
Modulus of Elasticity E= 70000 Mpa, Allowable
stresses: Bending Po = 160 Mpa, Axial Pa= 175 Mpa,
Shear Pv=95 Mpa, Density of Aluminum (KN/m3) γ
=27, Coefficient of thermal expansion α = 23x10-6
Figure 2: Composite section of the main beam
MUHAMMAD TAYYAB NAQASH
International Journal of Advanced Structures and Geotechnical Engineering
ISSN 2319-5347, Vol. 04, No. 03, July 2015, pp 120-127
The louvers are connected to the Aluminum plate. The
adopted Aluminum plate is not enough to satisfy the
limit states; therefore it is reinforced with a steel tube
(200 x 100 x 6) and therefore a composite section is
adopted in the SAP 2000 numerical model. In order to
avoid any galvanic reaction between the two materials,
3mm EPDM sheet is provided. The section adopted in
the numerical model is not taken into account the
existence of the EPDM sheet and is shown in Fig 3.
C/S Airfoil blades are extruded in grade 6063- T6
Aluminium alloy as shown in Fig 4.
Figure 3: Louver profiles
This tube is considered only to produce the dead load
of the louver and to apply linear load on the louver so
to create SAP 2000 model. The properties shown in
Fig 5 are for vertical Tube but as it is rotated at 450 in
the numerical model, therefore will represent the
geometric properties of the Louver which are installed
inclined.
Figure 4: Adopted equivalent tube for louver
Design Criteria:
Ultimate Limit State:
Aluminum 160 MPa [8, 9]
Steel 275 MPa
Serviceability Limit State:
Aluminum deflection = Span/175, and Steel deflection
= span/200.
Loading Considered for the Design Purpose:
Louvers, Aluminum plate, steel tube, the deal load is
calculated by the software (SAP 2000) [2]. The wind
load of 1.2 KN/m2 as per British Standards [1, 10, 11]
is calculated. The calculated wind load was quite less
than the one adopted for the design, furthermore,
needless to mention that wind can blows through the
louver, so quite low wind can be consider for the
design of the louvers. Thermal loadings
The thermal loading is an indirect loading and in Qatar
for such long spans are considerable, therefore, they
are assumed as described here.
Assume temperature variation = ± 35 °C. Maximum
Length of Aluminum plate equals 4,000mm (as three
plates are provided for all the length). Coefficient of
thermal expansion (α) of Aluminum material is 23x10-
6.
ΔL = α x ΔL x L = 23x10-6
x35x4000 = 3.2 mm. In the
case of Aluminum, the expansion is more critical than
that of steel material, therefore gap (minimum 5mm)
are provided to accommodate thermal expansion and
contraction, and hence temperature load is not
accounted for in the analysis. In the case, if gap will
not be provided, stresses due to temperature need to be
verified prior to the installation.
When designing Aluminum structures to British
Standards, the relevant load factors are specified in BS
8118: Part 1: Clause 3.2.3 Factored loading [8], [9].
According to Clause 3.2.3 the overall load factor γf is
calculated as follows:
1 2f f f
Where γf1 and γf2 are partial load factors and their
values can be found in Tables 3.1 and 3.2 of BS 8118.
For standard design situations with the imposed load
or wind action giving the most severe loading action
on the structure or component.
Overall load factors according to BS 8118:
Loads Serviceability
Limit State
Ultimate
Limit State
Dead Load 1.0 1.2
Imposed Load 1.0 1.33
Wind Load 1.0 1.2
In contrast to BS 8118, the load factors for designing
Aluminum structures are given in the Eurocode 0, BS
EN 1990 [12, 13] and its National Annex. Further it is
seen that design loads generated with the procedure of
Eurocode 0 generates higher values for the design
actions for the ULSs [14].
The design load combinations in the present case are
the various combinations of the load cases for which
the model needs to be checked. Since, curtain walls
consist of Aluminum material therefore, according to
the BS 8118 code, they are assumed subjected to dead
load (DL), and Wind load (WL), and the following
load combinations may need to be considered.
1.2 DL
1.2 DL ± 1.2 WL
Structural Design of Pergola with Airfoil Louvers
International Journal of Advanced Structures and Geotechnical Engineering
ISSN 2319-5347, Vol. 04, No. 03, July 2015, pp 120-127
Nevertheless, the main beams and connections are
checked for load combinations with load factor 1.4.
Modeling of the Pergola:
The numerical model of SAP 2000 is shown here,
where the longitudinal members are pinned connected
to the main reinforced Aluminum tubes.
Figure 5: Frame of the SAP 2000 Numerical model
Figure 6: Wind loading on louvers (1.2 Kpa)
Stresses in the main members are checked here.
Figure 7: Stress diagram under ULS
Maximum Induced Stress in steel tube under ULS
with 1.2 is 131.8 Mpa, Therefore, Maximum Induced
Stress in steel tube under ULS with 1.4 will be 131.8
Mpa x 1.4/1.2 = 153.7 < The allowable bending stress
= 275Mpa for steel and 160Mpa for Aluminum.
Maximum Induced Stress in Louvers under ULS is
20.1 Mpa < The allowable bending stress 160Mpa for
Aluminum.
Figure 8: Deflection due to SLS
(scaled to 10 for clear visibility)
MUHAMMAD TAYYAB NAQASH
International Journal of Advanced Structures and Geotechnical Engineering
ISSN 2319-5347, Vol. 04, No. 03, July 2015, pp 120-127
Maximum deflection in steel tube =48.1 mm, Limiting
value = Span/200 = 10500/200 = 52.5 mm
48.1mm < 52.2mm, Hence SAFE
Maximum deflection in Louvers =0.47 mm
Limiting value = Span/175 = 2300/175 = 13.1 mm.
0.47mm < 13.1mm, Hence SAFE.
Verification of the Main Steel Tube:
Maximum demand to capacity under ULS with 1.2
factor is 0.479, therefore the demand to capacity under
ULS with 1.4 factor will be 0.479 x 1.4/1.2 = 0.56 <
1.0, Hence Safe
For the adopted span (2300mm), AF-200 blade can
resist a wind load of more than 2.0kpa. Hence SAFE
Enough.
Design of Connections:
Maximum induced reaction in shear is Fr = 8.2 KN.
For connection design the forces need to be factored
by 1.4. Since, the total shear force at the support is 8.2
KN; therefore the connection is checked for the shear
force of 8.2 KN x 1.4/1.2 = 9.6 KN. [15]. A sleeve of
composed of 8mm thick 2 plates and 2 # of M12 SS
bolts are adopted for the connection,
The shear capacity of a bolt, Psb, should be taken as:
Psb = psb A where:
psb is the shear strength of bolt As is the shear area,
usually taken as the tensile stress area, unless it can be
guaranteed that the threaded portion will be excluded
from the shear plane, in which case it can be taken as
the unthreaded shank area.
The tension capacity Pnom is given by Pnom = 0.8 ptb At
where: ptb= 0.7 Usb (U is the tensile strength)
Structural Design of Pergola with Airfoil Louvers
International Journal of Advanced Structures and Geotechnical Engineering
ISSN 2319-5347, Vol. 04, No. 03, July 2015, pp 120-127
Figure 9: Elevation of end details
Figure 10: End details (bracket) Shear capacity of M12 SS bolt equals to 26.22 KN
MUHAMMAD TAYYAB NAQASH
International Journal of Advanced Structures and Geotechnical Engineering
ISSN 2319-5347, Vol. 04, No. 03, July 2015, pp 120-127
As the maximum induced reaction at the support is
only 9.6 KN < 2x2 x 26.55 KN. (two shear planes and
two bolts).
Total shear applied is Fv = 10 KN
Fv/2 (two bolts)= 10/2 (2 bolts)= 5 kN
Checking plain shear
Considering only two bolts (M12), and considers
that e1 is only 30mm, being S275 material used
for 6mm thick tube,
Pv = 0.6 Py Av = 0.6 (275) (0.9x 2x 30) 6= 53.4
KN > 5 KN -----OK
Block shear check
Pr = 0.6 py tc (Lv + Ke (Lt-kD)), therefore,
Pr= 0.6 x 275 x 6 x (30) = 29.7 KN > 5 kN -----
OK
Bearing check
Pbs = kbs d tc pbs, therefore
Pbs = 1x 12 x 6 x 460 = 33.12 KN > 5 kN -----OK
Using M12 bolts are safe
Total shear applied is Fv = 10 KN
Fv/2 (two bolts)= 10/2 (2 bolts)= 5 kN
Checking plain shear
Considering only two bolts (M12) on one side,
and consider that e1 is only 30mm, being S275
material used for 6mm thick plate,
Pv = 0.6 Py Av = 0.6 (275) (0.9x 2x 30) 5= 44.5
KN > 5 KN -----OK
Block shear check
Pr = 0.6 py tc (Lv + Ke (Lt-kD)), therefore,
Pr= 0.6 x 275 x 5 x (30) = 24.75 KN > 5 kN -----
OK
Bearing check
Pbs = kbs d tc pbs, therefore
Pbs = 1x 12 x 5 x 460 = 27.6 KN > 5 kN -----OK
Using M12 bolts are safe
Maximum shear is only 9.2KN, which is transferred to
the bracket through the use of two M12 bolts,
Consider the centroid of the bolts to be 75mm from
the base of the 8mm thick plate, therefore induced
bending moment will be 9.2 x 0.075 = 0.69 KNm
resisted by two plates, provided plates are 8mm thick.
Countersunk M10 stainless self-drilling screws are
provided for connecting Aluminum plate to steel tube.
These screws are assumed subjected to shear forces
and therefore and transferring the forces to the main
steel tube. The shear capacity of SS M10 screw is
18.04KN
Stainless Steel Bolts (Shear Strength in KN)
Diameter Class 50 Class 70 Class 80
M 10 8.41 18.04 22.27
Figure 11: Other end details
Since 10Kn is the total shear acting, therefore the
adopted M10 SS screws at 500mm C/C are safe in
transferring the shear forces from the Aluminum plate
to the Main Steel tube.
Since, the main tube is quite long, therefore a sleeve
connection at 6m is proposed.
Lever arm equals (500-60-60-134/2) = 313mm,
Therefore, net shear from the moment on the bolts
Structural Design of Pergola with Airfoil Louvers
International Journal of Advanced Structures and Geotechnical Engineering
ISSN 2319-5347, Vol. 04, No. 03, July 2015, pp 120-127
equals 21.4/0.313 = 68.7 KN, Induced shear equals 1.1
KN, Total shear = 68.7 + 1.1 = 69.5 KN. Factored
shear = 69.5 x 1.4/1.2 = 81 KN
Using 4 M12 SS through bolts on one side, the shear
capacity of one bolt with a single shear plan as
calculated in the previous section equals 26.22 KN
Therefore, the shear capacity of 4 bolts with 2 shear
planes = 4x2x26.22 = 209.76 KN > 81 KN ---- Hence
Safe.
Figure 12: Elevation of sleeve connection
Figure 13: Section of sleeve connection
The sleeve is located at the center of the steel tube, so
the shear is almost negligible (it is only 1.1KN), even
though at it is combined with the shear induced from
the bending moment. The sleeve is of the same size as
that of the steel tube in thickness, in the present case
the adopted bolts govern the design. The lever arm
between the bolts is the governing factor for the length
of a sleeve when subjected to bending moment. The
total length of the sleeve is 500mm. It is not subjected
to buckling as there is no axial compression moreover;
there are no such verifications to check the deflection
of a sleeve tube. The sleeve is provided only for the
continuation of the main steel tube.
Conclusions:
The adopted Aluminum Airfoil louvers meets the
acceptance criteria both for ULS and SLS
3mm EPDM sheet in between Aluminum plate and
steel tube for avoiding any galvanic reaction
Reinforce the main 8mm thick Aluminum plate
connecting the louvers with a MS tube 200 x 100 x
MUHAMMAD TAYYAB NAQASH
International Journal of Advanced Structures and Geotechnical Engineering
ISSN 2319-5347, Vol. 04, No. 03, July 2015, pp 120-127
6 which then satisfy the acceptance criteria both for
ULS and SLS
Use stainless steel M12 countersunk bolts
Use 8mm thick MS S275 grade, sleeve plates and
sleeve tube
Use M12 chemical anchors
References
[1] BS 6399-2, "Loading for buildings, Part 2: Code
of practice for wind loads," British Standard, 1997
[2] CSI SAP V15, "Integrated Finite Element
Analysis and Design of Structures Basic Analysis
Reference Manual," Computers and Structures,
Inc., Berkeley, CA, USA, 2002.
[3] prEN 13474-2, "Glass in building- Design of
glass panes-Part 2: Design for uniformly
distributed loads," European Standard, 2000.4]
prEN 13474-3, "Glass in building -
Determination of the strength of glass panes - Part
3: General method of calculation and
determination of strength of glass by testing,"
European Standard, 2009.
[4] BS 4360, "Specification for Weldable Structural
Steel," British Standard, 1990.
[5] BS 5950-1, "Structural use of steelwork in
building," British Standard, 2000.
[6] BS 5950-2, "Specification for materials,
fabrication and erection — Rolled and welded
sections," British Standard, 2001.
[7] BS 8188-1, "Structural use of aluminium, Part 1:
Code of Practice for Design," British Standard,
1991.
[8] BS 8188-2, "Structural use of aluminium, Part 2:
Specification for materials, workmanship and
protection," British Standard, 1991.
[9] BS 6399-1, "Loading for buildings, Part 1: Code
of practice for dead and imposed loads," British
Standard, 1996.
[10] BS 6399-3, "Loading for buildings, Part 3: Code
of practice for imposed roof loads," British
Standard, 1988.
[11] EN-1991-1-1, "Eurocode 1, Actions on structures
- Part 1-1: General actions - Densities, self-
weight, imposed loads for buildings," in European
Committee for Standardization, CEN, ed. 36 B-
1050, Brussels, 2004.
[12] EN-1990, "Eurocode 0, Basis of structural
design," in European Committee for
Standardization, CEN, ed. 36 B-1050, Brussels,
2002.
[13] Ulrich Muller., Introduction to Structural
Aluminium Design: Whittles Publishing, 2011.
[14] N. S. Trahair, et al., The Behaviour and Design of
Steel Structures to EC3 4E: Taylor & Francis,
2008.