Structural Design of Pergola with Airfoil Louvers

Transcription

1 International Journal of Advanced Structures and Geotechnical Engineering ISSN , Vol. 04, No. 03, July 2015 Structural Design of Pergola with Airfoil Louvers MUHAMMAD TAYYAB NAQASH Aluminium TechnologyAauxiliary Industries w.l.l. P.o box 40625, Doha, Qatar, 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 f y 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= MPa Allowable stresses: Strength P y = 275 Mpa (for t 16mm), Poisson Ratio µ=0.3, Shear Modulus G=E/ (2(1+ µ)), Coefficient of thermal expansion α=12x10-6 / 0 C Aluminum extrusions used 52i54 alloy to Structural Use of Aluminum BS 8118 Part 1: 1991 [8, 9] Modulus of Elasticity E= Mpa, Allowable stresses: Bending P o = 160 Mpa, Axial P a = 175 Mpa, Shear P v =95 Mpa, Density of Aluminum (KN/m 3 ) γ =27, Coefficient of thermal expansion α = 23x10-6 Figure 2: Composite section of the main beam IJASGE Copyright 2015 BASHA RESEARCH CENTRE. All rights reserved

2 MUHAMMAD TAYYAB NAQASH 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 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 45 0 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/m 2 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. Δ L = α x Δ L 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 Factored loading [8], [9]. According to Clause the overall load factor γ f is calculated as follows: f f 1 f 2 Where γ f1 and γ f2 are partial load factors and their values can be found in Tables 3.1 and 3.2 of BS 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 Imposed Load Wind Load 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

3 Structural Design of Pergola with Airfoil Louvers 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 Maximum Induced Stress in steel tube under ULS with 1.2 is Mpa, Therefore, Maximum Induced Stress in steel tube under ULS with 1.4 will be Mpa x 1.4/1.2 = < The allowable bending stress = 275Mpa for steel and 160Mpa for Aluminum. Figure 6: Wind loading on louvers (1.2 Kpa) Stresses in the main members are checked here. Maximum Induced Stress in Louvers under ULS is 20.1 Mpa < The allowable bending stress 160Mpa for Aluminum. Figure 7: Stress diagram under ULS Figure 8: Deflection due to SLS (scaled to 10 for clear visibility)

4 MUHAMMAD TAYYAB NAQASH Maximum deflection in Louvers =0.47 mm Limiting value = Span/175 = 2300/175 = 13.1 mm. 0.47mm < 13.1mm, Hence SAFE. Maximum deflection in steel tube =48.1 mm, Limiting value = Span/200 = 10500/200 = 52.5 mm 48.1mm < 52.2mm, 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 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 F r = 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, P sb, should be taken as: P sb = p sb A where: p sb is the shear strength of bolt A s 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 P nom is given by P nom = 0.8 p tb A t where: p tb = 0.7 U sb (U is the tensile strength)

5 Structural Design of Pergola with Airfoil Louvers Figure 9: Elevation of end details Figure 10: End details (bracket) Shear capacity of M12 SS bolt equals to KN

6 MUHAMMAD TAYYAB NAQASH As the maximum induced reaction at the support is only 9.6 KN < 2x2 x KN. (two shear planes and two bolts). Total shear applied is F v = 10 KN F v /2 (two bolts)= 10/2 (2 bolts)= 5 kn Checking plain shear Considering only two bolts (M12), and considers that e 1 is only 30mm, being S275 material used for 6mm thick tube, P v = 0.6 P y A v = 0.6 (275) (0.9x 2x 30) 6= 53.4 KN > 5 KN -----OK Block shear check P r = 0.6 p y t c (L v + K e (L t -k D )), therefore, P r = 0.6 x 275 x 6 x (30) = 29.7 KN > 5 kn OK Bearing check P bs = k bs d t c p bs, therefore P bs = 1x 12 x 6 x 460 = KN > 5 kn -----OK Using M12 bolts are safe Total shear applied is F v = 10 KN F v /2 (two bolts)= 10/2 (2 bolts)= 5 kn Checking plain shear Considering only two bolts (M12) on one side, and consider that e 1 is only 30mm, being S275 material used for 6mm thick plate, P v = 0.6 P y A v = 0.6 (275) (0.9x 2x 30) 5= 44.5 KN > 5 KN -----OK Block shear check P r = 0.6 p y t c (L v + K e (L t -k D )), therefore, P r = 0.6 x 275 x 5 x (30) = KN > 5 kn OK Bearing check P bs = k bs d t c p bs, therefore P bs = 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 = 0.69 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 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 ( /2) = 313mm, Therefore, net shear from the moment on the bolts

7 Structural Design of Pergola with Airfoil Louvers equals 21.4/0.313 = 68.7 KN, Induced shear equals 1.1 KN, Total shear = = 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 KN Therefore, the shear capacity of 4 bolts with 2 shear planes = 4x2x26.22 = KN > 81 KN ---- Hence Safe. Figure 12: Elevation 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; Figure 13: Section of sleeve connection 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

8 MUHAMMAD TAYYAB NAQASH 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 , "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, [3] pren , "Glass in building- Design of glass panes-part 2: Design for uniformly distributed loads," European Standard, ] pren , "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, [4] BS 4360, "Specification for Weldable Structural Steel," British Standard, [5] BS , "Structural use of steelwork in building," British Standard, [6] BS , "Specification for materials, fabrication and erection Rolled and welded sections," British Standard, [7] BS , "Structural use of aluminium, Part 1: Code of Practice for Design," British Standard, [8] BS , "Structural use of aluminium, Part 2: Specification for materials, workmanship and protection," British Standard, [9] BS , "Loading for buildings, Part 1: Code of practice for dead and imposed loads," British Standard, [10] BS , "Loading for buildings, Part 3: Code of practice for imposed roof loads," British Standard, [11] EN , "Eurocode 1, Actions on structures - Part 1-1: General actions - Densities, selfweight, imposed loads for buildings," in European Committee for Standardization, CEN, ed. 36 B- 1050, Brussels, [12] EN-1990, "Eurocode 0, Basis of structural design," in European Committee for Standardization, CEN, ed. 36 B-1050, Brussels, [13] Ulrich Muller., Introduction to Structural Aluminium Design: Whittles Publishing, [14] N. S. Trahair, et al., The Behaviour and Design of Steel Structures to EC3 4E: Taylor & Francis, 2008.