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Analysis of timber-framed wall elements with openings
Construction and Building Materials 24 (2010) 1656–1663
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Analysis of timber-framed wall elements with openings E. Kozem Šilih, M. Premrov * University of Maribor, Faculty of Civil Engineering, Smetanova 17, SI-2000 Maribor, Slovenia
a r t i c l e
i n f o
Article history: Received 17 March 2009 Received in revised form 8 February 2010 Accepted 11 February 2010 Available online 12 March 2010 Keywords: Timber structures Timber-framed wall element Openings Fibre-plaster boards Experiments
a b s t r a c t This paper presents an experimental analysis of timber-framed wall elements with openings, coated with single fibre-plaster boards (FPB) fastened to a timber frame. The aim of the study presented here was to provide the information about the influence of the openings on the wall’s racking load-carrying capacity as well as on the horizontal stiffness of the timber-framed wall element. The tests were carried out on three groups of full-scale wall panels with different areas of openings. The measured results were compared to the results of wall panels without openings (having the same dimensions and material properties) obtained from the previous research work. Subsequently, the strength/stiffness ratios, defined as the ratios of strength/stiffness of wall panels with openings to those of no-opening wall panels, were calculated. Finally, the obtained results were compared to two analytical procedures from the literature, namely the equations proposed by Yasumura and Sugiyama and by the Method B from Eurocode 5. The comparison shows that the present results are more comparable to the former procedure, while the later one in general gives higher values of strength/stiffness ratios. The presented experimental study also emphasizes the conclusion that the timber-framed wall elements containing an opening may be accounted to contribute to the overall horizontal load-carrying capacity, especially when a considerable part of the structure is made of such panels. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Timber construction is an important part of the infrastructure in a number of areas around the world. In addition, the flexibility of mechanical fasteners provides a high damping capacity between the connected timber elements. Well-built timber structures maintain a good performance particularly under the influence of wind and especially earthquake forces. In addition to the important applications of timber in bridges, railroad infrastructure and many other applications, there is an increasing tendency worldwide toward building multi-level prefabricated timber structures with timber-framed walls as the main bearing capacity elements. In this system, the basic vertical load-bearing elements are panel walls that consist of load-bearing timber frame and sheathing boards, while horizontal floor load-bearing elements are slabs constructed of roof beams and load-bearing wood-based sheathing boards on the upper side of the roof beams. The construction performs systematic floor-by-floor building; after the walls are constructed, the floor platform for the next level is built. Consequently, this system is very useful for the multi-level buildings; therefore, the interest in the world is rising. As the treated timber-framed wall elements are a composite system composed of a timber frame and fibre-plaster-coating * Corresponding author. Tel.: +386 2 22 94 303; fax: +386 25 24 179. E-mail address: [email protected] (M. Premrov). 0950-0618/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2010.02.026
boards which are connected to the timber frame by mechanical fasteners, it is possible to assure with suitable boundary conditions a composite behaviour between the boards and the timber frame along the whole element and consequently to increase the wallbearing capacity. Because the tensile strength of the boards is smaller as the strength of the timber frame, the boards present the weaker part of the treated composite system. The present study is a continuation of the research work realized in the last years in reinforcing of the prefabricated timberframed wall elements without any openings. The results can be found in Premrov and Kuhta [3]. The problem of reinforcing can be simply solved by inserting of additional boards, which assure an increase in elasticity but not in satisfactory resistance and especially in ductility of the structure, which is indispensable for seismic and windy safe buildings [4]. Thus, more suitable is the method by inserting of steel diagonals which create the truss system and thus essentially increase the resistance and ductility of the panel wall [4]. While the diagonals must be anchored into the timber frame, the procedure of their inserting can be much timeconsuming; thus, we plan to take a special attention in developing more simple solutions. In this sense, we already investigated an alternative reinforcing option by inserting of CFRP strips in the diagonal tensile direction of the board using two different strip connections to the timber frame [5]. Based on the obtained experimental results, we developed special mathematical models which would render a possibility to simple and fast calculation of
E. Kozem Šilih, M. Premrov / Construction and Building Materials 24 (2010) 1656–1663
mentioned reinforced composite systems without openings (noopening wall panels) [6,7]. Of course, in an apartment building, many walls may have one or more openings for functional reasons, doors or windows (Fig. 1), where a concentration of the tensile stresses around the corners appears and consequently results in essential decrease in the wall’s bearing capacity and the horizontal stiffness. Because of a very low tensile strength, which is approximately 10-times lower than the compressive one, these stresses could be very dangerous in a case of fibre-plaster boards (FPB). Eurocode 5 [2] thus describes that the walls which contain a door or window opening should not be considered to contribute to the racking load-carrying capacity, Method A. In Method B, the lengths of panel on each side of the opening should be considered as separate panels, see (b b) in Fig. 2. It is important to underline that the Method B is applicable only for wood-based sheathing boards, while in the publication of Yasumura and Sugiyama [1], the plywood-sheathed wall panels with openings are used. In the available publications, there is no information about the influence of the area of opening on the timber-framed wall elements with FPB. 2. Mathematical modelling of the walls 2.1. Design methods According to the computational Eurocode 5 model, the panel walls can be regarded separately, for design purposes, as vertical cantilever beams with a horizontal force (FHx = xFH,tot/n) acting at the top, see Fig. 2. The compressed and the tensional supports approximate an influence on the neighboring panel walls and assure an elastic-clamped boundary conditions for the treated fundamental unit, as can also be found in Faherty and Williamson [8], Brüninghoff [9] and Schulze [10]. The treated timber frame panel wall is a composite element consisting of framed panels made from sheets of board-material fixed by mechanical fasteners to one or both sides of a timber frame. In the final version of Eurocode 5 [2], two simplified computational methods are given in order to determine the load-carrying capacity of wall diaphragms. The first-simplified analysis – Method A is identical to the ‘‘Lower bound plastic method”, presented by Källsner and Lam [11]. The method defines the shear resistance of the wall (Fv,Rd) as the sum of the shear resistance of all mechanical fasteners (Ff,Rd) along the loaded edges in the form of:
X b F v ;Rd ¼ F f ;Rd c s ( 1 for b P b0 c¼ b for b 6 b0 b0
ð1aÞ where b0 ¼ h=2
ð1bÞ
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where Ff,Rd is the lateral design capacity per fastener; bi is wall panel width; and s is the fastener spacing. This is only an approximated and simplified definition, which can be applicable for wood-based panels where the tensile strength is relatively high and the elements tend to fail because of fastener yielding. In this method, wall panels which contain a door or window opening should not be considered to contribute to the racking load-carrying capacity. The second simplified analysis – Method B is applicable to walls being made from sheets of wood-based panel products only fastened to a timber frame. The fastening of the sheets to the timber frame should be either by nail or by screws, and the fasteners should be equally spaced around the perimeter of the sheet. Method B is practically a modified formula of Method A. According to the Method A, the sheathing material factor, the fastener spacing factor, the vertical load factor and the dimension factor for the panel are included in the design procedure. Using this method, where an opening is formed in a panel, the lengths of panel on each side of the opening should be considered as separate panels, see Fig. 2. In the available publications, there are not many information about the behaviour of the treated timber-framed walls with FPB as a sheathing boards under horizontal actions. Beside the mentioned [3–6] in Toratti [12] and Ceccotti and Karacabeyli [13], it is proposed to decrease the seismic behaviour factor (q) from 3 to 2 in a case of using FPB. It means that timber-framed walls with FPB sheathing boards usually behave less ductile as the walls with wood-based sheathing boards. The publication of Yasumura and Sugiyama [1] provides the information for the estimation of racking strength of a plywoodsheathed wall panel with an opening and investigates the influence of the shape and area of opening. According to [1], both strength and stiffness ratio (F) should be calculated using Eq. (2), where the opening coefficient (r) is calculated by Eqs. (3a) (3c), see Fig. 3. The proposed analytical procedure is based on a series of reduced-scale racking tests of plywood-sheathed wall panels with openings. This proposal is used as an orientation for our research, which is based on the investigation of the influence of the area of the opening on the timber-framed wall elements.
F¼
r 32r
ð2Þ
In this study, we would like to show the influence of the area of the opening on the stiffness and bearing capacity of timber-framed wall panels with openings. The obtained experimental results are compared with the measured ones for no-opening wall panels. 3. Experimental studies 3.1. Test configuration In the following analysis, we will limit our attention to the panel walls with window or door openings, with single fibre-plastercoating boards. We tested three groups of test samples in order to carry out an appropriate research about the influence of the area of opening on the stiffness and load-carrying capacity of the panels. The panels are normally produced as in case of the O1 test samples. The O3 test samples represent an alternative solution where the opening is cut out from the FPB. The sample groups (O1, O2, O3) of nine test samples all together will be compared with the tested group (G2), presented by Premrov and Kuhta [3].
Fig. 1. Wall panel with an opening.
3.1.1. The first group (O1) The first group of three test samples consisted of panel walls of actual dimensions h = 264 cm and b = 125 cm. The dimensions
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FH
F H,tot
h
x
⇒
b* b
bd b
n tot·b
FH =
y
FH ,tot
zt
n
timber frame
sheathing board
Fig. 2. Static design for the wall assembly in one level.
A0 .....sum of opening areas A0 ..opening area ratio H ⋅L
α=
β= r=
∑L
i
L
(3a)
..wall length ratio
(3b)
1 ..opening coefficient ⎛α ⎞ 1 + ⎜⎜ ⎟⎟ ⎝β ⎠
(3c)
Fig. 3. Definition of opening coefficient.
Fig. 4. Cross-section of the test sample for the first test group (O1).
of the opening are ho = 127.2 cm and bo = 84.2 cm. The cross-section presented in Fig. 4 was composed of timber studs (9 9 cm and 4.4 9 cm), timber girders (8 9 cm) and single Knauf
fibre-plaster boards made of several pieces [14] of thickness t = 15 mm. They were fixed to the timber frame using staples of U1.53 mm at a constant spacing of s = 7.5 cm.
E. Kozem Šilih, M. Premrov / Construction and Building Materials 24 (2010) 1656–1663
3.1.2. The second group (O2) The second group of three test samples consisted of panel walls of actual dimensions h = 264 cm and b = 125 cm. The dimension of the opening is smaller than in the first group, ho = 127.2 cm and bo = 57.2 cm. The cross-section presented in Fig. 5 was composed of timber studs (9 9 cm and 4.4 9 cm), timber girders (8 9 cm) and single Knauf fibre-plaster boards made of several pieces of thickness t = 15 mm. They were fixed to the timber frame using staples of U1.53 mm at a constant spacing of s = 7.5 cm.
3.1.3. The third group (O3) The third group of three test samples consisted of panel walls of the same dimensions and the same material properties as the first group, but the single Knauf fibre-plaster boards are made of a single piece and the openings are cut out from the FPB (see Fig. 6).
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They were fixed to the timber frame using staples of U1.53 mm at a constant spacing of s = 7.5 cm. 3.1.4. The group (G2) The group G2 of three test samples consisted of the no-opening wall panels of the same dimensions and the same material properties as the previous groups. The single Knauf fibre-plaster boards are made of a single piece. They were fixed to the timber frame using staples of U1.53 mm at a constant spacing of s = 7.5 cm. More details are described in Premrov and Kuhta [3]. The results are presented for information and comparison only. The static model according to Fig. 2 was used for all three groups of test samples. Each sample was actually rotated by 90°, and it was therefore subjected to a vertical force acting at the free end of the cantilevered element. To prevent lateral torsional buckling on the free side of the element, the vertical roller support was
Fig. 5. Cross-section of the test sample for the second test group (O2).
Fig. 6. Cross-section of the test sample for the third test group (O3).
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Fig. 8a. F–w diagrams for O1 test samples. Fig. 7. Experiment setup; test sample subjected to vertical point load.
introduced. Fig. 7 shows the test setup for racking test of a wall panel. The load was applied using a load cell connected to a hydraulic jack. In all tests, the specimens were loaded until failure under one-way loading. The load increased at the rate of 0.008 kN per second (or 1 kN in each 125 s). Using the strain gauges incorporated in the load cell, the vertical displacement (w) at the free end was automatically measured and saved each second. The slips between the FPB and the timber frame were measured using the manual deflection metres (‘‘clocks” with the precision of 0.01 mm) at four positions, two above and two below the opening (see Fig. 7). The slips were read and saved manually at the force interval of 1 kN. The average slip in the upper (tension) zone (Dt) was calculated as the average value of both measurements, i.e. the measurements at the above and at the below edge of the upper (tensile) chord. Equivalently, the average slip in the lower (compression) zone (Dc) was calculated as the average of both measurements at the edges of the lower chord. Material properties for the timber of quality C22 are taken from EN 338 [15]. All material properties are listed in Table 1. Fig. 8b. F–w diagrams for O2 test samples.
3.2. Test results Using the saved measurement histories, the corresponding diagrams F–w, F–Dt and F–Dc were constructed. In addition, during each test, the force forming the first crack in the FPB (Fcr), as well as the ultimate failure force (Fu), was documented. Figs. 8a–8c show the F–w diagrams for all the tested samples. It is evident that the differences in the results between individual samples inside each group are relatively small. Therefore, in the further discussion, the average values of test results for each group are presented and compared to the measured values for the no-opening test samples taken from [3]. Table 2 shows the ratios (in %) between Fcr,i/Fcr,G2 and Fu,i/Fu,G2 and the ‘‘safety factors” ci obtained by the measured results. The ‘‘safety factor” (ci) is declared as a quotient between the ultimate failure force (Fu) and the force forming the first crack in FPB (Fcr). Comparing the safety factor c1x = 2.07 for O1 (O3) and c2x = 1.80 for the O2 test group, we observe a big influence of the area of the opening. It is evident from the relationship between
Fig. 8c. F–w diagrams for O3 test samples.
Table 1 Properties of used materials.
Timber C22 FPB
E0,m (N/mm2)
Gm (N/mm2)
fm,k (N/mm2)
ft,0,k (N/mm2)
fc,0,k (N/mm2)
fv,k (N/mm2)
qm (kg/m3)
10,000 3000
630 1200
22 4.0
13 2.5
20 20
2.4 5.0
410 1050
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Fcr (kN)
Fu (kN)
Safety factor (ci), Fu/Fcr
O1 O2 O3 G2
4.30 7.16 4.31 17.06
8.91 12.85 8.95 26.17
2.07 1.80 2.07 1.53
Ratio (%) Fcr
Fu
25 42 25 100
34 49 34 100
the measured forces forming the first crack that the area of the opening is very important. In addition, the elastic resistance (force forming the first crack) and especially the average failure force essentially depend on the area of wall panel opening. The influence is more evident by the failure force (Fu). As expected, the force forming the first crack in the FPB (Fcr) above and below an opening consequently causes the failure of FPB around the corners of an opening. The stiffness of the connecting shear plane increased with smaller area of the opening according to composite behaviour. It can be concluded from the test results that in the second group (O2) of the test samples, the first crack in the fibreboards appeared under a 66.51% greater horizontal force than in the first group (O1). This is important if we wish to improve only the elastic behaviour of the panels. In the second group, the destruction force increased for 44.22% according to the first group presents an average measured vertical displacement (w) according to area of opening under the acting vertical force (F). Fig. 9 presents an average measured vertical displacement (w) according to area of opening under the acting vertical force (F). Comparing test groups O1 and O2, it is obvious that the function inclination, which physically presents the stiffness, depends on the area of the wall panel opening, as shown in Table 3. There is a clear difference when comparing the stiffness functions of O1–O3 with G2 test samples. Before any cracks appearing in FPB, the bending stiffness of the G2 test samples is higher according to all other test
F (kN)
Test samples
groups. Therefore, we can conclude that no-opening wall panels have a relatively higher stiffness and load-bearing capacity than wall panels with openings. Comparing the results shown in Tables 2 and 3, it is evident that there are some differences between the values of the strength ratios and the stiffness ratios. As the stiffness
28.0 26.0 24.0 22.0 20.0 18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
O1 O2 O3 G2 s=7.5 cm
2.2 2.4 2.6
Tension slip (mm) Fig. 10a. F–Dt diagrams (average values of test groups).
F (kN)
Table 2 Numerical results for Fcr and Fu, their safety factors and ratios.
28.0 26.0 24.0 22.0 20.0 18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 0.0
O1 O2 O3 G2 s=7.5 cm
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
Compression slip (mm) Fig. 10b. F–Dc diagrams (average values of test groups).
Fig. 9. F–w diagrams (average values of test groups).
Table 3 Stiffness ratio for the measured test samples. Test samples
F (kN) (w = 10 mm)
Ratio (%)
O1 O2 O3 G2
3.90 4.82 4.51 10
39 48 45 100
Fig. 11. The appearance of the first crack in the O1 test samples.
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E. Kozem Šilih, M. Premrov / Construction and Building Materials 24 (2010) 1656–1663 Table 5 Comparison of the strength ratios for the measured test samples.
Fig. 12. The appearance of the first crack in the O3 test samples.
ratios show higher values, they should be considered in the design of such kind of timber structures. The appearance of the first crack is noticed from F–Dt diagrams in Figs. 10a and 10b; it is evident that slip before the first crack in FPB is higher for O1 samples and seems to be logical as the stiffness of the connecting shear plane is lower in this case. Fig. 11 shows the appearance of the first crack in the O1 test samples with single Knauf fibre-plaster boards made of several pieces. The dashed line in Fig. 11 presents the position of the glued connection between two pieces of FPB. It is obvious that the first crack has formed above the opening and not in the corner. As seen in Fig. 12, in the O3 test samples made of a single Knauf fibre-plaster board, the first crack has appeared in the corner of the opening, which is expected from the analytical theory. In the wall panel with opening and sheathed with a piece of FPB, side wall is bent because of the existence of wall parts above and below an opening consequently causes the failure of FPB around the corners of an opening. In generally, there are not significant differences for stiffness and load-bearing capacity between the O1 and O3 test samples.
4. Discussion of results According to the publication of Yasumura and Sugiyama [1], we calculated the opening coefficient (r) regarding the areas of openings for the three test groups used in our research as shown in Table 4. The calculated opening coefficient (r) amounts to 0.62 for the groups O1 and O3 and 0.70 for the group O2. As was demonstrated before, the horizontal stiffness of wall element increased with a smaller area of the opening. The measured results evidently prove that the panels with a larger opening coefficient (r) show higher values of the stiffness ratio and the shear strength ratio. According to the measured results presented in Tables 2 and 3, we can affirm that the area of the opening has a big influence on the stiffness and load-bearing capacity of the timber-framed wall elements. The stiffness ratio amounts to 39% for the group O1 and 48% for the group O2, whilst the strength ratio amounts to
Table 4 Opening coefficient for the measured test samples. Test samples
O1 O2 O3
Opening dimensions h (cm)
b (cm)
127.2 127.2 127.2
84.2 57.2 84.2
Opening coefficient (r)
0.62 0.70 0.62
Test samples
Opening coefficient (r)
Strength ratio F = r/(3 2r) [1]
Method B [2]
Fu,i/ Fu,G2
O1 O2 O3
0.62 0.70 0.62
0.35 0.44 0.35
0.42 0.51 0.43
0.34 0.49 0.34
34% for the group O1 (O3) and 49% for the group O2. Therefore, we can conclude that the stiffness and load-bearing capacity of the timber-framed wall panels should not be completely neglected as proposed in Method A of Eurocode 5. More suitable is the simplified Method B where the lengths of the panel on each side of the opening are considered as separate panels. Table 5 shows the comparison between the strength ratios calculated by the equation proposed in Yasumura and Sugiyama [1] and by the Method B proposed in EC 5 [2]. The comparison shows that Method B gives the highest values, while the present results are more comparable to the method presented in [1]. It is important to underline that the method proposed in [1] is applicable only for plywood-sheathed wall panels with opening. The results evidently prove that the timber-framed wall elements with a larger opening coefficient (r) show a higher strength ratio and consequently a higher stiffness ratio. 5. Conclusion Whilst there is an increasing tendency worldwide to build multi-level prefabricated timber structures, with timber panel walls as the main bearing capacity elements, it is important to increase their resistance and especially their ductility. We have proved that no-opening wall panels have a relatively higher horizontal stiffness and load-bearing capacity than wall panels with openings. However, the measured ultimate resistances of the wall panels with openings amounted to up to 50% of the ultimate resistances of the panels without openings. Therefore we conclude that the timber-framed wall elements which contain a door or window opening may be considered to contribute to the racking load-carrying capacity, especially when a considerable part of the structure is made of such panels. Additionally, we present that the test samples made of several pieces (O1) or of one piece (O3) of FPB with the area of opening of the same dimensions show practically identical experimental results. The results of the strength ratios obtained by the three proposed methods are presented in Table 5. The comparison of the three methods shows that the differences amount to less than 10%. Consequently, we recommend in designing of such kind of wall elements with openings to use the methods presented in [6,7], and to simulate the influence of openings on horizontal bearing capacity using Eqs. (1a) and (1b). In the next research, we would like to show that with a suitable position of the CFRP strips around the openings corners (the strips are glued to the board in direction of maximal tensile stresses), the wall´s racking load-carrying capacity could be essentially improved and therefore such walls can be considered by determination of the horizontal resistance of the whole wall system. The work will be based on a detail experimental analysis on the test samples of actual production dimensions. Since the designing methods proposed in Eurocode 5 are not applicable for the treated timber-framed walls with fibre-plaster sheathing boards, the results of the experimental analyses will be a base for a semi-analytical and numerical modelling of the wall elements with openings for doors and windows. The obtained results would be additionally verified by
E. Kozem Šilih, M. Premrov / Construction and Building Materials 24 (2010) 1656–1663
computer programmes using finite element method including s.c. ‘‘super elements” based on condensation matrix, Kim and Lee [16]. References [1] Yasumura M, Sugiyama H. Shear properties of plywood-sheathed wall panels with opening. Trans Architect Instit Jpn 1984;338(April). [2] CEN/TC 250/SC5 N173. Eurocode 5: design of timber structures, Part 1-1. General rules and rules for buildings, EN 1995-1-1, Brussels; 2004. [3] Premrov M, Kuhta M. Influence of fasteners disposition on behaviour of timber-framed walls with single fibre-plaster sheathing boards. Constr Build Mater 2008. [4] Dobrila P, Premrov M. Reinforcing methods for composite timber framefibreboard wall panels. Eng Struct 2003;25(11):1369–76. [5] Premrov M, Dobrila P, Bedenik BS. Analysis of timber-framed walls coated with CFRP strips strengthened fibre-plaster boards. Int J Solid Struct 2004;41(24/ 25):7035–48. [6] Premrov M, Dobrila P, Bedenik BS. Approximate analytical solutions for diagonal reinforced timber-framed walls with fibre-plaster coating material. Constr Build Mater 2004;18(10):727–35.
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[7] Premrov M, Dobrila P. Modelling of fastener flexibility in CFRP strengthened timber-framed walls using modified c-method. Eng Struct 2007;30(2):368–75. [8] Faherty KF, Williamson TG. Wood engineering and construction handbook. Mc Graw-Hill Publishing Company; 1989. [9] Brüninghoff H et al. Eine Ausführliche Erlüterung zu DIN 1052, Teil 1 bis Teil 3. Berlin: Beuth-Kommentare, Beuth Bauverlag; 1988. [10] Schulze H, Holzbau: Wände–Decken–Dächer, Konstruktion, Bauphysik, Holzshutz, B.G. Teubner. Stuttgart; 1996. [11] Källsner B, Lam F. Diaphragms and shear walls. Holzbauwerke: Grundlagen, Entwicklungen, Ergänzungen nach Eurocode 5, Step 3, Fachverlag Holz, Düsseldorf; 1995. p.15/1–19. [12] Toratti T. Seismic design of timber structures – prestudy. Tekes research project – final report, VTT/ Building and Transport, Espoo, April 2001. [13] Ceccotti A, Karacabeyli E. Seismic design considerations on multi-storey woodframe structures. Cost E5 workshop on constructional aspects of multi-storey timber buildings, June 1998, UK. [14] Knauf Gipsfaserplatten Vidiwall und Vidifloor – company catalogue; 2002. [15] European Committee for Standardization. EN 338:2003 E: Structural timber – strength classes. Brussels; 2003. [16] Kim H-S, Lee D-G. Analysis of shear wall with openings using super elements. Eng Struct 2003;25(8):981–91.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Analysis of timber-framed wall elements with openings E. Kozem Šilih, M. Premrov * University of Maribor, Faculty of Civil Engineering, Smetanova 17, SI-2000 Maribor, Slovenia
a r t i c l e
i n f o
Article history: Received 17 March 2009 Received in revised form 8 February 2010 Accepted 11 February 2010 Available online 12 March 2010 Keywords: Timber structures Timber-framed wall element Openings Fibre-plaster boards Experiments
a b s t r a c t This paper presents an experimental analysis of timber-framed wall elements with openings, coated with single fibre-plaster boards (FPB) fastened to a timber frame. The aim of the study presented here was to provide the information about the influence of the openings on the wall’s racking load-carrying capacity as well as on the horizontal stiffness of the timber-framed wall element. The tests were carried out on three groups of full-scale wall panels with different areas of openings. The measured results were compared to the results of wall panels without openings (having the same dimensions and material properties) obtained from the previous research work. Subsequently, the strength/stiffness ratios, defined as the ratios of strength/stiffness of wall panels with openings to those of no-opening wall panels, were calculated. Finally, the obtained results were compared to two analytical procedures from the literature, namely the equations proposed by Yasumura and Sugiyama and by the Method B from Eurocode 5. The comparison shows that the present results are more comparable to the former procedure, while the later one in general gives higher values of strength/stiffness ratios. The presented experimental study also emphasizes the conclusion that the timber-framed wall elements containing an opening may be accounted to contribute to the overall horizontal load-carrying capacity, especially when a considerable part of the structure is made of such panels. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Timber construction is an important part of the infrastructure in a number of areas around the world. In addition, the flexibility of mechanical fasteners provides a high damping capacity between the connected timber elements. Well-built timber structures maintain a good performance particularly under the influence of wind and especially earthquake forces. In addition to the important applications of timber in bridges, railroad infrastructure and many other applications, there is an increasing tendency worldwide toward building multi-level prefabricated timber structures with timber-framed walls as the main bearing capacity elements. In this system, the basic vertical load-bearing elements are panel walls that consist of load-bearing timber frame and sheathing boards, while horizontal floor load-bearing elements are slabs constructed of roof beams and load-bearing wood-based sheathing boards on the upper side of the roof beams. The construction performs systematic floor-by-floor building; after the walls are constructed, the floor platform for the next level is built. Consequently, this system is very useful for the multi-level buildings; therefore, the interest in the world is rising. As the treated timber-framed wall elements are a composite system composed of a timber frame and fibre-plaster-coating * Corresponding author. Tel.: +386 2 22 94 303; fax: +386 25 24 179. E-mail address: [email protected] (M. Premrov). 0950-0618/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2010.02.026
boards which are connected to the timber frame by mechanical fasteners, it is possible to assure with suitable boundary conditions a composite behaviour between the boards and the timber frame along the whole element and consequently to increase the wallbearing capacity. Because the tensile strength of the boards is smaller as the strength of the timber frame, the boards present the weaker part of the treated composite system. The present study is a continuation of the research work realized in the last years in reinforcing of the prefabricated timberframed wall elements without any openings. The results can be found in Premrov and Kuhta [3]. The problem of reinforcing can be simply solved by inserting of additional boards, which assure an increase in elasticity but not in satisfactory resistance and especially in ductility of the structure, which is indispensable for seismic and windy safe buildings [4]. Thus, more suitable is the method by inserting of steel diagonals which create the truss system and thus essentially increase the resistance and ductility of the panel wall [4]. While the diagonals must be anchored into the timber frame, the procedure of their inserting can be much timeconsuming; thus, we plan to take a special attention in developing more simple solutions. In this sense, we already investigated an alternative reinforcing option by inserting of CFRP strips in the diagonal tensile direction of the board using two different strip connections to the timber frame [5]. Based on the obtained experimental results, we developed special mathematical models which would render a possibility to simple and fast calculation of
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mentioned reinforced composite systems without openings (noopening wall panels) [6,7]. Of course, in an apartment building, many walls may have one or more openings for functional reasons, doors or windows (Fig. 1), where a concentration of the tensile stresses around the corners appears and consequently results in essential decrease in the wall’s bearing capacity and the horizontal stiffness. Because of a very low tensile strength, which is approximately 10-times lower than the compressive one, these stresses could be very dangerous in a case of fibre-plaster boards (FPB). Eurocode 5 [2] thus describes that the walls which contain a door or window opening should not be considered to contribute to the racking load-carrying capacity, Method A. In Method B, the lengths of panel on each side of the opening should be considered as separate panels, see (b b) in Fig. 2. It is important to underline that the Method B is applicable only for wood-based sheathing boards, while in the publication of Yasumura and Sugiyama [1], the plywood-sheathed wall panels with openings are used. In the available publications, there is no information about the influence of the area of opening on the timber-framed wall elements with FPB. 2. Mathematical modelling of the walls 2.1. Design methods According to the computational Eurocode 5 model, the panel walls can be regarded separately, for design purposes, as vertical cantilever beams with a horizontal force (FHx = xFH,tot/n) acting at the top, see Fig. 2. The compressed and the tensional supports approximate an influence on the neighboring panel walls and assure an elastic-clamped boundary conditions for the treated fundamental unit, as can also be found in Faherty and Williamson [8], Brüninghoff [9] and Schulze [10]. The treated timber frame panel wall is a composite element consisting of framed panels made from sheets of board-material fixed by mechanical fasteners to one or both sides of a timber frame. In the final version of Eurocode 5 [2], two simplified computational methods are given in order to determine the load-carrying capacity of wall diaphragms. The first-simplified analysis – Method A is identical to the ‘‘Lower bound plastic method”, presented by Källsner and Lam [11]. The method defines the shear resistance of the wall (Fv,Rd) as the sum of the shear resistance of all mechanical fasteners (Ff,Rd) along the loaded edges in the form of:
X b F v ;Rd ¼ F f ;Rd c s ( 1 for b P b0 c¼ b for b 6 b0 b0
ð1aÞ where b0 ¼ h=2
ð1bÞ
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where Ff,Rd is the lateral design capacity per fastener; bi is wall panel width; and s is the fastener spacing. This is only an approximated and simplified definition, which can be applicable for wood-based panels where the tensile strength is relatively high and the elements tend to fail because of fastener yielding. In this method, wall panels which contain a door or window opening should not be considered to contribute to the racking load-carrying capacity. The second simplified analysis – Method B is applicable to walls being made from sheets of wood-based panel products only fastened to a timber frame. The fastening of the sheets to the timber frame should be either by nail or by screws, and the fasteners should be equally spaced around the perimeter of the sheet. Method B is practically a modified formula of Method A. According to the Method A, the sheathing material factor, the fastener spacing factor, the vertical load factor and the dimension factor for the panel are included in the design procedure. Using this method, where an opening is formed in a panel, the lengths of panel on each side of the opening should be considered as separate panels, see Fig. 2. In the available publications, there are not many information about the behaviour of the treated timber-framed walls with FPB as a sheathing boards under horizontal actions. Beside the mentioned [3–6] in Toratti [12] and Ceccotti and Karacabeyli [13], it is proposed to decrease the seismic behaviour factor (q) from 3 to 2 in a case of using FPB. It means that timber-framed walls with FPB sheathing boards usually behave less ductile as the walls with wood-based sheathing boards. The publication of Yasumura and Sugiyama [1] provides the information for the estimation of racking strength of a plywoodsheathed wall panel with an opening and investigates the influence of the shape and area of opening. According to [1], both strength and stiffness ratio (F) should be calculated using Eq. (2), where the opening coefficient (r) is calculated by Eqs. (3a) (3c), see Fig. 3. The proposed analytical procedure is based on a series of reduced-scale racking tests of plywood-sheathed wall panels with openings. This proposal is used as an orientation for our research, which is based on the investigation of the influence of the area of the opening on the timber-framed wall elements.
F¼
r 32r
ð2Þ
In this study, we would like to show the influence of the area of the opening on the stiffness and bearing capacity of timber-framed wall panels with openings. The obtained experimental results are compared with the measured ones for no-opening wall panels. 3. Experimental studies 3.1. Test configuration In the following analysis, we will limit our attention to the panel walls with window or door openings, with single fibre-plastercoating boards. We tested three groups of test samples in order to carry out an appropriate research about the influence of the area of opening on the stiffness and load-carrying capacity of the panels. The panels are normally produced as in case of the O1 test samples. The O3 test samples represent an alternative solution where the opening is cut out from the FPB. The sample groups (O1, O2, O3) of nine test samples all together will be compared with the tested group (G2), presented by Premrov and Kuhta [3].
Fig. 1. Wall panel with an opening.
3.1.1. The first group (O1) The first group of three test samples consisted of panel walls of actual dimensions h = 264 cm and b = 125 cm. The dimensions
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FH
F H,tot
h
x
⇒
b* b
bd b
n tot·b
FH =
y
FH ,tot
zt
n
timber frame
sheathing board
Fig. 2. Static design for the wall assembly in one level.
A0 .....sum of opening areas A0 ..opening area ratio H ⋅L
α=
β= r=
∑L
i
L
(3a)
..wall length ratio
(3b)
1 ..opening coefficient ⎛α ⎞ 1 + ⎜⎜ ⎟⎟ ⎝β ⎠
(3c)
Fig. 3. Definition of opening coefficient.
Fig. 4. Cross-section of the test sample for the first test group (O1).
of the opening are ho = 127.2 cm and bo = 84.2 cm. The cross-section presented in Fig. 4 was composed of timber studs (9 9 cm and 4.4 9 cm), timber girders (8 9 cm) and single Knauf
fibre-plaster boards made of several pieces [14] of thickness t = 15 mm. They were fixed to the timber frame using staples of U1.53 mm at a constant spacing of s = 7.5 cm.
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3.1.2. The second group (O2) The second group of three test samples consisted of panel walls of actual dimensions h = 264 cm and b = 125 cm. The dimension of the opening is smaller than in the first group, ho = 127.2 cm and bo = 57.2 cm. The cross-section presented in Fig. 5 was composed of timber studs (9 9 cm and 4.4 9 cm), timber girders (8 9 cm) and single Knauf fibre-plaster boards made of several pieces of thickness t = 15 mm. They were fixed to the timber frame using staples of U1.53 mm at a constant spacing of s = 7.5 cm.
3.1.3. The third group (O3) The third group of three test samples consisted of panel walls of the same dimensions and the same material properties as the first group, but the single Knauf fibre-plaster boards are made of a single piece and the openings are cut out from the FPB (see Fig. 6).
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They were fixed to the timber frame using staples of U1.53 mm at a constant spacing of s = 7.5 cm. 3.1.4. The group (G2) The group G2 of three test samples consisted of the no-opening wall panels of the same dimensions and the same material properties as the previous groups. The single Knauf fibre-plaster boards are made of a single piece. They were fixed to the timber frame using staples of U1.53 mm at a constant spacing of s = 7.5 cm. More details are described in Premrov and Kuhta [3]. The results are presented for information and comparison only. The static model according to Fig. 2 was used for all three groups of test samples. Each sample was actually rotated by 90°, and it was therefore subjected to a vertical force acting at the free end of the cantilevered element. To prevent lateral torsional buckling on the free side of the element, the vertical roller support was
Fig. 5. Cross-section of the test sample for the second test group (O2).
Fig. 6. Cross-section of the test sample for the third test group (O3).
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Fig. 8a. F–w diagrams for O1 test samples. Fig. 7. Experiment setup; test sample subjected to vertical point load.
introduced. Fig. 7 shows the test setup for racking test of a wall panel. The load was applied using a load cell connected to a hydraulic jack. In all tests, the specimens were loaded until failure under one-way loading. The load increased at the rate of 0.008 kN per second (or 1 kN in each 125 s). Using the strain gauges incorporated in the load cell, the vertical displacement (w) at the free end was automatically measured and saved each second. The slips between the FPB and the timber frame were measured using the manual deflection metres (‘‘clocks” with the precision of 0.01 mm) at four positions, two above and two below the opening (see Fig. 7). The slips were read and saved manually at the force interval of 1 kN. The average slip in the upper (tension) zone (Dt) was calculated as the average value of both measurements, i.e. the measurements at the above and at the below edge of the upper (tensile) chord. Equivalently, the average slip in the lower (compression) zone (Dc) was calculated as the average of both measurements at the edges of the lower chord. Material properties for the timber of quality C22 are taken from EN 338 [15]. All material properties are listed in Table 1. Fig. 8b. F–w diagrams for O2 test samples.
3.2. Test results Using the saved measurement histories, the corresponding diagrams F–w, F–Dt and F–Dc were constructed. In addition, during each test, the force forming the first crack in the FPB (Fcr), as well as the ultimate failure force (Fu), was documented. Figs. 8a–8c show the F–w diagrams for all the tested samples. It is evident that the differences in the results between individual samples inside each group are relatively small. Therefore, in the further discussion, the average values of test results for each group are presented and compared to the measured values for the no-opening test samples taken from [3]. Table 2 shows the ratios (in %) between Fcr,i/Fcr,G2 and Fu,i/Fu,G2 and the ‘‘safety factors” ci obtained by the measured results. The ‘‘safety factor” (ci) is declared as a quotient between the ultimate failure force (Fu) and the force forming the first crack in FPB (Fcr). Comparing the safety factor c1x = 2.07 for O1 (O3) and c2x = 1.80 for the O2 test group, we observe a big influence of the area of the opening. It is evident from the relationship between
Fig. 8c. F–w diagrams for O3 test samples.
Table 1 Properties of used materials.
Timber C22 FPB
E0,m (N/mm2)
Gm (N/mm2)
fm,k (N/mm2)
ft,0,k (N/mm2)
fc,0,k (N/mm2)
fv,k (N/mm2)
qm (kg/m3)
10,000 3000
630 1200
22 4.0
13 2.5
20 20
2.4 5.0
410 1050
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Fcr (kN)
Fu (kN)
Safety factor (ci), Fu/Fcr
O1 O2 O3 G2
4.30 7.16 4.31 17.06
8.91 12.85 8.95 26.17
2.07 1.80 2.07 1.53
Ratio (%) Fcr
Fu
25 42 25 100
34 49 34 100
the measured forces forming the first crack that the area of the opening is very important. In addition, the elastic resistance (force forming the first crack) and especially the average failure force essentially depend on the area of wall panel opening. The influence is more evident by the failure force (Fu). As expected, the force forming the first crack in the FPB (Fcr) above and below an opening consequently causes the failure of FPB around the corners of an opening. The stiffness of the connecting shear plane increased with smaller area of the opening according to composite behaviour. It can be concluded from the test results that in the second group (O2) of the test samples, the first crack in the fibreboards appeared under a 66.51% greater horizontal force than in the first group (O1). This is important if we wish to improve only the elastic behaviour of the panels. In the second group, the destruction force increased for 44.22% according to the first group presents an average measured vertical displacement (w) according to area of opening under the acting vertical force (F). Fig. 9 presents an average measured vertical displacement (w) according to area of opening under the acting vertical force (F). Comparing test groups O1 and O2, it is obvious that the function inclination, which physically presents the stiffness, depends on the area of the wall panel opening, as shown in Table 3. There is a clear difference when comparing the stiffness functions of O1–O3 with G2 test samples. Before any cracks appearing in FPB, the bending stiffness of the G2 test samples is higher according to all other test
F (kN)
Test samples
groups. Therefore, we can conclude that no-opening wall panels have a relatively higher stiffness and load-bearing capacity than wall panels with openings. Comparing the results shown in Tables 2 and 3, it is evident that there are some differences between the values of the strength ratios and the stiffness ratios. As the stiffness
28.0 26.0 24.0 22.0 20.0 18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
O1 O2 O3 G2 s=7.5 cm
2.2 2.4 2.6
Tension slip (mm) Fig. 10a. F–Dt diagrams (average values of test groups).
F (kN)
Table 2 Numerical results for Fcr and Fu, their safety factors and ratios.
28.0 26.0 24.0 22.0 20.0 18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 0.0
O1 O2 O3 G2 s=7.5 cm
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
Compression slip (mm) Fig. 10b. F–Dc diagrams (average values of test groups).
Fig. 9. F–w diagrams (average values of test groups).
Table 3 Stiffness ratio for the measured test samples. Test samples
F (kN) (w = 10 mm)
Ratio (%)
O1 O2 O3 G2
3.90 4.82 4.51 10
39 48 45 100
Fig. 11. The appearance of the first crack in the O1 test samples.
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Fig. 12. The appearance of the first crack in the O3 test samples.
ratios show higher values, they should be considered in the design of such kind of timber structures. The appearance of the first crack is noticed from F–Dt diagrams in Figs. 10a and 10b; it is evident that slip before the first crack in FPB is higher for O1 samples and seems to be logical as the stiffness of the connecting shear plane is lower in this case. Fig. 11 shows the appearance of the first crack in the O1 test samples with single Knauf fibre-plaster boards made of several pieces. The dashed line in Fig. 11 presents the position of the glued connection between two pieces of FPB. It is obvious that the first crack has formed above the opening and not in the corner. As seen in Fig. 12, in the O3 test samples made of a single Knauf fibre-plaster board, the first crack has appeared in the corner of the opening, which is expected from the analytical theory. In the wall panel with opening and sheathed with a piece of FPB, side wall is bent because of the existence of wall parts above and below an opening consequently causes the failure of FPB around the corners of an opening. In generally, there are not significant differences for stiffness and load-bearing capacity between the O1 and O3 test samples.
4. Discussion of results According to the publication of Yasumura and Sugiyama [1], we calculated the opening coefficient (r) regarding the areas of openings for the three test groups used in our research as shown in Table 4. The calculated opening coefficient (r) amounts to 0.62 for the groups O1 and O3 and 0.70 for the group O2. As was demonstrated before, the horizontal stiffness of wall element increased with a smaller area of the opening. The measured results evidently prove that the panels with a larger opening coefficient (r) show higher values of the stiffness ratio and the shear strength ratio. According to the measured results presented in Tables 2 and 3, we can affirm that the area of the opening has a big influence on the stiffness and load-bearing capacity of the timber-framed wall elements. The stiffness ratio amounts to 39% for the group O1 and 48% for the group O2, whilst the strength ratio amounts to
Table 4 Opening coefficient for the measured test samples. Test samples
O1 O2 O3
Opening dimensions h (cm)
b (cm)
127.2 127.2 127.2
84.2 57.2 84.2
Opening coefficient (r)
0.62 0.70 0.62
Test samples
Opening coefficient (r)
Strength ratio F = r/(3 2r) [1]
Method B [2]
Fu,i/ Fu,G2
O1 O2 O3
0.62 0.70 0.62
0.35 0.44 0.35
0.42 0.51 0.43
0.34 0.49 0.34
34% for the group O1 (O3) and 49% for the group O2. Therefore, we can conclude that the stiffness and load-bearing capacity of the timber-framed wall panels should not be completely neglected as proposed in Method A of Eurocode 5. More suitable is the simplified Method B where the lengths of the panel on each side of the opening are considered as separate panels. Table 5 shows the comparison between the strength ratios calculated by the equation proposed in Yasumura and Sugiyama [1] and by the Method B proposed in EC 5 [2]. The comparison shows that Method B gives the highest values, while the present results are more comparable to the method presented in [1]. It is important to underline that the method proposed in [1] is applicable only for plywood-sheathed wall panels with opening. The results evidently prove that the timber-framed wall elements with a larger opening coefficient (r) show a higher strength ratio and consequently a higher stiffness ratio. 5. Conclusion Whilst there is an increasing tendency worldwide to build multi-level prefabricated timber structures, with timber panel walls as the main bearing capacity elements, it is important to increase their resistance and especially their ductility. We have proved that no-opening wall panels have a relatively higher horizontal stiffness and load-bearing capacity than wall panels with openings. However, the measured ultimate resistances of the wall panels with openings amounted to up to 50% of the ultimate resistances of the panels without openings. Therefore we conclude that the timber-framed wall elements which contain a door or window opening may be considered to contribute to the racking load-carrying capacity, especially when a considerable part of the structure is made of such panels. Additionally, we present that the test samples made of several pieces (O1) or of one piece (O3) of FPB with the area of opening of the same dimensions show practically identical experimental results. The results of the strength ratios obtained by the three proposed methods are presented in Table 5. The comparison of the three methods shows that the differences amount to less than 10%. Consequently, we recommend in designing of such kind of wall elements with openings to use the methods presented in [6,7], and to simulate the influence of openings on horizontal bearing capacity using Eqs. (1a) and (1b). In the next research, we would like to show that with a suitable position of the CFRP strips around the openings corners (the strips are glued to the board in direction of maximal tensile stresses), the wall´s racking load-carrying capacity could be essentially improved and therefore such walls can be considered by determination of the horizontal resistance of the whole wall system. The work will be based on a detail experimental analysis on the test samples of actual production dimensions. Since the designing methods proposed in Eurocode 5 are not applicable for the treated timber-framed walls with fibre-plaster sheathing boards, the results of the experimental analyses will be a base for a semi-analytical and numerical modelling of the wall elements with openings for doors and windows. The obtained results would be additionally verified by
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computer programmes using finite element method including s.c. ‘‘super elements” based on condensation matrix, Kim and Lee [16]. References [1] Yasumura M, Sugiyama H. Shear properties of plywood-sheathed wall panels with opening. Trans Architect Instit Jpn 1984;338(April). [2] CEN/TC 250/SC5 N173. Eurocode 5: design of timber structures, Part 1-1. General rules and rules for buildings, EN 1995-1-1, Brussels; 2004. [3] Premrov M, Kuhta M. Influence of fasteners disposition on behaviour of timber-framed walls with single fibre-plaster sheathing boards. Constr Build Mater 2008. [4] Dobrila P, Premrov M. Reinforcing methods for composite timber framefibreboard wall panels. Eng Struct 2003;25(11):1369–76. [5] Premrov M, Dobrila P, Bedenik BS. Analysis of timber-framed walls coated with CFRP strips strengthened fibre-plaster boards. Int J Solid Struct 2004;41(24/ 25):7035–48. [6] Premrov M, Dobrila P, Bedenik BS. Approximate analytical solutions for diagonal reinforced timber-framed walls with fibre-plaster coating material. Constr Build Mater 2004;18(10):727–35.
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[7] Premrov M, Dobrila P. Modelling of fastener flexibility in CFRP strengthened timber-framed walls using modified c-method. Eng Struct 2007;30(2):368–75. [8] Faherty KF, Williamson TG. Wood engineering and construction handbook. Mc Graw-Hill Publishing Company; 1989. [9] Brüninghoff H et al. Eine Ausführliche Erlüterung zu DIN 1052, Teil 1 bis Teil 3. Berlin: Beuth-Kommentare, Beuth Bauverlag; 1988. [10] Schulze H, Holzbau: Wände–Decken–Dächer, Konstruktion, Bauphysik, Holzshutz, B.G. Teubner. Stuttgart; 1996. [11] Källsner B, Lam F. Diaphragms and shear walls. Holzbauwerke: Grundlagen, Entwicklungen, Ergänzungen nach Eurocode 5, Step 3, Fachverlag Holz, Düsseldorf; 1995. p.15/1–19. [12] Toratti T. Seismic design of timber structures – prestudy. Tekes research project – final report, VTT/ Building and Transport, Espoo, April 2001. [13] Ceccotti A, Karacabeyli E. Seismic design considerations on multi-storey woodframe structures. Cost E5 workshop on constructional aspects of multi-storey timber buildings, June 1998, UK. [14] Knauf Gipsfaserplatten Vidiwall und Vidifloor – company catalogue; 2002. [15] European Committee for Standardization. EN 338:2003 E: Structural timber – strength classes. Brussels; 2003. [16] Kim H-S, Lee D-G. Analysis of shear wall with openings using super elements. Eng Struct 2003;25(8):981–91.