International Workshop on Wind-Related Disasters and Mitigation Tohoku University, Sendai, Japan March 11-14, 2018
A stochastic model for predicting wind-induced damage to wooden houses in snowy cold regions
Sachiko YOSHIDA1, Daisuke KONNO1, Kosuke SATO1, Eri GAVANSUKI2, and Yasushi UEMATSU1
1Tohoku University, Sendai, Japan, [email protected] 2Osaka City University, Osaka, Japan, [email protected]
Abstract A stochastic model for predicting wind-induced damage to wooden houses in snowy cold region has been developed, focusing on the roof frame joints. The model consists of ‘wind load model’ and ‘wind resistance model’. Pulling-up load tests were carried out to evaluate the wind-resistant performance of roof frame joints. The test specimens were designed based on a questioner survey on the change in material and construction of roofs, which had been given to the house builders in Tohoku District, a snowy cold region of Japan.
Keywords: Wind-related disasters, Damage prediction, Wooden house, Snowy cold region
1 INTRODUCTION When designing buildings in the snowy cold region of Japan, the structural engineers pay less attention to the wind resistance than to the snow and earthquake resistances. The wooden houses in this region have some specific features that are not good for the wind resistance, such as roofing materials and window system. The deterioration may proceed faster than in the other regions due to the effect of snow. Therefore, old wooden houses have been seriously damaged by strong typhoons that hit once in several decades, such as Typhoons 91191) and 04182). Most damage was done to roof cladding and structures. The damage investigations implied that the practical wind speeds had been lower than the design values in many cases. The objective of the present study is to develop a stochastic model for predicting wind-induced damage to roof structures of wooden houses in snowy cold region, in which the features of wooden houses in this region are taken into account. Special attention is paid to the joints of rafter and pole plates (see Figure 1), because this part is often damaged and its failure cause serious damage to the roof structures. Pulling-up load tests were carried out with specimens designed based on a questionnaire survey on the material and structure of wooden houses in snowy cold region, which had been given to the house builders, in order to construct the wind resistance model. The proposed damage prediction model may be useful for investigating the countermeasures against the wind-induced damage as well as for improving the wind resistance of wooden houses. This model doesn’t consider the effect of aging deterioration because its effect seems to be small if the attic ventilation is made appropriately. It is hoped that a more precise model considering the effect of aging deterioration on the strength of the joints will be developed. It is the subject of future study.
Purlin Ridgepole
Tie Beam Rafter
Vertical Roof Strut Pole Plate
Figure 1. Roof structure of typical wooden houses in Japan
2 OUTLINE OF THE DAMAGE PREDICTION MODEL The damage prediction model consists of ‘wind load model’ and ‘wind resistance model’, focusing on the joints of rafter and pole plates. The wind load S is evaluated based on the building code, while the resistance R of the joints is evaluated from the results of a pulling-up load test with full-scale specimens. S and R are both stochastic values whose characteristics are represented by probability density functions, fS(s) and fR(r). Assuming that S and R follow log-normal distributions, the probability of failure, pf, may be given by the following equation:
(1) ln(RS / ) pf P[ R S ] 1 22 RS where S and R are the mean values of S and R, respectively; S and R are the coefficients of variance (C.V.) of S and R, respectively; and represents the cumulative distribution function of standard normal distribution. Wind loads S acting on the roof depend on the roof shape and roof pitch. The wind resistance R depends on the material and construction of roof structure as well as on the roof pitch. These parameters depend on the area and the time of construction. Therefore, a questionnaire survey was given to the house builders in Tohoku District, a snowy cold region of Japan, to obtain the information on these parameters. Wooden houses in this region have the following specific features; that is, (1) they are not installed with shutters that protect windows against flying debris and (2) thin sheet metal is widely used for roofing material. The roofs are generally light and the weight of roofing material may affect the wind resistance of roof structure, significantly. In the wind load model, sudden increase in internal pressure due to the failure of windows by flying debris is also considered.
3 EXPERIMENT FOR LOAD RESISTANCE OF ROOF FRAME JOINTS 3.1 Questionnaire on Roof Construction Methods We conducted a questionnaire survey on the roof construction methods of wooden houses in snowy cold region, which were given to 16 house builders in Tohoku District. Focus is on the change in roof construction methods and roofing materials from the 1960s to the 2010s. The response rate was 44%. Figure 2 shows the results on the joining method and wood used for pole plates. The figures indicate the numbers of answers. It is found that the joining method used for rafter-to-pole plate joints has changed from nailing to the use of twisted metal fitting. Japanese cedar has been used for pole plates in any time. Recently, however, Douglas fir and North American hemlock have become popular.
nailing Twisted metal fitting and nailing Japanese cedar Douglas fir Folded metal fitting and nailing Hemlock No response Twisted clamp 2010s 1 7 1 2010s 5 2 2 2000s 7 1 2000s 5 2 2 1990s 1 7 1990s 6 1 2 1980s 4 3 1 1980s 6 1 1 1970s 6 2 1 1970s 7 1960s 7 1 1960s 7 1
(a) Joining method for rafter-to-pole plate joints (b) Wood used for pole plate
Figure 2. Change in roof construction method with time (multiple answers)
3.2 Outline of Pulling-up Load Test for the Roof Frame Joints Pulling-up load test is conducted on rafter-to-pole plate joints. The parameters of the test are joining method, wood used for pole plates, and roof pitch, as listed in Table 1. The loading method is shown in Figure 3. Because the wind force acts on the rafter in the normal direction, positive upward, test specimen is inclined and the load is applied in the vertical direction. The pole plate is fixed to the base of the testing machine using a lower test jig; the rafter is supported at two points; and the load is applied to the upper test jig at a constant loading rate of 2 kN/min. Two kinds of rafter-to-pole plate joints shown in Figure 4 are tested. That is, these are joining by toenailing (Figure 4(a)) and joining by twisted metal fitting together with toenailing used for positioning (Figure 4(b)). Wood of the rafter is Japanese cedar for all specimens. The number of specimens is 6 for each test parameter.
Table 1. Test specimens Specimen Wood used for Roof Joining method name pole plates pitch N-C-2.5 Toenailing (two N75 nails) Japanese cedar 14.0 N-C-3.5 Toenailing (two N75 nails) Japanese cedar 19.3 N-C-6 Toenailing (two N75 nails) Japanese cedar 31.0 N-F-2.5 Toenailing (two N75 nails) Douglas fir 14.0 N-F-3.5 Toenailing (two N75 nails) Douglas fir 19.3 N-F-6 Toenailing (two N75 nails) Douglas fir 31.0 T-C-2.5 Twisted metal fitting (ST-12) and toenailing Japanese cedar 14.0 T-C-3.5 Twisted metal fitting (ST-12) and toenailing Japanese cedar 19.3 T-C-6 Twisted metal fitting (ST-12) and toenailing Japanese cedar 31.0 T-F-2.5 Twisted metal fitting (ST-12) and toenailing Douglas fir 14.0 T-F-3.5 Twisted metal fitting (ST-12) and toenailing Douglas fir 19.3 T-F-6 Twisted metal fitting (ST-12) and toenailing Douglas fir 31.0
Test Jig
Rafter
Pole Plate
Test Jig 300 300 (mm)
Figure 3. Loading method
Twisted Metal Fitting Rafter Nail (2-N75) Rafter (ST-12, ZN-40) (45×60×540 mm) (45×60×540 mm) Pole Plate Pole Plate (105×105×300 mm) (105×105×300 mm) Nail (2-N75)
(a) Toenailing (b) Twisted metal fitting and toenailing Figure 4. Details of the specimens
3.3 Result of Pulling-up Load Test for Roof Frame Joints Table 2 summarizes the mean, the maximum and minimum values and the coefficient of variance (C.V.) of the ultimate strength for the six specimens. The numbers in parentheses indicate the numbers of specimens that show the corresponding failure mode. Figures 5 and 6 show the fracture modes for the joining by nailing and those for the joining by twisted metal fitting and toenailing, respectively. The null hypothesis that the data of N-C-2.5, N-C-3.5, and N-C-6 are from the same continuous distribution is accepted with 95% confidence interval, using the Kolmogorov-Smirnov test. These tests for N-F-2.5, N-F-3.5, and N-F-6 get similar result. From these results, it is found that the influence of roof pitch on the ultimate strength is relatively small in the case of joining by nailing. Regarding the material for pole plates, Douglas fir provides larger ultimate strength than Japanese cedar by approximately 50% on average. The specific gravity of Douglas fir is larger than that of Japanese cedar. This is because Douglas fir with larger specific gravity provides larger pull-out resistance of nails than Japanese cedar3). In the case of joining by twisted metal fitting and toenailing, the steeper the roof pitch is, the smaller the mean value of ultimate strength is. This is because the distance from the nailing position to the edge of rafter becomes shorter as the roof pitch becomes steeper. When Douglas fir is used for the pole plate, failure occurs at the joint between rafter and twist metal fitting in any specimen. On the other hand, when Japanese cedar is used for the pole plate, failure occurs at the joint between pole plate and twist metal fitting in some cases. This may be due to a fact that Douglas fir is generally stronger than Japanese cedar3).
(a) Slip from pole plate (b) Punching out Figure 5. Failure modes of joining by nailing
(a) Crack of rafter (b) Slip from rafter (c) Crack of pole plate (d) Slip from pole plate Figure 6. Failure modes of joining by twisted metal fitting and toenailing
Table 2. Results of pulling-up load test
Specimen Mean C. V. Maximum Minimum Failure mode name (kN) (-) (kN) (kN) Slip from a pole plate (5) N-C-2.5 1.17 0.30 1.61 0.60 Punching out (1) N-C-3.5 0.94 0.19 1.18 0.63 Slip from a pole plate (6) N-C-6 0.96 0.12 1.12 0.78 Slip from a pole plate (6) N-F-2.5 1.55 0.34 2.43 1.01 Slip from a pole plate (6) N-F-3.5 1.66 0.17 1.99 1.07 Slip from a pole plate (6) N-F-6 1.53 0.14 1.77 1.27 Slip from a pole plate (6) Crack a rafter (2) Slip from a rafter (1) T-C-2.5 3.49 0.22 4.57 2.40 Crack a pole plate (1) Slip from a pole plate (2) Crack a rafter (1) T-C-3.5 3.27 0.15 3.80 2.51 Slip from a rafter (3) Crack a pole plate (2) Crack a rafter (5) T-C-6 2.57 0.18 3.58 2.15 Crack a pole plate (1) Crack a rafter (1) T-F-2.5 3.77 0.14 4.44 3.03 Slip from a rafter (5) T-F-3.5 3.21 0.11 3.87 2.82 Crack a rafter (6) T-F-6 3.08 0.19 3.98 2.05 Crack a rafter (6)
3.4 Outline of the Element Test This section explains the element test for the joint between rafter and twist metal fitting. The specimens are shown in Figure 7. The parameter of this test is roof pitch. A steel plate simulating the twisted metal fitting is attached to the rafter by nails with the same angle as the roof pitch. The location of nails depends on the roof pitch. Figure 8 shows the loading method. The steel plate is fixed to the test jig; the rafter is supported by a test jig at two points; and the load is increased at a rate of 2 kN/min in the same way as in the above-mentioned pulling-up load test. Wood of the rafter is Japanese cedar for all specimens. The number of specimens is 6 for each test parameter.
Rafter (45×60×450 mm) Rafter (45×60×450 mm) Rafter (45×60×450 mm) 17.69 mm 14.66 mm 7.52 mm Steel plate Steel plate Steel plate 14.0 19.3 31.0
(a) 14.0 (b) 19.3 (c) 31.0 Figure 7. Specimens for element test
Test Jig
Rafter Bolt Fixation Test Jig 300 (mm)
Figure 8. Loading method for element test
3.5 Result of the Element Test Table 3 shows the mean, the maximum and minimum values and the coefficient of variance (C.V.) for the ultimate strength, which are obtained from the results of six specimens. Table 4 shows the results of tests for the null hypothesis that the results of the element test and the pulling-up test for the same roof pitch are from the same continuous distribution using the two-sample Kolmogorov-Smirnov test with 95% confidence interval. In this test we exclude the results of the case where the pole plates were made of Japanese cedar and a failure occurred at the joint between the pole plate and the steel plate in the pulling-up load test. According to Table 4, when the roof pitch is 14.0or 19.3, it seems that the ultimate strength of the joint minutely depends on the kind of wood used for the rafter within the limits of the present test. However, in the case where Japanese cedar was used for the pole plate, some specimens were failed at the joint of the pole plate and the twist metal fitting. Further investigations are necessary to understand this feature in more detail. When the roof pitch is 31.0, the results for Douglas fir used for pole plates show a significant difference between the element test and the pulling-up test. In order to investigate this phenomenon further, load displacement curves for test specimens E-6, N-F-6, and T-F-6 are shown in Figure 9. The joining is done by nailing for N-F-6, while twist metal fitting together with the nailing for positioning is used for T-F-6. Both specimens have the same nailing. According to Figure 9, the displacement providing the ultimate strength in the T-F-6 case is located between those in the E-6 and N-F-6 cases. This feature implies that the nailing for positioning has an influence on the ultimate strength of the joints. Table 3. Results of element test
Specimen Roof Mean C.V. Maximum Minimum Failure mode name pitch (kN) (-) (kN) (kN)
Crack of rafter (3) E-2.5 14.0 3.63 0.07 4.05 3.32 Slip from rafter (3) E-3.5 19.3 3.34 0.03 3.55 3.24 Crack of rafter (6) E-6 31.0 2.18 0.11 2.49 1.75 Crack of rafter (6)
Table 4. Result of KS test (a) 14.0 (b) 19.3 (c) 31.0 T-C-2.5 T-F-2.5 T-C-3.5 T-F-3.5 T-C-6 T-F-6 E-2.5 〇 〇 E-3.5 〇 〇 E-6 〇 ×
〇: Adoption ×: Rejection
Load Load Load (kN) (kN) (kN) 4.0 4.0 4.0 3.5 3.5 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 1.5 1.5 1.5 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0.0 0 10 20 30 0 10 20 30 0 10 20 30 Displacement(mm) Displacement(mm) Displacement(mm)
(a) E-6 (b) N-F-6 (c) T-F-6 Figure 9. Load displacement curve
3.6 Wind Resistance Model Based on the Pulling-up Load Test Previous studies4) have shown that the load resistance of the joint is given by the result of the pulling-up load test multiplied by a factor α that takes into account the reduction of ultimate strength because of workability and so on. In this case, the mean R and the coefficient of variance R of the ultimate strength of the joint are given by Equations (2) and (3), respectively:
(2) R Rˆ
22 (3) R Rˆ
where Rˆ and Rˆ are the mean and coefficient of variance of the ultimate strength obtained from the pulling-up load test, respectively; and μα and να are the mean and coefficient of variance of the correction factor α, which are assumed to be 0.8 and 0.2, respectively4). 4 WIND LOAD MODEL
The mean value of wind load, μS, acting on the rafter-to-pole plate joint is estimated by the following equation, assuming that the rafter is represented as a cantilever beam as shown in Figure 10:
2 (4) w12 a w l S w1 a r 22l where a is the length of the eaves; l is the distance between the pole plate and the purlin; w1 is the uniformly distributed load per unit area on the eaves; w2 is the uniformly distributed load per unit area on the roof expect for the eaves; and r is the distance between adjacent rafters.
l
a w2 Purlin Rafter w1
Pole Plate
Figure 10. External forces acting on the roof
The practical load acting on the joint is calculated as the sum of the wind load and the dead load of members. Therefore, the load acting on the rafter is represented by uniformly distributed load whose value per unit area is given by the following equation:
1 (5) w U2 Cˆ w cos 2 HDC
ˆ where ρ is the air density; UH is the wind speed at the mean roof height H; CC is the peak wind force coefficient; wD is the dead load per unit area of the members; and θ is the roof pitch. For calculating the wind load on the eaves, given by the difference between the peak external pressures on the top and bottom surfaces of eaves, it is assumed that the peak pressure coefficient on the bottom surface is equal to that on the wall just below the eaves6). 5) The peak pressure coefficient Ĉpe on the windward wall is given by the following equation :
ˆ (6) Cpe kZZ(1 7 I ) where kZ is a factor for the vertical profile, which is specified in [5] and roughly proportional to the profile of the mean velocity pressure of approach flow; and Iz is the turbulence intensity at the height of eaves. The coefficient of variance νS of the wind load is assumed to be 0.36.5)
5 STOCHASTIC MODEL FOR PREDICTING WIND-INDUCED DAMAGE On the basis of the ultimate strength of the rafter-to-pole plate joint and the load acting on it, the probability of failure, pf, is obtained from Equation (1). In the calculation the following features of wooden houses in the snowy cold region are taken into account: (1) No shutter is installed on the window. Therefore, the window is exposed to strong winds and flying debris. Once window glasses are broken either by high pressure or by flying debris in strong winds, the internal pressure suddenly increases. In such a case, the internal pressure coefficient is set to +1.5 based on the Notification No. 454 of the Ministry of Construction, Japan. When the window glasses are not broken, the internal pressure coefficient is assumed to be zero. (2) Thin sheet metal is usually used for roofing material. Therefore, the weight of roof that resists against the wind forces is generally small. This feature is considered in the value of wD in Equation (5) Furthermore, the following assumptions are made for the following case studies: (1) The buildings under consideration are two-story residential houses with mean roof height H 7.5 m. (2) The length a of the eaves, the distance l between the pole plate and purlin, and the distance r between adjacent rafters are 0.6 m, 0.91 m, and 0.455 m, respectively. (3) The local pressure reduction coefficient kC, which considers the effect of tributary area of the joint on the peak wind loads, is set to 1. (4) The terrain category of surrounding area is assumed III5). Considering that H < 10 m, the 5) values of kZ and Iz in Equation (6) are calculated as 0.91 and 0.26, respectively . In this case, the value of Ĉpe in Equation (6) is calculated as 2.58. (5) The peak external pressure coefficient on the top surface of the eaves and roof are provided by [5], depending on the assumed roof pitch. (6) The roofing material is assumed to be thin sheet metal. The dead load per unit area wD in Equation (5) is set to 196 N/m2.
Sample results for the relationship between the velocity UH at the mean roof height H and the probability of failure, pf, are shown in Figure 11. In this figure the pole plate is Japanese cedar and the breakage of window glasses is assumed. The result without the window glass braekage is also shown for T-C-3.5. As might be expected, the larger the ultimate strength obtained from the pulling-up load test is, the smaller the probability of failure becomes. However, comparing the results for T-C-2.5 and T-C-3.5 with each other, it is found that the probability of failure for T-C-2.5 is almost the same as that for T-C-3.5 nevertheless the ultimate strength of T-C-3.5 is smaller than that for T-C-2.5. This feature implies that the probability of failure should be predicted based on the wind load as well as on the strength. As the roof pitch decreases, the magnitude of wind load acting on the joint increases, resulting in an increase in probability of failure if the strength is the same. However, the ultimate strength also increases with roof pitch. As a result, the probability of failure is almost the same for both T-C-2.5 and T-C-3.5. It is found from the results for T-C-3.5 that when the windows are protected from the flying debris, the probability of failure decreases significantly compared with the case of no protection.
1.0
f p 0.8 N-C-2.5 N-C-3.5 0.6 N-C-6 T-C-2.5 0.4 T-C-3.5 T-C-6 0.2
Failure Failure probability T-C-3.5 (window glasses aren't broken) 0.0 0 20 40 60 80 Velocity (m/s) Figure 11. Relationship between velocity and probability of failure 6 CONCLUDING REMARKS The present paper has proposed a stochastic model for predicting wind-induced damage to wooden houses in snowy cold region. Focus is on the damage to roof structure, particularly on the rafter-to-pole plate joints and its ultimate strength was evaluated by pulling-up load tests. The specimens of the tests were designed based on the results of a questionnaire survey on the roof materials and structures of wooden houses in snowy cold region, which had been given to the house builders in Tohoku District. The prediction mode consists of ‘wind load model’ and ‘wind resistance model’. The features of wooden houses in snowy cold region are considered in these models. That is, 1) they are not installed with shutters that protect windows against flying debris and 2) thin sheet metal is widely used for roofing material. The main findings of this study may be summarized as follows: (1) From the questionnaire survey on the roof construction method of wooden houses, it is found that the joining method for rafter-to-pole plate joints has changed from nailing to the use of twisted metal fitting together with the toenailing for positioning. Although Japanese cedar has always been used for pole plates, Douglas fir and North American hemlock have become popular recently. (2) The pulling-up load tests indicate that the influence of roof pitch on the ultimate strength is relatively small in the case of joining by nailing. In the case of joining by twisted metal fitting and toenailing, the ultimate strength generally decreases with the roof pitch. This is due to the effect of the distance from the nailing position to the edge of rafter. (3) The probability of failure of roof structure depends on the wind load as well as on the ultimate strength of the roof structure. The roof pitch strongly affects both of them. (4) When the windows are protected from the flying debris, the probability of failure decreases significantly compared with the case of no protection.
ACKNOWLEDGEMENTS This work was financially supported by JSPS KAKENHI (Grant Number 15K20861, E. Gavanski), The LIXIL JS Foundation (2014 FY, Y. Uematsu) and The Obayashi Foundation (2016 FY, Y. Uematsu). Their support is gratefully acknowledged.
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