Fragility assessment of wood sheathing panels and roof-to-wall connections subjected to wind loading

Abstract

The performance of the wood-frame buildings after tornadoes has shown that the majority of the wind damage resulted from building envelope failure most typically due to the loss of the roof. To assess the performance and the reliability of low-rise wood-frame residential buildings with a focus on the roofs, fragility analysis can be used to estimate the probability of failure of a roof when constructed with specified nails and sheathing sizes. Thus, this paper examines the fragility of specific types of nails, roof-to-wall (RW) connection details, and sheathing sizes based on the damaged roofs that were previously assessed in the Dunrobin area in Ottawa (Ontario) that was hit with an Enhanced Fujita (EF3) tornado on September 21, 2018. The presented fragility analysis considers four scenarios, including different sheathing and nail sizes. Dead loads, wind loads, and resistance on the sheathing panels were compiled and analyzed to determine the failure of the examined roofs. The eight fragility models suggest that the safest roof sheathing (RS) is the 1.22 m × 1.22 m sheathing panel with 8 d nails, and the safest RW connections is achieved by using H2.5 hurricane clips.

Graphical abstract

Keywords

tornadoes / wind loads / low-rise buildings / fragility analysis / risk assessment / structural failures

1 Introduction

Tornadoes are destructive natural disasters that affect communities by causing damage to infrastructure, deaths, and financial repercussions. A tornadic event can cost over 1 billion dollars in insurance losses and cause hundreds of casualties [ 1].

During a tornado, gradient wind speeds and wind turbulence dominate, causing high fluctuations in the lower part of the atmospheric boundary layer that mainly affects low-rise buildings, i.e., buildings with height-to-width ratio not greater than 0.5, for which reference height does not exceed 20 m with gabled or single ridged roofs (NBCC 2015). Air that flows over and around these buildings is causing aerodynamic wind pressures, while the external negative pressure may separate the roof and the walls. As the air particles pass the sharp corners of a building, the external pressures (suction forces) are the greatest in the ridge, roof corners, eaves, and wall corners. Failures between the top of the wall and the roof connections, and sheathing failures, are caused by these high wind pressures since the siding materials and roof are likely to be displaced [ 2]. Due to the roof’s vulnerability in high wind events, roofs can suffer severe damages that may include the loss of shingles, the loss of sheathing, damaged rafters, and connection failures leading to a collapse [ 3]. Figure 1 illustrates a damaged roof sheathing (RS) in Dunrobin, Ontario, that was hit with an Enhanced Fujita (EF3) tornado in 2018. Another common failure (roof-to-wall (RW) connection) that can occur after a tornado is shown in Fig. 2. The roof was attached to the wall with a toe-nail connection with around 2–3 inclined nails. This type of connection does not resist uplift forces caused by an EF3 tornado, and thus, such a failure is observed often after tornado aftermath.

The above-mentioned structural failures can be prevented in low to moderate tornado wind loadings by improving the individual components of the building along the vertical load path [ 4]. Thus, it is essential to better understand the structural performance of the residential wood-frame low-rise buildings under high wind loads to develop design solutions that will strengthen the structural elements of the buildings. Such design solutions to building practices require probabilistic approaches to assessing the reliability of low-rise wood-frame buildings in tornado-prone areas. This study uses fragility analysis methodologies to determine the structural performance of the roof components. Although tornadoes have been occurring for hundreds of years, the ability to quantify tornado-induced risk has been only recently attempted [ 5– 8]. These researchers have conducted fragility assessments due to heavy winds on wood construction, RW connections in wood-frame houses, and RS. Ellingwood et al. [ 5] in 2004 performed fragility analysis of wooden low-rise buildings and suggested that the height of the house has little impact on the fragility analysis as the exposure factor is approximately the same for one- and two-story houses. Instead, the fastener selection was crucial, as different nail sizes have different mean values of resistance. Other research has shown that clips provide more resistance to uplift forces than 8 d toe-nails [ 7].

This paper develops conditional fragility models for the structural risk assessment of wooden roofs subjected to extreme winds. One type of single-family light-frame residential house was considered representative of the building inventory in the examined area of Ontario (Ottawa): a one-story building with a gable roof without roof overhang. First, presenting the adopted models for the demand and the capacity estimation, and the general framework for developing the fragility models. Then, the proposed framework for developing the fragility models is applied in two major structural components along the vertical load path, i.e., the RS and the RW connection. The proposed models provide a tool for rapid risk assessment of wooden houses subjected to different wind scenarios. The main objective of this paper is to illustrate the effectiveness of fragility analysis in the performance assessment of wood sheathing panels and RW connections subjected to high winds. This is done by comparing 8 different scenarios that can be used to construct typical low-rise wood-frame residential buildings. In addition, the study also develops new fragility models using Canadian standards for the demand estimates.

2 Capacity statistics of roofs

The capacity of the roof is the summation of the dead load and the strength of the connection used. When the structural performance of the RS is assessed (i.e., in scenarios 1–4 presented later), the weight of the RS together with the nail connection strength resist the uplift load on the roof. Thus, the dead load is assumed to be constant in time, and the total uplift capacity ( C) is calculated as:

(1) C=R_{\mathrm{W}}+R_{\mathrm{C}},

where R _W denotes the resistance due to the dead load of the roof panel and R _C denotes the resistance of the connection due to the type of nail/clip in the RS panel.

When the structural performance of the RW is assessed (i.e., in scenarios 5–8 presented later), the weight of the roof connections and the nail/clip connection strength resist the uplift load on the roof. Thus, RW connections resist the point loads from the end of the rafters, and the total uplift capacity ( C) is calculated as:

(2) C=R_{\mathrm{D}}+R_{\mathrm{C}},

where R _D denotes the resistance due to the dead load of the RW connections and R _C denotes the resistance of the connection due to the type of nails or clip used.

Structural details such as the dimensions of the roof and the type of nails, affect the capacity estimates for both the RS and the RW structural cases. Therefore, this study investigates the structural performance of sheathing panels and connection details used to construct typical residential houses found in the path of the recent tornadoes in Ottawa, Canada [ 3].

The most common sheathing panels consist of 12 mm thick CDX plywood with dimensions of 1.22 m × 1.22 m and 1.22 m × 2.44 m. The sheathing panels, rafter spaces, and roof spans that have been chosen in all analyses represent typical houses found in the Dunrobin area, ON, and are similar to the ones used by Clemson University’s Wind Load Test Facility and the National Association of Home Builders [ 9, 10]. These sheathing panels are connected to the wall using 50.8 mm long 6 d nails (i.e., 6 d nails have 2.87 mm nominal diameter) and 63.5 mm long 8 d nails (i.e., 8 d nails have 3.33 mm nominal diameter) and are also connected to rafters spaced at 610 mm center-to-center. RS panel failures are measured in kPa as the wind force is exerted on the panel area, creating a pressure that is resisted by the sheathing nail. The rafters are 50 mm by 100 mm spruce-pine-fur (SPF), and the nails are spaced 150 mm at the edge and 300 mm intermediate in the interior panel. The dimensions of the sheathing panels connected by 6 d or 8 d nails to the wall and their statistics are presented in Table 1, while Fig. 3 illustrates the schematic drawings and the dimensions of all examined scenarios.

For the fragility analyses presented in this study, RW connections (rafter/truss to wall) are considered point loads and measured in kN as they exert a force to a single point (i.e., to the RW connection). This paper investigates typical connection types that include: a) H2.5 hurricane clip; b) 2–16 d (i.e., 16 d nails are 4.11 mm in diameter and 88.9 mm long) toe-nails; c) 3–16 d (i.e., 4.11 mm in diameter and 88.9 mm long) toe-nails; and d) 3–8 d (i.e., 8 d nails have 3.33 mm nominal diameter and are 63.5 mm long) toe-nails which connect the rafter/truss to the wall, and in Ontario, Canada, these connections are commonly spaced every 16 inches [ 11]. Also, the rafters used are 50 mm by 100 mm SPF. The RW connections’ statistics are presented in Table 2.

The roof dead-load on the RS panels is 0.17 kPa (3.5 psf), while the strength of the RW connections is 0.72 kPa (15 psf). The values of the mean-to-nominal ratio and the coefficient of variation (COV) were found to be 1.05 and 0.10, respectively. These values were calculated using estimated weights of materials such as plywood [ 12]. The RW connection weight is converted into a force since the connection strength is simulated as a point load (kN). The RW connection weight is multiplied by the common spacing requirement of 16 inches (0.41 m) and an estimated span of 4 m from Fig. 3 to generate a load. The dead load applied to the wood-framed roof structures is assumed to be uniformly distributed [ 13].

3 Wind load

The wind loading is the primary external force applied to the structure during a tornadic event. The National Building Code of Canada [ 14] has no wind load provisions for tornadic episodes; thus, the wind load provisions for general wind loads are adopted in this study as:

(3) W_{\mathrm{p}}=I_{\mathrm{w}}q{C}_{\mathrm{e}} C_{\mathrm{t}} C_{\mathrm{g}} C_{\mathrm{p}},

where W_p denotes the specified external pressure caused by the wind (kN/m ²), I_w indicates the important factor for the wind load, q denotes the reference velocity pressure (kN/m ²), C_e denotes the exposure factor, C_t denotes the topographic factor, C_g denotes the gust effect factor, and C_p shows the external pressure coefficient which is averaged over the considered area. Equation (3) provides the wind pressure applied to residential roofs in both the vertical and the horizontal directions. The demand being exerted on the RS panels is the wind pressure estimated using the EF3 scale and represents the wind pressures of tornadic events. The demand exerted on the RW connections is the wind load estimated using the EF scale. To categorize a tornado, the EF Scale is used, which was adopted in Canada in April 2013 [ 15]. Environment Canada provides the wind speeds of the EF scale shown in Table 3. This scale is demonstrated by the amount of wind in kilometers per hour applied to a residential roof during a tornado. The EF scale is a methodology to predict wind speed based on detected damage to building infrastructure. The wind speed provided by Environment Canada has been converted to pressures and loads to allow for the limit state equations to be created with consistent units. The fragility analysis is performed using Monte Carlo Simulation (MCS) and considers categorized wind speeds that demonstrate the tornadoes. Wind pressures between EF1 and EF4 scales are used, as the possibility of an EF5 tornado occurring is unlikely.

4 Fragility methodology

Fragility analysis aids engineers in estimating the structural risk of individual structural components and/or the whole structure [ 16]. Fragility analysis has been used for multi-hazard assessment of highway bridges and multi-bridge classes vulnerable to hurricanes [ 17], pile-supported wharves and piers exposed to storm surges and waves [ 18], aboveground storage tanks after extreme storm events [ 19], light-frame wood construction subjected to wind and earthquake hazards [ 12], hurricane damage to residential construction [ 20], isolated skewed bridges [ 21], earthquake risk assessment of underground railway stations [ 22], single-story RC precast structures [ 23], and residential wood-framed structures subjected to tornadoes [ 6].

Fragility analysis requires the development of fragility curves representing the conditional probability of exceeding a given damage state (e.g., the collapse of the roof) as a function of the demand parameter (e.g., the intense winds from tornado analysis). Thus, fragility analysis is related to specific limit state functions, and the conditional probability of the limit state being violated can be expressed as:

(4)

where LS denotes the limit state function in terms of pressure for the examined case in this study, C denotes the capacity, D denotes the demand, and IM denotes the intensity measure (e.g., wind pressure).

RS failure and RW connection failure due to wind loads happen when internal and external pressures cause uplift to the roof framing. As it was also mentioned in the previous section, such a type of failure is influenced by three major factors: resistance, dead load, and wind load. Resistance is providing by the nails, while dead load refers to the self-weight of RS panel acting in the opposite direction to uplift pressure that is the wind loading. Thus, for the scenarios 1–4 presented later, the limit state function can be described in terms of capacity and demand as:

(5) LS(\mathit{x})=C(\mathit{x})-D (\mathit{x})=R_{\mathrm{W}} (\mathit{x})+R_{\mathrm{C}} (\mathit{x})-W_{\mathrm{p}}(\mathit{x}).

Also, for the scenarios 5–8 presented later, the limit state function can be described in terms of capacity and demand as:

(6) LS(\mathit{x})=C(\mathit{x})-D (\mathit{x})=R_{\mathrm{D}} (\mathit{x})+R_{\mathrm{C}} (\mathit{x})-W_{\mathrm{F}}(\mathit{x}),

where x denotes a vector of the random variables associated for the calculation of capacity and demand, R _W is the resistance due to the weight of the roof panel, R _D denotes the resistance due to the weight RW connections, R _C is the resistance of the connection due to the type of nails/clip in the RS panel and the RW connection, W _p describes the wind pressure acting on the sheathing panel and W _F denotes the wind load acting on the RW connection. Thus, three parameters are involved in the evaluation of the limit state function defined in Eqs. (5)–(6), where two are related to the capacity and one is related to the demand. The adopted models for the estimation of these parameters are presented in the following sections. During a tornado, the internal and external pressures affect the integrity of the structure due to the high levels of wind, i.e., internal and external pressure that acts on a roof panel is combined, creating a large uplift force on the panel that may cause RS and RW failure [ 24].

The fragility function of the structural system is commonly described using the lognormal Cumulative Distribution Function (CDF) as:

(7) Fr(x)= \varphi \left[\frac{\mathrm{l}\mathrm{n}(x)-{\lambda }_{\mathrm{R}}}{{\xi }_{\mathrm{R}}}\right],

where x denotes the intensity measure in the fragility analysis (e.g., wind speed), ϕ denotes the standard normal distribution, ξ _R is the logarithmic standard deviation of capacity and λ _R is the logarithmic median of capacity. Once, ξ _R and λ _R are known the fragility curved is plotted using Eq. (7) where the horizontal axis shows the intensity measure and the vertical shows the conditional probability. The shape ( λ _R) and scale ( ξ _R) parameters can be evaluated using the Probability Paper Plot through a Monte Carlo Simulation (MCS) to evaluate the limit state function.

Figure 4 shows the flowchart of the proposed framework for the development of the fragility curves. First is choosing the examined scenario that forms the limit state function. Then, demand and capacity are estimated, where n denotes the different wind speeds associated with the demand and m denotes the number of the Monte Carlo Simulations. Then, a n × m matrix is created for both demand and capacity, and the limit state function is evaluated. Using the data reported after evaluating the LS function, the Probability Paper Plot is applied to find the parameters of the fragility models. The demand is considered the wind load from the EF scale, where 221 different wind speeds were converted to pressures and used to calculate the demand of the sheathing panels. Whereas the capacity is considered the dead-load and the uplift capacity of the nails. The MCS were considered 1000 trials to create a n × m matrix, where n is equal to 1000 and m is equal to 221. This matrix was used to calculate the capacity of the RS panels and the RW connections. Then, the LS function was evaluated using the demand and capacity calculated in the previous step. The demand includes the wind pressure and wind forces that act as the uplift force on the RS panels and RW connections which can occur in multiple directions and is taken from the EF scale. The demand of the wind pressure and the wind force is in Table 3. The dead load includes the self-weight of the roof, including the RS panels and the RW connections that act in the opposite direction to the uplift force seen in Section 2.2.

The resistance properties are provided from the nails/clips and were used on the specified RS panels (Table 1) and RW connections (Table 2). The RS panels have nails that are 6 or 8 d, and this means one is slightly longer than the other; however, the spacing for both these nails is consistent. The nails for the RW connections are usually toe-nails (8 or 16 d) as well as hurricane clips (H2.5). A schematic drawing in Fig. 5 shows a typical RW connection with hurricane clips. The fragility equations used to create the fragility curves are described for the RS panels Eq. (5), and the RW connections Eq. (6).

The MCS is applied to create the fragility models. Random variables, including the dead load and the uplift capacity (resistance), are defined based on a probability distribution and assigned to each trial (i.e., 1000 random variables per trial). Once the random variable is generated, it is placed into the limit state equation with the wind pressures used for these models. This procedure is repeated for the duration of MCS, and a probability paper plot is applied to find the fragility parameters (i.e., the lambda and zeta values). The residual R ² is also calculated to examine how many data points surround the line of best fit, accounting for the accuracy of the data.

5 Case studies

5.1 Baseline of scenarios

Table 4 illustrates the baseline of the RS panel scenarios used in this research, together with the characteristics and dimensions of each scenario. Different roof geometries are analyzed to represent the different roofs that can be constructed and the most popular roofs that were seen in Dunrobin tornadoes [ 3]. The scenarios presented herein are selected as common practice residential roofs analyzed during the primary field investigation. The houses with the most damage that were inspected were primarily gable roofs and represented a prevalent roof type used in the construction of residential houses. Table 5 illustrates the baseline of the 4 different RW scenarios used in this research that have been chosen using common nails/clips used in residential construction.

5.2 Fragility analysis results

5.2.1 Sheathing failures

Individual panel failure fragilities can be defined using Eq. (4). Using the LS function, MCS has developed fragility analysis for all scenarios shown in Table 4. An enclosed structure is assumed until the first panel fails, so it is important to calculate the probability of an individual sheathing panel before evaluating the reliability of the roof system. All sheathing panels are assumed to be used on one-story gable roofs. All panels are 12 mm thick and made of plywood.

Scenario 1 demonstrates the probability of failure for a 1.22 m × 2.44 m sheathing panel with 6 d nails when exposed to different wind pressures. The fragility analysis results predict that the sheathing panels would fail at an applied pressure of approximately 1.7 kPa (i.e., at a wind speed of 192 km/h). This indicates that the sheathing on the roof would start failing during an EF2 tornado which agrees with the damages seen in Dunrobin during the EF3 tornado. Scenario 2 demonstrates the probability of failure for a 1.22 m × 1.22 m sheathing panel with 6 d nails when exposed to different wind pressures. The fragility analysis results predict that the sheathing panels would fail at an applied pressure of approximately 2.1 kPa (i.e., at a wind speed of 213 km/h). This also indicates that the sheathing on the roof would start failing during an EF2 tornado which agrees with the damages seen in Dunrobin during the EF3 tornado. Scenario 3 demonstrates the probability of failure for a 1.22 m × 2.44 m sheathing panel with 8 d nails when exposed to different wind pressures. The fragility analysis results predict the sheathing panels would fail at an applied pressure of approximately 4.1 kPa (i.e., at a wind speed of 298 km/h). This indicates that the sheathing on the roof would start failing during an EF4 tornado. Scenario 4 demonstrates the probability of failure for a 1.22 m × 1.22 m sheathing panel with 8 d nails when exposed to different wind pressures.

The presented predictions are based on developed fragility models developed using the probability paper plot. Indicatively, Fig. 6 shows the lognormal probability paper plot used to find the parameters λ and ξ for scenario 1.

The lognormal probability paper plots produce Eq. (8):

(8) \ln \left(x_i\right)=\xi S_i+\lambda ,

where ξ represents the slope, and λ represents the intercept. The parameters of the fragility models for the RS and the R² values are presented in Table 6. The high R² values indicate that the lognormal distribution can fit very well the data produced after the Monte Carlo simulation, and thus the presented fragility models can be described using a lognormal distribution with ξ and λ reported in Table 6.

Figure 7 shows the fragility curves for scenarios 1–4 plotted using the developed fragility models. Comparison of the fragility curves shows that the 1.22 m × 2.44 m sheathing panel with 6 d nails (i.e., scenario 1) provides the least stability to roofs exposed to high wind pressures. On the other hand, the 1.22 m × 1.22 m sheathing panel with 8 d nails (i.e., scenario 4) provides the greatest stability to roofs exposed to high wind pressures. Thus, bigger nails together with smaller panel sizes is preferable for reducing the risk of uplift failure. In addition, a comparison of scenario 1 and scenario 3 indicates that using 8 d nails for large panels may significantly increase the uplift resistance compared to the 6 d nails. Thus, the use of longer nails with larger diameters may be preferable for resisting higher wind pressures.

5.2.2 RW connection failures

RW connection fragility failures can be defined using Eq. (5). Similar to sheathing panel failures, using the limit state function, MCS has been used to develop fragility analysis using the scenarios in Table 5. All connections exist on one-story gable roofs, as it was assumed for the sheathing failures. All panels are 12 mm thick and made of plywood.

Scenario 5 demonstrates the probability of failure for a H2.5 hurricane clip fastener used as an RW connection when exposed to different wind loads. The fragility analysis results predict that the RW connection fails at approximately 8.7 kN (i.e., at a wind speed of 304 km/h). This indicates that the RW connection would fail during an EF4 tornado. Thus, the use of hurricane clips would have allowed the houses to withstand the Dunrobin tornado. Scenario 6 demonstrates the probability of failure if 2–16 d toe-nails are used for an RW connection when exposed to different wind loads. The fragility analysis results predict that the RW connection fails at approximately 3.9 kN (i.e., at a wind speed of 204 km/h). This indicates that the RW would fail during an EF2 tornado which agrees with the damages seen in Dunrobin. Scenario 7 demonstrates the probability of failure if 3–16 d toe-nails are used for an RW connection when exposed to different wind loads. The fragility analysis results predict that the RW connection fails at approximately 5.8 kN (i.e., at a wind speed of 248 km/h). This indicates that the RW connection would fail during an EF3 tornado which agrees with the damages seen in Dunrobin. Scenario 8 demonstrates the probability of failure if 3–8 d toe-nails are used for an RW connection when exposed to different wind loads. The fragility analysis results predict that the RW connection fails at approximately 4.8 kN (i.e., at a wind speed of 226 km/h). This indicates that the RW connection would fail during an EF3 tornado which agrees with the damages seen in Dunrobin.

The presented predictions are based on developed fragility models developed using the probability paper plot, as described in the previous section. Using Eq. (8), the parameters of the fragility models for the RW together with the R² values are reported in Table 7. The high R² values indicate that the lognormal distribution can fit very well the data produced after the Monte Carlo simulation, and thus the presented fragility models can be described using a lognormal distribution with ξ and λ reported in Table 7.

Figure 8 shows the fragility curves for scenarios 5–8 plotted using the developed fragility models. A comparison of the fragility curves shows that H2.5 hurricane clips (i.e., scenario 5) would provide the best protection. On the other hand, 2–16 toe-nails (i.e., scenario 6) would provide the least amount of stability for RW connections when exposed to high wind loads. Therefore, hurricane clips seem to provide better RW resistance than nails because hurricane clips are specifically made to resist extreme wind pressures and provide a higher structural capacity to roofs exposed to extreme wind loads.

6 Conclusions

This study proposed an easy-to-implement framework for developing fragility models to estimate the structural risk of typical wood houses exposed to tornadoes. Thus, eight failure scenarios are examined that may happen on low-rise wooden residential houses and specifically on roofs. Four scenarios are related to RS failures, and the other four are related to the RW connection failures. For each scenario, the Monte Carlo simulation is used to evaluate the limit state function, together with the probability plot to derive the parameters needed to plot the fragility curves.

The results indicate that the predictions of the developed fragility models align with the damages observed in the Dunrobin area in Ottawa (Ontario) that was hit with an EF3 tornado on September 21, 2018. For example, for the RS connections, a 1.22 m × 2.44 m sheathing panel with 6 d nails (i.e., scenario 1) is the most vulnerable to high wind pressures, and a 1.22 m × 2.44 m sheathing panel with 8 d nails (i.e., scenario 3) would significantly reduce this vulnerability. Also, for the RW connections, H2.5 hurricane clips would significantly reduce the probability of failure compared to nails. Thus, the fragility curves suggest that using 8 d nails with smaller panel sizes for the RS connections and using H2.5 hurricane clips for the RW connections would resist higher wind loads. The presented fragility methodology can provide effective strategies to improve structural safety and lead to more structural sound wooden residential homes.

Notations

C: structural capacity

C _e: exposure factor

C _g: gust effect factor

C _p: external pressure coefficient

C _t: topographic factor

D: structural demand

Fr: fragility function

I _w: importance factor

ln: lognormal function

LS: limit state

p _f: probability of failure

q: reference velocity pressure

R _C: resistance of the nail/clip connection

R _D: resistance of the dead load of the connection

RS: roof sheathing

R _W: resistance of the dead load on the roof panel

RW: roof-to-wall

R ²: residual

S _i : inverse of cumulative distribution function (CDF)

W _L: wind force

W _p: wind pressure

IM: intensity measure

x : a vector of the random variables associated for the calculation of capacity and demand

λ: slope of probability paper plot

λ _R: lognormal median of capacity

ξ _R: lognormal standard deviation of capacity

ξ: slope of probability paper plots

ϕ: standard normal cumulative distribution

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