Asce 7-16 Kz Table

[Karoline Oum]

BalancedSnow Load is the weight of snow buildup on a structure, neglecting any drifting that may occur. Weather conditions can greatly influence how heavy snow is, but ASCE offers us an equation for snow density as a function of depth, up to 30 lbs/ft, per ASCE 7-16 eq 7.7-1.

The Flat Roof Snow Load is either the final output (for roof planes with less than 15 slope or curved roofs with less than 10 between eaves and crown) or an intermediate step in developing the sloped roof snow load.

Note: 7.3.4 specifies a minimum required flat roof snow load, essentially limiting the amount of reduction allowed from favorable adjustment factors. Where ground snow loads are less than 20 psf, the minimum required load is the importance factor times the ground snow load (I.s * p.g), otherwise the minimum is 20 psf * I.s where the mapped ground snow load exceeds 20 psf.

Wind tends to blow snow off of more exposed roofs, while a roof surrounded by taller buildings or trees can be sheltered from such effects. To capture this, we use the Exposure Factor from Table 7.3-1. This table makes use of the same surface roughness/exposure definitions as the wind loads in Chapter 26.

The Flat Roof and Sloped Roof Snow Loads only reflect the uniform loads on our roofs. Any discontinuity, such as a ridge, hip, or step in a roof has the potential to cause an aerodynamic drift which must be considered in design.

Eric is a licensed Professional Engineer working as a structural engineer for an architectural facade manufacturer, which straddles the line between structural and mechanical engineering. He holds an MS in Structural Engineering from the University of Minnesota.

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Tornado and straight-line wind events are often discussed and compared in terms of their intensity, e.g., maximum wind speed, however, it is unclear to what extent tornado-induced and straight-line wind-induced wind loads are equivalent even for the same nominal intensity. This lack of understanding inhibits both tornado design philosophies and policies, and communication of tornado risk to the public. This study directly compares existing wind tunnel databases of tornado-induced and straight-line wind-induced pressures, for a similar building model, to evaluate to what extent the induced surface pressures on a typical building differ. The existing datasets used in the study are enhanced with a numerical internal pressure model to facilitate the comparison across a range of opening configurations that would be common in typical buildings. The analysis finds that differences are most pronounced in the overall distribution of pressures across the building surface, and in the magnitudes of pressures in regions of strong flow separation. However, overall the magnitudes of the peak tornado-induced pressures are reasonably similar to straight-line wind-induced pressures, with tornado-induced pressures on average 13% higher than equivalent straight-line wind-induced pressures. Ultimately, this study demonstrates a framework for such comparisons, while recognizing key sources of uncertainty and further research needs.

Haan et al. (2010) measured external tornado pressures on a gable building model using a translating vortex simulator at Iowa State University. The building model contained 89 pressure taps (46 wall and 43 roof taps), and had plan dimensions of 91 mm by 91 mm, an eave height of 36 mm and a roof angle of 35. One hundred forty test cases were considered, consisting of different building orientations with respect to the vortex translation path, different tornado vortex structures and tornado vortex translation speeds. For each case, a tornado-like vortex was translated directly over the building model ten times to capture the variability in the measured tornado pressures. External pressures were sampled at 430 Hz, and were corrected for the dynamic tubing response. Of the 140 cases conducted by Haan et al. (2010), results from six are selected for the current study, corresponding to Cases 4, 16, 28, 116, 128, and 140. These six cases are chosen to capture the effects of swirl ratio and building orientation. Table 2 summarizes the parameters of each case, which include the vortex translation speed, building orientation, radius to maximum winds, Reynolds number (which is based on maximum mean horizontal velocity at the building height and the height of the building as the characteristic length), and swirl ratio reported for each in the original study. The swirl ratio is a measure of the relative magnitude of the angular and radial momentum in the vortex, and can be defined as given in Eq. (1),

The Footprint Area Ratios given in Table 2 represent the area of the building footprint relative to the area of the vortex core and have values of 13 and 1.6% respectively for the Vane 15 and Vane 55 cases. Assuming the building has full-scale footprint dimensions of 9.1 m by 9.1 m, this would equate to a tornado with core radius of 14 m for the low swirl ratio case (Vane 15) and 41 m for the high swirl ratio case (Vane 55). The core radii of tornadoes are difficult to measure in the field, and so the width of damaging winds is typically recorded instead. Strader et al. (2015) report that EF2 (maximum wind speeds between 50 m/s and 60 m/s) tornadoes in the US between 1995 and 2013 on average have a maximum path width of 288 m. Fan and Pang (2019) report the following relationship between core radius and path width assuming a Rankine vortex and the edge of the tornado being equivalent to a tangential wind speed of 30 m/s:

where p is the measured pressure on the building model surface, pᥗ is the ambient pressure far from the influence of the vortex, ρ is the density of air, and Vref is the reference wind velocity, defined in Eq. (4):

where z is the height above floor level, H is the roof height of the building, n is the number of ensemble runs, r is the radial distance between the center of the building model and the center of the vortex, R defines the domain of the vortex translation path relative to the building model, and is the 3-s gust (in full-scale, based on a full-scale velocity of 60 m/s, representing the upper limit of an EF2 tornado) wind speed measured at a specific distance, r, from the vortex center and height, z above the smooth floor. These wind speeds were captured by Fleming et al. (2013) by translating the tornado vortex past a stationary Cobra probe (2500 samples/second), in the absence of the building model, five times (i.e., number of ensemble, n = 5) for heights varying from 0.6 to 38 m in full-scale. The resulting horizontal velocity profile is shown in Figure 1A, normalized by Vref and the roof height of the building model, h. The velocity profile as shown represents the maximum horizontal wind speed at every height, independent of the time at which each maximum occurs, and therefore is different from the instantaneous profile present at any given time. The max-at-every-height velocity profiles for both swirl ratios show highest wind speeds at the lowest heights (no roughness elements were present), a general phenomenon that has been witnessed in field measurements as well (Kosiba and Wurman, 2013; Wurman et al., 2013; Kosiba et al., 2014). As a result, the maximum peak horizontal velocity anywhere below the height of the building is used as the reference velocity for evaluating tornado-induced pressure coefficients rather than restricting the reference velocity to a specific height as is common in boundary layer wind tunnel testing. Figure 1B shows a typical velocity time history for one ensemble run, both the raw instantaneous values and the 3-s (full-scale) moving average velocity. Here the time axis is converted to a non-dimensional distance from the center of the building model to the center of the approaching vortex, r, divided by the radius of maximum winds, Rmax. It is worth nothing that the velocities presented here should be treated with some caution as they were measured using a TFI Cobra probe, which has a 45 cone of acceptance for a given orientation, which is not ideal for measuring velocities in complex, vortex-driven flows. More details concerning the challenges and resulting impacts on the experimental setup can be found in Fleming et al. (2013). Fleming et al. (2013) also provides more details of the laboratory tornado wind field, including the presence of a significant vertical velocity component that is not found in most straight-line winds.

(A) Horizontal velocity profile for low and high swirl ratio tornado-like vortices, normalized to the mean roof height of the building model, h, and the peak horizontal velocity,Vhor,max.. (B) Sample velocity time history for one ensemble run of the Vane 55 vortex translating past a stationary Cobra probe measuring at the roof height of the building model.

The Tokyo Polytechnic University aerodynamic database (Tamura, 2012) contains external wind pressure coefficients for 116 different models of gable, hip and flat roof, low rise structures. Data are available for wind angles between 0 and 90 in 15 increments, and the symmetry of the building model and pressure taps are used to simulate pressure data for wind angles between 90 and 360. Tamura (2012) states that the full scale gradient height of the boundary layer was 450 m, with a turbulence intensity of 0.25 at 10 m full-scale height, and power law coefficient of 0.2, matching terrain category III in the Architectural Institute of Japan (AIJ) wind loads guide (AIJ, 2004). This corresponds to a roughness length of approximately 0.068 m using the relationship between α and z0 given in Holmes (2015). The pressures were originally referenced to the mean roof height velocity, reported as 7.4 m/s, in this terrain. Using the assumed 1/3 velocity scale from Tamura (2012), the full scale duration of the testing was 10 min. Hagos et al. (2014) confirmed the suitableness of this database for use in wind engineering applications.

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