3-31 Hazus-MH Technical Manual Figure 3.24. Galveston-Texas City-Santa Fe Area, TX (upper: Aerial photo; lower: NLCD). 3-32 Chapter 3. Surface Roughness Modeling Figure 3.25. Close-up of Santa Fe Area, TX (upper: Aerial photograph; lower: NLCD). 3-33 Hazus-MH Technical Manual Figure 3.26. Northeast Suburb of Houston, TX (upper: Aerial photograph; lower: NLCD). 3-34 Chapter 3. Surface Roughness Modeling Table 3.9. Roughness Length for NLCD Land Cover Classes State/Region Land Cover Class Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Water 11 Open Water 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 12 Perennial Ice/Snow 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 Developed 21 Low Intensity Residential 0.35 0.10 0.33 0.13 0.33 0.11 0.33 0.11 0.33 0.11 0.34 0.12 0.34 0.11 0.33 0.12 0.35 0.11 0.36 0.11 0.35 0.10 0.35 0.15 22 High Intensity Residential 0.55 0.10 0.50 0.14 0.53 0.14 0.53 0.14 0.53 0.14 0.54 0.15 0.57 0.18 0.54 0.14 0.57 0.11 0.57 0.16 0.55 0.11 0.53 0.19 23 Commercial/Industrial/Transportation 0.44 0.38 0.39 0.35 0.35 0.21 0.35 0.21 0.35 0.21 0.39 0.27 0.38 0.26 0.34 0.26 0.35 0.20 0.34 0.20 0.33 0.21 0.38 0.20 Barren 31 Bare Rock/Sand/Clay 0.10 0.04 0.09 0.05 0.09 0.05 0.09 0.05 0.09 0.05 0.10 0.06 0.09 0.04 0.09 0.05 0.10 0.05 0.10 0.06 0.10 0.05 0.10 0.04 32 Quarries/Strip Mines/Gravel Pits 0.14 0.08 0.18 0.09 0.18 0.09 0.18 0.09 0.18 0.09 0.17 0.09 0.20 0.09 0.18 0.08 0.17 0.06 0.17 0.07 0.17 0.09 0.12 0.05 33 Transitional 0.15 0.09 0.18 0.10 0.20 0.07 0.20 0.07 0.20 0.07 0.17 0.09 0.19 0.08 0.16 0.09 0.13 0.06 0.17 0.10 0.15 0.09 0.20 0.09 Forested Upland 41 Deciduous Forest 0.55 0.16 0.65 0.19 0.68 0.17 0.68 0.17 0.68 0.17 0.65 0.18 0.69 0.13 0.72 0.13 0.76 0.15 0.79 0.19 0.78 0.15 0.79 0.16 42 Evergreen Forest 0.56 0.14 0.72 0.20 0.73 0.12 0.73 0.12 0.73 0.12 0.76 0.13 0.71 0.10 0.74 0.14 0.75 0.15 0.82 0.14 0.81 0.15 0.82 0.11 43 Mixed Forest 0.55 0.14 0.71 0.21 0.71 0.12 0.71 0.12 0.71 0.12 0.74 0.13 0.71 0.10 0.73 0.15 0.76 0.14 0.80 0.16 0.80 0.14 0.81 0.14 Shrubland 51 Shrubland 0.10 0.05 0.12 0.03 0.12 0.03 0.12 0.03 0.12 0.03 0.12 0.04 0.12 0.03 0.12 0.03 0.11 0.03 0.13 0.04 0.10 0.03 0.12 0.03 Non-Natural Woody 61 Orchards/Vineyards/Other 0.25 0.11 0.27 0.13 0.25 0.13 0.25 0.13 0.25 0.13 0.24 0.12 0.27 0.14 0.24 0.12 0.26 0.14 0.29 0.16 0.25 0.10 0.24 0.15 Herbaceous Upland 71 Grasslands/Herbaceous 0.04 0.02 0.04 0.01 0.04 0.01 0.04 0.01 0.04 0.01 0.04 0.02 0.04 0.02 0.04 0.02 0.05 0.02 0.04 0.02 0.04 0.02 0.04 0.02 Herbaceous Planted / Cultivated 81 Pasture/Hay 0.04 0.02 0.06 0.02 0.05 0.02 0.05 0.02 0.05 0.02 0.05 0.02 0.05 0.02 0.06 0.01 0.05 0.02 0.06 0.02 0.06 0.02 0.05 0.02 82 Row Crops 0.06 0.02 0.06 0.02 0.05 0.02 0.05 0.02 0.05 0.02 0.06 0.03 0.06 0.02 0.06 0.02 0.06 0.03 0.06 0.02 0.06 0.02 0.05 0.02 83 Small Grains 0.04 0.02 0.05 0.02 0.06 0.02 0.06 0.02 0.06 0.02 0.05 0.03 0.06 0.02 0.07 0.02 0.06 0.03 0.07 0.03 0.06 0.02 0.06 0.02 84 Fallow 0.03 0.02 0.04 0.02 0.04 0.02 0.04 0.02 0.04 0.02 0.03 0.01 0.03 0.02 0.04 0.02 0.04 0.02 0.03 0.01 0.03 0.02 0.04 0.01 85 Urban/Recreational Grasses 0.07 0.04 0.05 0.03 0.03 0.04 0.03 0.04 0.03 0.04 0.04 0.04 0.06 0.03 0.06 0.04 0.06 0.04 0.06 0.03 0.07 0.04 0.05 0.04 Wetland 91 Woody Wetlands 0.50 0.20 0.55 0.21 0.58 0.21 0.58 0.21 0.58 0.21 0.59 0.22 0.54 0.20 0.57 0.26 0.60 0.27 0.61 0.22 0.60 0.21 0.59 0.24 92 Emergent Herbaceous Wetlands 0.10 0.05 0.11 0.05 0.09 0.04 0.09 0.04 0.09 0.04 0.08 0.04 0.04 0.01 0.09 0.03 0.10 0.04 0.10 0.04 0.10 0.05 0.10 0.05 State/Region Land Cover Class Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Ave Stdev Water 11 Open Water 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 12 Perennial Ice/Snow 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 Developed 21 Low Intensity Residential 0.35 0.15 0.35 0.15 0.36 0.14 0.35 0.14 0.43 0.17 0.50 0.10 0.42 0.17 0.34 0.10 0.34 0.10 0.36 0.10 0.29 0.10 0.29 0.10 22 High Intensity Residential 0.53 0.19 0.53 0.19 0.62 0.17 0.58 0.21 0.73 0.34 0.84 0.42 0.62 0.18 0.48 0.16 0.48 0.16 0.59 0.18 0.53 0.08 0.53 0.08 23 Commercial/Industrial/Transportation 0.38 0.20 0.38 0.20 0.44 0.33 0.42 0.22 0.92 0.82 1.55 0.93 0.44 0.12 0.35 0.15 0.35 0.15 0.51 0.38 0.31 0.15 0.31 0.15 Barren 31 Bare Rock/Sand/Clay 0.10 0.04 0.10 0.04 0.14 0.04 0.08 0.03 0.09 0.04 0.09 0.04 0.09 0.04 0.10 0.04 0.10 0.04 0.12 0.05 0.12 0.05 0.12 0.05 32 Quarries/Strip Mines/Gravel Pits 0.12 0.05 0.12 0.05 0.12 0.06 0.15 0.08 0.17 0.08 0.17 0.08 0.17 0.08 0.15 0.08 0.15 0.08 0.16 0.10 0.15 0.06 0.15 0.06 33 Transitional 0.20 0.09 0.20 0.09 0.14 0.09 0.22 0.08 0.21 0.10 0.21 0.10 0.21 0.10 0.17 0.09 0.17 0.09 0.19 0.07 0.13 0.09 0.13 0.09 Forested Upland 41 Deciduous Forest 0.79 0.16 0.79 0.16 0.77 0.11 0.78 0.15 0.78 0.19 0.78 0.19 0.78 0.19 0.79 0.09 0.79 0.09 0.77 0.14 0.78 0.13 0.78 0.13 42 Evergreen Forest 0.82 0.11 0.82 0.11 0.77 0.16 0.82 0.10 0.78 0.12 0.78 0.12 0.78 0.12 0.80 0.15 0.80 0.15 0.78 0.14 0.78 0.13 0.78 0.13 43 Mixed Forest 0.81 0.14 0.81 0.14 0.78 0.14 0.80 0.12 0.79 0.12 0.79 0.12 0.79 0.12 0.80 0.16 0.80 0.16 0.79 0.12 0.79 0.13 0.79 0.13 Shrubland 51 Shrubland 0.12 0.03 0.12 0.03 0.14 0.04 0.13 0.04 0.13 0.04 0.13 0.04 0.13 0.04 0.11 0.02 0.11 0.02 0.13 0.03 0.11 0.04 0.11 0.04 Non-Natural Woody 61 Orchards/Vineyards/Other 0.24 0.15 0.24 0.15 0.22 0.15 0.24 0.16 0.26 0.11 0.26 0.11 0.26 0.11 0.26 0.12 0.26 0.12 0.26 0.14 0.25 0.13 0.25 0.13 Herbaceous Upland 71 Grasslands/Herbaceous 0.04 0.02 0.04 0.02 0.04 0.02 0.04 0.02 0.05 0.02 0.05 0.02 0.05 0.02 0.04 0.02 0.04 0.02 0.04 0.02 0.04 0.02 0.04 0.02 Herbaceous Planted / Cultivated 81 Pasture/Hay 0.05 0.02 0.05 0.02 0.05 0.02 0.06 0.02 0.05 0.02 0.05 0.02 0.05 0.02 0.05 0.02 0.05 0.02 0.05 0.02 0.06 0.02 0.06 0.02 82 Row Crops 0.05 0.02 0.05 0.02 0.05 0.03 0.05 0.01 0.06 0.03 0.06 0.03 0.06 0.03 0.06 0.03 0.06 0.03 0.06 0.03 0.06 0.02 0.06 0.02 83 Small Grains 0.06 0.02 0.06 0.02 0.06 0.03 0.06 0.02 0.06 0.03 0.06 0.03 0.06 0.03 0.06 0.02 0.06 0.02 0.06 0.02 0.07 0.03 0.07 0.03 84 Fallow 0.04 0.01 0.04 0.01 0.04 0.02 0.03 0.01 0.04 0.02 0.04 0.02 0.04 0.02 0.03 0.01 0.03 0.01 0.04 0.02 0.04 0.02 0.04 0.02 85 Urban/Recreational Grasses 0.05 0.04 0.05 0.04 0.07 0.05 0.05 0.04 0.08 0.03 0.08 0.03 0.08 0.03 0.05 0.04 0.05 0.04 0.06 0.04 0.03 0.04 0.03 0.04 Wetland 91 Woody Wetlands 0.59 0.24 0.59 0.24 0.60 0.24 0.60 0.24 0.60 0.22 0.60 0.22 0.60 0.22 0.58 0.22 0.58 0.22 0.58 0.21 0.61 0.20 0.61 0.20 92 Emergent Herbaceous Wetlands 0.10 0.05 0.10 0.05 0.10 0.04 0.08 0.04 0.10 0.04 0.10 0.04 0.10 0.04 0.09 0.05 0.09 0.05 0.09 0.04 0.09 0.04 0.09 0.04 TX GA SC NC MA NH ME LA MS AL FL Pan FL W FL SE FL NE VA MD DE PA NJ NY (Man&LI) Manhattan Long Is. CT RI 3.5.3 Census Tract-Averaged Roughness Length Using the roughness length-mapped NLCD data, census tract-averaged roughness lengths have been computed for the Year 2000 census tracts. Examples developed using the 1990 census tract shapes are presented in Figures 3.27 and 3.28 for North Carolina and Texas, respectively, where two counties are shown for each state, one coastal county and another relatively inland. For North Carolina, New Hanover County is the coastal county and Wake County is the inland county. For Texas, two adjacent counties were arbitrarily selected. The results are reasonable. 3-35 Hazus-MH Technical Manual Figure 3.27. Census Tract-Averaged Roughness Length Derived from NLCD Data, NC. 3-36 Chapter 3. Surface Roughness Modeling Figure 3.28. Census Tract-Averaged Roughness Length Derived from NLCD Data, Texas. 3.5.4 Comparisons of z0 Values Computed from NLCD Data on Rectangular Grids with Empirically Assigned z0 Values Averaged z0 values are also computed from NLCD data on 1.8km x 1.2km rectangular grids and compared to empirically assigned z0 values based on observations from aerial photographs. Examples of the comparison are presented in Figures 3.29 through 3.32 for selected locations in Texas, Florida, North Carolina and Rhode Island, respectively. The correlation between the two sets of z0 values is shown in Figures 3.33 through 3.36 for these four locations, respectively. The correlation coefficients are, respectively, 0.88, 0.93, 0.63 and 0.77 for the four locations. The results from all four locations are combined in Figure 3.37, for which the correlation coefficient is 0.926, which is higher than the average of the four individual correlation coefficients. This reflects that estimation of z0 values using NLCD data provides better relative accuracy when involving a larger variety of land cover characteristics than for a smaller, localized land area. These comparisons serve as a check on the reasonableness of averaged z0 values computed from NLCD data. It indicates that the degree of agreement is acceptable in general, except for a few grid cells that, in particular, involve commercial high-rise buildings in downtown areas, such as for the studied cases of Raleigh, NC, and Miami, FL. 3-37 Hazus-MH Technical Manual 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Assigned Zo 1 2 3 4 5 6 7 1 0.45 0.45 0.45 0.40 0.40 0.40 0.40 2 0.40 0.45 0.32 0.30 0.40 0.40 0.40 3 0.45 0.48 0.40 0.32 0.33 0.30 0.35 4 0.50 0.45 0.42 0.40 0.45 0.30 0.28 5 0.42 0.30 0.40 0.35 0.32 0.32 0.35 6 0.42 0.30 0.42 0.40 0.35 0.40 0.38 7 0.40 0.45 0.48 0.32 0.32 0.40 0.42 Computed Zo 1 2 3 4 5 6 7 1 0.447 0.441 0.438 0.367 0.372 0.384 0.408 2 0.418 0.428 0.372 0.320 0.414 0.341 0.414 3 0.471 0.483 0.399 0.332 0.330 0.341 0.373 4 0.491 0.468 0.429 0.403 0.421 0.339 0.305 5 0.416 0.304 0.385 0.358 0.361 0.327 0.389 6 0.448 0.319 0.409 0.410 0.397 0.429 0.418 7 0.394 0.439 0.431 0.391 0.389 0.403 0.423 Figure 3.29. z0 Values Computed from NLCD Data and Assigned Empirically for a Location in East Suburban of Houston, TX. 3-38 Chapter 3. Surface Roughness Modeling 1 2 3 4 5 6 1 2 3 4 5 6 Assigned Zo 1 2 3 4 5 6 1 0.45 0.42 0.20 0.01 0.10 0.30 2 0.42 0.45 0.10 0.02 0.15 0.25 3 0.45 0.50 0.15 0.01 0.20 0.30 4 0.52 0.60 0.35 0.10 0.10 0.30 5 0.55 0.50 0.40 0.15 0.10 0.25 6 0.55 0.50 0.50 0.02 0.10 0.10 Computed Zo 1 2 3 4 5 6 1 0.472 0.470 0.192 0.014 0.113 0.300 2 0.447 0.464 0.140 0.036 0.129 0.260 3 0.494 0.463 0.178 0.017 0.160 0.290 4 0.463 0.447 0.225 0.127 0.137 0.306 5 0.423 0.426 0.255 0.196 0.093 0.266 6 0.485 0.468 0.224 0.040 0.107 0.114 Figure 3.30. z0 Values Computed from NLCD Data and Assigned Empirically for Miami, FL, Including Downtown (Cell # 6-3). 3-39 Hazus-MH Technical Manual 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 Figure 3.31. z0 Values Computed from NLCD Data and Assigned Empirically for Raleigh, NC, Including Downtown (Cell # 10-4) 3-40 Chapter 3. Surface Roughness Modeling Assigned Zo 1 2 3 4 5 6 1 0.60 0.60 0.55 0.45 0.50 0.55 2 0.60 0.65 0.60 0.50 0.55 0.50 3 0.60 0.55 0.52 0.55 0.55 0.48 4 0.60 0.60 0.60 0.60 0.58 0.50 5 0.50 0.58 0.50 0.55 0.55 0.55 6 0.50 0.55 0.58 0.55 0.50 0.50 7 0.55 0.55 0.45 0.50 0.45 0.50 8 0.50 0.60 0.60 0.55 0.48 0.55 9 0.35 0.55 0.50 0.48 0.50 0.55 10 0.42 0.42 0.45 0.62 0.45 0.40 11 0.45 0.40 0.35 0.62 0.45 0.45 12 0.50 0.50 0.35 0.45 0.55 0.55 Computed Zo 1 2 3 4 5 6 1 0.557 0.546 0.518 0.482 0.619 0.666 2 0.567 0.562 0.604 0.498 0.521 0.491 3 0.622 0.580 0.514 0.535 0.534 0.479 4 0.607 0.597 0.542 0.533 0.569 0.495 5 0.519 0.587 0.524 0.522 0.525 0.520 6 0.537 0.528 0.542 0.490 0.487 0.476 7 0.573 0.572 0.499 0.529 0.448 0.500 8 0.491 0.552 0.535 0.487 0.449 0.536 9 0.365 0.521 0.489 0.465 0.513 0.524 10 0.418 0.430 0.451 0.399 0.495 0.462 11 0.527 0.466 0.428 0.411 0.508 0.539 12 0.554 0.522 0.375 0.430 0.532 0.524 Figure 3.31. z0 Values Computed from NLCD Data and Assigned Empirically for Raleigh, NC, Including Downtown (Cell#10-4) (concluded). 3.6 Example of Roughness Length (z0) Calculation Using Lettau’s Formula The empirical relationship between z0 and the ground roughness physical dimensions proposed by Lettau (1969) forms the basis of the methodology given in ASCE-7-02 for the computation of the roughness length (z0) for the purpose of determining if a building is located in Exposure B (defined as Suburban Terrain) or Exposure C (defined as Open Terrain). In ASCE-7-02, a building is considered to be located in a suburban terrain (Exposure B) if the value of z0 computed using Lettau’s method is greater than or equal to 0.15 m and less than 0.7 m. The representative value of Exposure B in ASCE-7-02 is defined with a surface roughness of 0.3 m. Recall that Lettau’s formula for estimating the surface roughness length, z0, is: z0 . 0.5HS/A (3.2) 3-41 Hazus-MH Technical Manual 1 2 3 4 5 6 1 2 3 4 5 Assigned Zo 1 2 3 4 5 1 0.38 0.35 0.32 0.34 0.32 2 0.40 0.32 0.35 0.40 0.30 3 0.45 0.35 0.28 0.20 0.40 4 0.40 0.40 0.32 0.35 0.40 5 0.40 0.30 0.38 0.42 0.38 6 0.45 0.40 0.38 0.45 0.32 Computed Zo 1 2 3 4 5 1 0.409 0.368 0.367 0.397 0.318 2 0.382 0.346 0.357 0.388 0.324 3 0.406 0.354 0.312 0.250 0.419 4 0.394 0.364 0.305 0.349 0.389 5 0.427 0.381 0.330 0.380 0.367 6 0.507 0.447 0.328 0.405 0.351 Figure 3.32. z0 Values Computed from NLCD Data and Assigned Empirically for a Location in South Suburban of Providence, RI. 3-42 Chapter 3. Surface Roughness Modeling Computed Zo vs Assigned Zo 0.2 0.3 0.4 0.5 0.6 0.2 0.3 0.4 0.5 0.6 Assigned Computed Correl. Coef. = 0.883 Figure 3.33. Comparison Between z0 Values Computed from NLCD Data and Assigned Empirically for a Location in East Suburban of Houston, TX. Computed Zo vs Assigned Zo 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Assigned Computed Correl. Coef. = 0.931 Figure 3.34. Comparison Between z0 Values Computed from NLCD Data and Assigned Empirically for Miami, FL, Including Downtown Area. 3-43 Hazus-MH Technical Manual Computed Zo vs Assigned Zo 0.2 0.3 0.4 0.5 0.6 0.7 0.2 0.3 0.4 0.5 0.6 0.7 Assigned Computed Correl. Coef. = 0.627 Figure 3.35. Comparison Between z0 Values Computed from NLCD Data and Assigned Empirically for Raleigh, NC, Including Downtown Area. Computed Zo vs Assigned Zo 0.1 0.2 0.3 0.4 0.5 0.6 0.1 0.2 0.3 0.4 0.5 0.6 Assigned Computed Correl. Coef. = 0.773 Figure 3.36. Comparison Between z0 Values Computed from NLCD Data and Assigned Empirically for a Location in Southern Providence, RI. 3-44 Chapter 3. Surface Roughness Modeling Computed Zo vs Assigned Zo 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Assigned Computed Correl. Coef. = 0.926 Figure 3.37. Comparison Between z0 Values Computed from NLCD Data and Assigned Empirically for the Four Locations Studied. where H = average height of the obstacle in the upwind terrain, S = the average projected frontal area per obstruction presented to the wind, and A = the average area of ground occupied by each obstruction (including the open area surrounding it). When calculating an average value of z0 over a region, S and A can be substituted by the total projected frontal area of all the obstacles upwind of a site and the total ground area these obstacles collectively occupy. When trees or bushes are present, their contribution to the frontal area must also be considered. ASCE-7-02 suggests that for conifers and other evergreens no more than 50% of their gross frontal area can be taken to be effective in obstructing the wind. For deciduous trees and bushes ASCE-7-02 states that no more than 15% of the their gross frontal area can be taken to be effective in obstructing the wind, however in hurricane prone regions, trees are generally still in full leaf during the time period hurricanes are likely to impact a region, thus an effective area of 50% is probably more appropriate. Recall, that the objective in estimating the surface roughness is to enable a realistic estimate of losses, and thus there should not be any tendency to choose a low value of frontal area in an attempt to obtain a conservative (low) value of z0 as may be done in a building design situation. Following is a step-by-step demonstration to show how to use the DOQQs to obtain the information required for Lettau’s formula and the logic in defining the input parameters. For demonstration purpose, the DOQQs from one medium density residential area in 3-45 Hazus-MH Technical Manual each of five counties in Florida (Escambia, Lee, Dade, Palm Beach, and Duval, see Figures 3.38 through 3.42) are used. Medium density residential areas are selected because: 1. Building density is in such a range that the possibility of a building being shadowed by trees is small and ambiguity does not exist in distinguishing two separate buildings 2. Building heights for a residential area are relatively uniform and relatively easy to estimate, thus providing more reliable results. It may be difficult to accurately determine an obstacle’s height by looking at the DOQQs or aerial photography. Sometimes, the length of the sun shadow projected by an obstacle can help if any known reference object exists. Familiarity with a region will aid considerably in reducing errors associated with estimates of both building and tree heights. Here, using Figure 3.38 as an example, the steps used to calculate the roughness length with Lettau’s method are demonstrated. This is a medium density residential area in the Panhandle of Florida (Escambia County). The wind was assumed coming from the direction shown by the arrow in Figure 3.38. The study area defined by the polygon shown in Figure 3.38 has a total ground area of about 60800 m2. By counting all the MDR 50 0 50 100 150 Meters Figure 3.38. Medium Density Residential Area in Escambia County. Wind Direction 3-46 Chapter 3. Surface Roughness Modeling MDR 100 0 100 200 Meters Figure 3.39. Medium Density Residential Area in Lee County. MDR 100 0 100 200 M Figure 3.40. Medium Density Residential Area in Dade County. Wind Direction Wind Direction 3-47 Hazus-MH Technical Manual 100 0 100 200 Meters Figure 3.41. Medium Density Residential Area in Palm Beach County. MDR 100 0 100 200 Mete Figure 3.42. Medium Density Residential Area in Duval County. Wind Direction Wind Direction 3-48 Chapter 3. Surface Roughness Modeling buildings in the study area, a total frontal (perpendicular to the wind direction) length of about 630 m was estimated. In this example, the homes are assumed to exist in a subdivision having a mixture of one and two story homes, with an assumed average roof height of about 6m. Therefore, the total frontal area from all the buildings is: 6 m . 630 m = 3780 m2. The trees were assumed to be about 15m tall. The gross tree frontal area is estimated to be roughly 1.5 times the building frontal area by looking at Figure 3.38. Therefore, the total effective tree frontal area is about (1.5 . 3780) . 50% = 2835 m2, given that the ratio of effective area to gross frontal area is assumed to be 50% for both deciduous and coniferous trees during hurricane seasons. Then by using Latteus equation, the roughness length for this area is calculated from: . . . m A ( HS ) ( HS ) . A z . HS bldg tree 0 56 60800 0 5 22680 42525 60800 0 5 0 5 0 5 6 3780 15 2835 0 . . . . . . . . . . Note that when the trees are the major obstacles in the areas being investigated (which is common), significant uncertainties may exist in the estimated tree heights, frontal areas, and relative densities but as seen in the example given above, trees account for about two-thirds of the surface roughness length computed using Lettau’s approach. Similar procedures have been applied to the other DOQQs included in this section. The parameter values determined at each step for the five examples are listed in Table 3.10. The assumed wind directions are shown in Figures 3.38 to 3.42, respectively. The computed roughness lengths all fall into the definition of Exposure B (as defined in ASCE 7), and all roughness lengths fall within the roughness length ranges given in Tables 3.6 and 3.8 for Medium Density Residential. Table 3.10. Examples for Roughness Length Calculation Using Lettau’s Formula Parameter Fig. 1(Escambia County) Fig. 2(Lee County) Fig. 3(Dade County) Fig. 4(Palm Beach County) Fig. 5(Duval County) Ground Area (m2) 60800 225000 77000 150000 35000 Estimated Mean Roof Height (m) 6 5 4.5 4.5 6 Building Frontal Length (m) 630 2800 1000 2900 240 Building Frontal Area (m2) 3780 14000 4500 13050 1440 Mean Tree Height (m) 15 6 - 6 15 Tree/Building Area Ratio 1.50 0.15 0.00 0.10 3.00 Tree Frontal Area (m2) 5670 2100 0 1305 4320 SH (building) 22680 70000 20250 58725 8640 Effective SH (trees) 42525 6300 0 3915 32400 Roughness Length z0 (m) 0.56 0.17 0.13 0.21 0.59 Note that the calculated roughness length is wind-direction dependent. For uniform building orientations within a region, the difference in the computed roughness lengths for different wind directions can be significant. For instance, in the Palm Beach County 3-49 Hazus-MH Technical Manual example, if the wind direction changes .90., the projected width of the buildings is in the range of 50% to 70% of that seen in the worked example, and thus the computed roughness length reduces to 50% to 70% of the original value. To remove the effect of directionality associated with building orientation, the frontal width of the building can be substituted with an effective width defined as the square root of the estimated plan area. Although Lettau’s method provides a convenient and quantitative means to estimate roughness length from DOQQs, aerial photography, etc., it should be used with caution. Engineering judgment needs to be applied to the results through comparisons with estimates of z0 given in the literature. Inevitably, some variations and uncertainties are associated with the estimation of the surface roughness length in any terrain, but as will be shown later, this parameter plays a very important role in the estimation of wind induced damage and loss. 3.7 Effect of Surface Roughness on Near Ground Gust Wind Speeds In this section, the effects of z0 on gust wind speeds (defined as a 3 second average) near the ground surface and on the hourly mean wind speed near the ground surface are shown. It is important to note that changes in wind speeds in areas of transitioning surface roughness are not treated in the default Hazus surface roughness model. However, a discussion of transition effects is provided in this section to assist the user in understanding their possible impact on damage and loss estimates. Transition effects are illustrated using the methodology described in ESDU (1983). The ESDU methodology forms the basis of the fetch length requirements given in ASCE-7-02 to enable the user to determine what exposure category a building is in given information on the upstream fetch lengths. Figure 3.43 shows the ratio of the wind speed, as normalized by the reference open terrain value, as a function of surface roughness and height above ground. Wind speed ratios are given for both the peak gust wind speed and the one hour mean wind speed. The data in Figure 3.43 clearly show that the effect of surface roughness is greatest near the ground (z = 3 m and z = 5 m), around the eave height of most single story buildings. Figure 3.43, also shows that the change in wind speed (with respect to the reference terrain value) is less for the peak gust wind speed than for the mean wind speed. For example, at a height of 10 m, a change in z0 from 0.03 m (open terrain) to 0.35 m (typical suburban terrain), the peak gust wind speed reduces by about 18%, whereas the hourly average wind speed reduces by about 32%. The reduction in the wind speed associated with an averaging time of one minute is about 25%, falling almost exactly half way between the reduction in gust wind speed and the reduction in the one hour mean wind speed. In Hazus, all damage and loss functions are given as a function of peak gust wind speed, not the one minute wind speed. The wind speed ratio data given in Figure 3.43 are for the case of a fully transitioned boundary layer (i.e., the wind has blown over a long enough fetch of new terrain that the flow characteristics are influenced only by the local terrain, and not the previous terrain). In reality, the wind at a given height does not change immediately to reflect the new 3-50 Chapter 3. Surface Roughness Modeling 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 0.001 0.01 0.1 1 Surface Roughness Length (m) Gust Wind Speed Ratio z=3 m z=5 m z=10 m z=20 m z=50 m z=100 m 0.3 0.5 0.7 0.9 1.1 1.3 1.5 0.001 0.01 0.1 1 Surface Roughness Length (m) Mean Wind Speed Ratio z=3 m z=5 m z=10 m z=20 m z=50 m z=100 m Figure 3.43. Wind Speed Ratios as a Function of Surface Roughness for Various Heights. terrain, but rather the flow gradually makes a transition, changing to reflect the characteristics associated with the new terrain. The distance over which this transition takes place varies with height, with the wind at lower heights changing more rapidly than wind at higher levels. Figures 3.44, 3.45 and 3.46 show examples of the rates of change of the mean and gust wind speeds as the terrain changes from an open terrain (z0 = 0.03m) to an example suburban terrain (z0 = 0.3 m) for heights of 3 m, 10 m and 50 m, respectively. In each of Figures 3.44 through 3.46, the upper plot shows the wind speed ratio with respect to open terrain as a function of the distance into the new terrain, and the lower plot shows the percentage adjustment of the wind to the new terrain as a 3-51 Hazus-MH Technical Manual Z0(1)=0.03m, Z0(2)=0.3m, z=3m 0 0.2 0.4 0.6 0.8 1 10 100 1000 10000 Fetch (m) Wind Speed Ratio Mean Ratio Gust Ratio Mean Ratio (Infinite Fetch) Gust Ratio (Infinite Fetch) 0 10 20 30 40 50 60 70 80 90 100 10 100 1000 10000 Fetch (m) % Adjustment of Wind Speed to Local Roughness Mean Gust Figure 3.44. Reduction in Wind Speed at a Height of 3 m (Open Terrain to Suburban Terrain). function of the distance. The lower plots suggest that the wind speed in the new terrain asymptotically approaches (but never reaches) the fully transitioned value. In ASCE-7- 02, this problem was handled by defining the fetch required to assume a fully transitioned case as the distance over which the wind speed adjustment reaches about 80% of the fully transitioned value. Notice in the 3 m height example, about 50% of the reduction occurs within the first 10m of the terrain change. Thus, homes located on the front row of a barrier island, or the front row in a subdivision facing open farmland, are actually situated within a transition zone. The effective wind speeds that these front row structures experience will be notably higher than those experienced by homes located even as close as one row back from these front line homes. In cases where loss studies are being performed in relatively small regions that encompass significant changes in terrain, it would be advisable to properly estimate the fraction of buildings that are likely to experience winds associated with terrains other than the default suburban values that would be appropriate for most of the building population. 3-52 Chapter 3. Surface Roughness Modeling z0(1)=0.03m, z0(2)=0.3m, z=10m 0 0.2 0.4 0.6 0.8 1 10 100 1000 10000 Fetch (m) Wind Speed Ratio Mean Ratio Gust Ratio Mean Ratio (Infinite Fetch) Gust Ratio (Infinite Fetch) 0 10 20 30 40 50 60 70 80 90 100 10 100 1000 10000 Fetch (m) % Adjustment of Wind Speed to Local Roughness Mean Gust Figure 3.45. Reduction in Wind Speed at a Height of 10 m (Open Terrain to Suburban Terrain). In the case of the 50 m height example (Figure 3.46), it is readily seen that even for a fetch distance of 1 km, the wind speed has only undergone 30% of the full adjustment. This example indicates that for taller buildings relatively isolated or in front row, the appropriate terrain selection is governed by the terrain at distances of 1km or more away from the building rather than at the location of the building itself. It should also be recognized, that the taller the building, the less the effect of terrain on the wind speeds at roof height. Figure 3.47 shows the rapid and significant reduction in wind speed at a height of 3m associated with a change in terrain from an open terrain to a heavily treed terrain. As shown in the upper graph, a 30% reduction in the peak gust wind speed (~70% reduction in wind load) occurs within the first 100 m of the transition. This example clearly shows why significant reductions in observed damage are seen when comparing damage on barrier islands to that seen within forested regions of the mainland, even right at the coast. 3-53 Hazus-MH Technical Manual Z0(1)=0.03m, Z0(2)=0.3m, z=50m 0 0.2 0.4 0.6 0.8 1 10 100 Fetch (m) 1000 10000 Wind Speed Ratio Mean Ratio Gust Ratio Mean Ratio (Infinite Fetch) Gust Ratio (Infinite Fetch) 0 10 20 30 40 50 60 70 80 10 100 1000 10000 Fetch (m) % Adjustment of Wind Speed to Local Roughness Mean Gust Figure 3.46. Reduction in Wind Speed at a Height of 50 m (Open Terrain to Suburban Terrain). Large changes in roughness associated with trees located very near the intra-coastal waterways are seen in many regions along the Gulf and Atlantic coasts. Examples of fully transitioned peak gust profiles are shown in Figure 3.48 for a range of roughness lengths. These examples are given to show the impact of z0 on the magnitude of the peak gust wind speed as a function of height. All gust profiles given in Figure3.7-6 are referenced to the peak gust wind speed at a height of 10 m in open terrain. 3-54 Chapter 3. Surface Roughness Modeling Z0(1)=0.03m, Z0(2)=1.0m,z=3m 0 0.2 0.4 0.6 0.8 1 10 100 1000 10000 Fetch (m) Wind Speed Ratio Mean Ratio Gust Ratio Mean Ratio (Infinite Fetch) Gust Ratio (Infinite Fetch) 0 10 20 30 40 50 60 70 80 90 100 10 100 1000 10000 Fetch (m) % Adjustment of Wind Speed to Local Roughness Mean Gust Figure 3.47. Reduction in Wind Speed at a Height of 10m (Open Terrain to Heavily Treed Terrain). Peak Gust Velocity Profiles 0 5 10 15 20 25 30 35 40 45 50 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 V(z)/V(z=10m,Z0=0.03m) Height (m) z0=0.01m z0=0.03m Z0=0.15m Z0=0.35m Z0=0.70m Z0=1.0m Figure 3.48. Examples of Peak Gust Velocity Profiles as a Function of z0. 3-55 Hazus-MH Technical Manual 3.8 Surface Roughness Updates for Hazus 2.0 Hazus 2.0 continues to use MRLC data in determining terrain roughness for the 22 hurricane states (including Hawaii) and the District of Columbia. It employs two new data sets: (1) the NLCD 2001 Land Cover data set and (2) the NLCD 2001 Percent Tree Canopy. Both are available as digital downloads from the MRLC website. The primary components of the 2001 MRLC-NLCD data set according to the MRLC website are: 1. Normalized imagery for three time periods per path/row 2. Ancillary data including a 30 m DEM, slope, aspect and a positional index 3. Per-pixel estimates of percent imperviousness and percent tree canopy 4. 21 classes of land cover data derived from the imagery, ancillary data and derivatives using a decision tree 5. Classification rules, confidence estimates and metadata from the land cover classification. Additional details as to how the data set was created can be found at the MRLC website. The NLCD 2001 Percent Canopy is an independent, per-pixel estimate derived from imagery and ancillary data using a regression tree used to describe tree cover. Figure 3.49 displays the percent canopy over Florida. Table 3.11 details the mapping between 2001 NLCD land use land cover (LULC) codes and 1992 NLCD LULC codes. Figure 3.49. Percent (Tree) Canopy for the State of Florida 3-56 Chapter 3. Surface Roughness Modeling Table 3.11. 1992 to 2001 LULC Class Mapping Class Description Class Description 11 Open Water 11 Open Water 12 Perennial Ice/Snow 12 Perennial Ice/Snow 21 Developed, Open Space** 31 Bare Rock/Sand/Clay 22 Developed, Low Intensity** 21 Low Intensity Residential 23 Developed, Medium Intensity 22 High Intensity Residential 24 Developed, High Intensity 23 Commercial/Industrial/Transportation 31 Barren Land 31 Bare Rock/Sand/Clay 32 Unconsolodated Shore* 31 Bare Rock/Sand/Clay 41 Deciduous Forest 41 Deciduous Forest 42 Evergreen Forest 42 Evergreen Forest 43 Mixed Forest 43 Mixed Forest 52 Shrub/Scrub 51 Shrubland 71 Grassland/Herbaceous 71 Grasslands/Herbaceous 81 Pasture/Hay 81 Pasture/Hay 82 Cultivated Crops 82 Row Crops 90 Woody Wetlands 91 Woody Wetlands 95 Emergent Herbaceaous Wetland 92 Emergent Herbaceous Wetlands * Classes not used NLCD 2001 Mapped to NLCD 1992 Class ** This mapping used as base only for Developed, Open Space and Developed, Low Intensity States were assigned specific terrain roughness values according to their LULC code, in tandem with aerial photography with the exception of Florida and New York. Florida was partitioned into 4 areas: panhandle, west, southeast and northeast and New York has specific values for Manhattan and Long Island. The z0 values assigned to each LULC code are displayed in Table 3.12 3.8.1 LULC codes 21 and 22 and MRLC-NLCD Data To account for increased terrain roughness by trees in developed open spaces and developed low intensity areas, LULC codes 21 and 22 make use of percent canopy from the MRLC according to the following equations: For Developed, Open Space (LULC 21): . . 2 2 0 2 0 2 0 0 * . . . . . . . . . . . Tef Tdos dos brsc ef brsc P z z z z P (3.3) 3-57 Hazus-MH Technical Manual Table 3.12. Assignment of z0 values to LULC Codes LULC CLASS DESCRIPTION HI TX LA MS AL PANHANDLE FLWEST FLSOUTHEAST FLNORTHEAST FL GA SC NC 11 OpenWater 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 12 Perennial Ice/Snow * 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 21 Developed, OpenSpace 0.080 0.100 0.090 0.090 0.090 0.090 0.100 0.090 0.090 0.100 0.100 0.100 22 Developed, Low Intensity 0.500 0.350 0.330 0.330 0.330 0.330 0.340 0.340 0.330 0.350 0.360 0.350 23 Developed, Medium Intensity 0.530 0.550 0.500 0.530 0.530 0.530 0.540 0.570 0.540 0.570 0.570 0.550 24 Developed, High Intensity 0.550 0.440 0.390 0.350 0.350 0.350 0.390 0.380 0.340 0.350 0.340 0.330 31 Barren Land 0.020 0.100 0.090 0.090 0.090 0.090 0.100 0.090 0.090 0.100 0.100 0.100 32 Unconsolodated Shore * 0.090 0.100 0.090 0.090 0.090 0.090 0.100 0.090 0.090 0.100 0.100 0.100 41 Deciduous Forest 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 42 Evergreen Forest 0.800 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 43 MixedForest 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 52 Shrubland 0.120 0.100 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.110 0.130 0.100 71 Grasslands/Herb aceous 0.085 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.040 0.050 0.040 0.040 81 Pasture/Hay 0.040 0.040 0.060 0.050 0.050 0.050 0.050 0.050 0.060 0.050 0.060 0.060 82 CultivatedCrops 0.030 0.060 0.060 0.050 0.050 0.050 0.060 0.060 0.060 0.060 0.060 0.060 90 WoodyWetlands 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 95 EmergentHerbac eousWetlands 0.150 0.100 0.110 0.090 0.090 0.090 0.080 0.040 0.090 0.100 0.100 0.100 * Class not used 3-58 Chapter 3. Surface Roughness Modeling Assignment of z0 values to LULC Codes Continued LULC CLASS DESCRIPTION VA MD DE PA NJ NY MAN LONGIS CT RI MA NH ME 11 OpenWater 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 12 Perennial Ice/Snow * 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 21 Developed, OpenSpace 0.100 0.100 0.100 0.140 0.080 0.090 0.090 0.090 0.100 0.100 0.120 0.120 0.120 22 Developed, Low Intensity 0.350 0.350 0.350 0.360 0.350 0.430 0.500 0.420 0.340 0.340 0.360 0.290 0.290 23 Developed, Medium Intensity 0.530 0.530 0.530 0.620 0.580 0.730 0.840 0.620 0.480 0.480 0.590 0.530 0.530 24 Developed, High Intensity 0.380 0.380 0.380 0.440 0.420 0.920 1.550 0.440 0.350 0.350 0.510 0.310 0.310 31 Barren Land 0.100 0.100 0.100 0.140 0.080 0.090 0.090 0.090 0.100 0.100 0.120 0.120 0.120 32 Unconsolodated Shore * 0.100 0.100 0.100 0.140 0.080 0.090 0.090 0.090 0.100 0.100 0.120 0.120 0.120 41 Deciduous Forest 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 42 Evergreen Forest 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 43 MixedForest 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 52 Shrubland 0.120 0.120 0.120 0.140 0.130 0.130 0.130 0.130 0.110 0.110 0.130 0.110 0.110 71 Grasslands/Herb aceous 0.040 0.040 0.040 0.040 0.040 0.050 0.050 0.050 0.040 0.040 0.040 0.040 0.040 81 Pasture/Hay 0.050 0.050 0.050 0.050 0.060 0.050 0.050 0.050 0.050 0.050 0.050 0.060 0.060 82 CultivatedCrops 0.050 0.050 0.050 0.050 0.050 0.060 0.060 0.060 0.060 0.060 0.060 0.060 0.060 90 WoodyWetlands 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 0.900 95 EmergentHerbac eousWetlands 0.100 0.100 0.100 0.100 0.080 0.100 0.100 0.100 0.090 0.090 0.090 0.090 0.090 * Class not used where: z0dos = z0 for Developed, Open Space z0brsc = z0 for Bare Rock/Sand/Clay (NLCD 2001) z0ef = z0 for Evergreen Forest PTdos = % tree canopy in Developed, Open Space (by county) PTef = % tree canopy in Evergreen Forest (by county) For Developed, Low Intensity (LULC 22): . . 2 2 0 2 0 2 0 0 * . . . . . . . . . . . Tef Tdli dli lir ef lir P z z z z P (3.4) where: z0dli = z0 for Developed, Low Intensity z0lir = z0 for Low Intensity Residential (NLCD 2001) z0ef = z0 for Evergreen Forest PTdli = % tree canopy in Developed, Low Intensity (by county) PTef = % tree canopy in Evergreen Forest (by county) 3-59 Hazus-MH Technical Manual As noted above, the variation in z0 mapping for these two particular LULC codes is implemented at the county level. 3.8.2 Implementation in Hazus 2.0 At the census block level, terrain roughness was computed by taking the average z0 value assigned to LULC data that overlapped the census block spatially. However, for those census blocks that had less than approximately less than one square kilometer in area, the average z0 value computed was based on a circular area one kilometer in diameter centered at the centroid of the census block. This was done to obtain a minimum fetch of approximately 500 meters for small census blocks. At the census tract level, z0 values were computed by weighting census block z0 values with building square footage as per equation 3.5. .. . n i Ti Ci t ci S Z Z S 1 * (3.5) where: Zt = Terrain roughness at the tract level Zci = Terrain roughness computed for census block i SCi = Total building square footage for census block i ST = Total building square footage for the census tract n = Number of Census blocks in the tract Weighting in this manner weights the census tract surface roughness towards those census blocks that have more buildings contained within them instead of simply taking an unweighted average of the census block surface roughnesses. 3-60 Chapter 3. Surface Roughness Modeling 4-1 Hazus-MH Technical Manual Chapter 4. Wind Loads 4.1 Introduction Background. Wind loads on buildings are usually estimated using either boundary layer wind tunnel tests performed for a specific building or using code-specified loads that have been developed by committees from boundary layer wind tunnel test data. If wind tunnel loads are used in the design of a building or its components, the wind loading coefficients are typically measured for 36 different wind directions, with the results combined with a statistical model of the wind climate for the location where the building is to be built. Using this approach, the design loads obtained for the building take into account the effect of the variation of the wind loads with the direction of the approaching wind, and how these variations in load with direction align with the directional characteristics of the wind. Essentially all low-rise buildings are designed using wind loads obtained from building codes. While the loading coefficients given in the codes have been developed using wind tunnel test data, the directional effects are not explicitly reproduced in North American building codes and standards. For simplicity, and ease of use, the loads given in building codes represent an estimate of the maximum load acting on a portion of the building. Different values of the loading coefficients are given in the codes for various zones on the roofs and walls. The selection of the number and size of these zones is a compromise between the true spatial variability of the maximum wind loads, and the use of as few zones as possible to simplify the design procedure. The greater the number of zones specified in a building code, the more accurate will be the final estimate of the distribution of the maximum loads acting on the building. The maximum values of the pressure coefficients given in the codes for each zone do not necessarily occur for winds approaching from the same wind direction, and therefore code-specified loads alone cannot be used to model wind loads on a building for wind approaching from a given direction. Designers are able to take advantage of the variation of the wind loads with wind direction in both the UK and Australia, if they chose to use the detailed design procedures given in their respective building codes. Approach. For predicting wind loads on buildings in the development of fast running damage and loss functions, it is necessary to model the variation in the wind loads acting on the building as a function of the location on the building and as a function of the direction and magnitude of the wind speed. Clearly, the best approach is to use the results from wind tunnel tests directly and combine these results with the simulated hurricane winds and directions to estimate the loads. Unfortunately, this approach is not viable since the detailed wind tunnel test data (if available) are limited by the number and locations of the pressure taps used in the models, the number of terrains in which the model buildings were tested, and the number of different geometries tested. Without the use of wind tunnel data, the next best method for developing wind loads as a function of 4-2 Chapter 4. Wind Loads direction is the development of an analytic or empirical model which is able to reasonably reproduce the variation of wind loads with direction, as well as the effects of aspect ration, terrain, etc. The Australian and UK wind loading provisions represent simple examples of such an approach. The methodology selected by the Hazus Wind Committee for developing damage and loss functions is to use code-specified loads as a the basis for the model. To treat wind directionality for roof loads, tabulated values of the pressure coefficients as a function of direction are estimated using wind tunnel data and the UK Building Code. In the case of wall loads, the pressure coefficients are modeled with cosine functions. Using this approach, the peak magnitudes of the loads correspond to the values specified in building code adopted “standards”. The pressure coefficients developed using this approach are discussed in the following sections, and the results of the empirical direction model are compared to measurements of loads acting on buildings determined from wind tunnel tests. The wind loads derived using the hybrid code/directional model are applied to a number of simply shaped buildings. The shapes of the buildings considered are all either square or rectangular in plan and have either flat, hip or gable shape roofs. 4.2 Wall Pressures – Low-Rise Buildings The magnitudes of the wall pressures used for modeling wind loads for the prediction of wind induced failures of components and cladding were derived considering the pressure coefficients given in North American wind loading standards and/or codes. The standards/codes considered in the development of the wind loads are ASCE-7-95, SBCCI (1998 Edition) and the 1995 edition of the National Building Code of Canada. In order to compare the magnitudes of the loading coefficients given in each standard/code, all coefficients were adjusted to be referenced to the mean hourly wind speed at roof height. In the case of both the NBCC and SBCCI pressure coefficients, the coefficients were divided by a value of 0.8 to remove the directionality factor that is explicitly included in the pressure coefficients given in the codes (Mehta, 1984). Additionally, in the case of the SBCCI coefficients, an internal pressure coefficient having a value of 0.2 was removed from the coefficients as given in the code before any comparisons were made. To convert the coefficients given in ASCE-7-95 from values which are normalized by the peak gust wind speed at roof height to the value which is normalized by the mean hourly wind speed, a gust factor of 1.57 was used. The gust factor (1.57) used for converting the mean hourly wind speed to a 3 second gust was derived from the ESDU (1982) gust factor models for open terrain conditions (z0 = 0.03 m) and a mean roof height of about 4 m. In the case of the SBCCI coefficients, which are referenced to the fastest mile wind speed at roof height, a gust factor of 1.27 was used in the change of the reference dynamic pressure to a mean hourly value. The 1.27 gust factor was also computed using the ESDU (1982) gust factor model assuming open terrain conditions at a height of 4 m and an averaging time of 32 seconds (i.e., 3600/110). Tables 4.1 through 4.4 show the comparison of the peak coefficients derived from the three sources for the edge and central regions of the walls (as shown in Figure 4.1) normalized by the mean hourly wind speed at the average roof height. 4-3 Hazus-MH Technical Manual Table 4.1. Comparison of Positive Wall Pressure Coefficients – Buildings with Roof Slopes Less than 10. Pressure Zone Pressure Coefficient NBCC SBCCI ASCE-7-95 NBCC SBCCI ASCE-7-95 e e 5 2.3 2.1 2.2 w w 4 2.3 2.1 2.2 Table 4.2. Comparison of Positive Wall Pressure Coefficients – Buildings with Roof Slopes Greater than 10. Pressure Zone Pressure Coefficient NBCC SBCCI ASCE-7-95 NBCC SBCCI ASCE-7-95 e e 5 2.3 2.3 2.5 w w 4 2.3 2.3 2.5 Table 4.3. Comparison of Negative Wall Pressure Coefficients – Buildings with Roof Slopes Less than 10. Pressure Zone Pressure Coefficient NBCC SBCCI ASCE-7-95 NBCC SBCCI ASCE-7-95 e e 5 -2.6 -2.5 -3.1 w w 4 -2.3 -2.1 -2.5 Table 4.4. Comparison of Negative Wall Pressure Coefficients – Buildings with Roof Slopes Greater than 10. Pressure Zone Pressure Coefficient NBCC SBCCI ASCE-7-95 NBCC SBCCI ASCE-7-95 e e 5 -2.6 -2.7 -3.5 w w 4 -2.3 -2.5 -2.7 Figure 4.1. Wall Pressure Zones as Defined in ASCE-7 (Left figure) and SBCCI and NBCC (Right figure). 4-4 Chapter 4. Wind Loads The coefficients given in the above tables represent the maximum (or minimum) values for design purposes and do not reflect the fact that the actual pressure coefficients vary as a function of wind direction. Effect of Wind Direction. In order to take into account the effect of wind direction, wind tunnel data obtained from various sources including Ho (1993), Stathopoulos (1978) and Lin and Surry (1997) were used to determine the variation of the pressure coefficients with wind direction. Tables 4.5 and 4.6 shows example positive and negative pressures acting on the walls of a rectangular building for wind directions in 30. increments. The locations where the pressure coefficients are computed are given in Figure 4.2. In the example given in Tables 4.5 and 4.6 the magnitudes of the maximum (or minimum) pressures are defined using the ASCE-7-95 values for the sloped roof case. Comparison of ASCE-7 Wall Pressures to Wind Tunnel Tests. Figures 4.3 and 4.4 show comparisons of wall pressures estimated using the ASCE-7 based model for roofs with slopes less than 10. to those obtained from boundary layer wind tunnel tests (Lin and Surry, 1997) in nominally open and suburban terrains. These plots compare pressure tap-by-pressure tap for a wind tunnel tested rectangular building, and show measured vs. ASCE-7 based-model pressure coefficients. The plot includes comparisons over the full azimuth range in 10. increments. The model building, tested at scales of 1:100 and 1:200 has an eave height of 30. and plan dimensions of 100..200.. The model was instrumented so that the full azimuthal range of data was available for 145 wall taps and 112 roof taps. In the comparisons given in Figures 4.3 and 4.4, the pressure coefficients are normalized by the mean hourly wind speed at roof height. Note that in the pressure modeling process, all pressure coefficients are based on the peak gust wind speed at roof height. The magnitudes of the coefficients, normalized by the mean wind speed at roof height, therefore increase with increasing surface roughness. The banding evident in Figures 4.3 and 4.4 arises primarily from the cosine functions used in the modeling of the code based pressures and suctions that limit the value a modeled pressure can have for any given wind direction, whereas the measured peak pressure data, while following a mean trend with azimuth, are scattered about the mean azimuthal trend curve. The agreement between the ASCE-7 based positive pressures and the measured positive pressures is reasonable. In the case of the negative pressures, there is significantly more scatter evident in the comparisons since the ASCE-7 loads for the negative pressures in Zone 4 (interior zone) have a minimum value of -2.1, whereas in reality, for long buildings, the minimum negative pressure will have a magnitude which is less than 2.1. 4.3 Roof Pressures – Low-Rise Buildings As in the case of the wall pressures, wind loads on the roofs of low-rise buildings used for the prediction of the failure of components and cladding were derived using North American based building codes and standards. As in the case of the wall pressures, comparisons of the roof pressures specified by ASCE-7, SBCCI and NBCC were 4-5 Hazus-MH Technical Manual Table 4.5. Positive Wall Pressure Coefficients Estimated for Building Shown in Figure 4.2 Given as a Function of Wind Direction Location Wind Direction (Clockwise from North) 0 30 60 90 120 150 180 210 240 270 300 330 1 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 2 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 3 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 4 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 5 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 6 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 7 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 8 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 9 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 10 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 11 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 12 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 13 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 14 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 15 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 16 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 17 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 18 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 19 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 20 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 21 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 22 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 23 0.1 1.2 2.2 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 24 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 25 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 26 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 27 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 28 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 29 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 30 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 31 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 32 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 33 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 34 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 35 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 36 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 37 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 38 2.5 2.2 1.2 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 39 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 40 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 41 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 42 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 43 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 44 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 45 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 46 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.2 2.5 2.2 1.2 4-6 Chapter 4. Wind Loads Table 4.6. Negative Wall Pressure Coefficients Estimated for Building Shown in Figure 4.2 Given as a Function of Wind Direction Location Wind Direction (Clockwise from North) 0 30 60 90 120 150 180 210 240 270 300 330 1 -.9 -.8 -.6 -1.1 -.8 -.3 -.4 -.2 -2.0 -3.5 -2.1 -2.1 2 -.7 -.6 -.5 -.9 -.6 -.2 -.3 -.2 -1.6 -2.7 -1.6 -1.3 3 -.7 -.6 -.5 -.9 -.6 -.2 -.3 -.2 -1.6 -2.7 -1.6 -1.0 4 -.7 -.6 -.5 -.9 -.6 -.2 -.3 -.3 -1.7 -2.7 -1.7 -.8 5 -.7 -.6 -.5 -.9 -.6 -.2 -.3 -.3 -1.7 -2.7 -1.7 -.7 6 -.7 -.6 -.5 -.9 -.6 -.2 -.3 -.4 -1.8 -2.7 -1.8 -.6 7 -.7 -.6 -.5 -.9 -.6 -.2 -.3 -.4 -1.8 -2.7 -1.8 -.6 8 -.7 -.6 -.5 -.9 -.6 -.2 -.3 -.5 -1.9 -2.7 -1.9 -.6 9 -.7 -.6 -1.8 -2.7 -1.8 -.4 -.3 -.2 -.6 -.9 -.5 -.6 10 -.7 -.6 -1.8 -2.7 -1.8 -.4 -.3 -.2 -.6 -.9 -.5 -.6 11 -.7 -.7 -1.7 -2.7 -1.7 -.3 -.3 -.2 -.6 -.9 -.5 -.6 12 -.7 -.8 -1.7 -2.7 -1.7 -.3 -.3 -.2 -.6 -.9 -.5 -.6 13 -.7 -1.0 -1.6 -2.7 -1.6 -.2 -.3 -.2 -.6 -.9 -.5 -.6 14 -.7 -1.3 -1.6 -2.7 -1.6 -.2 -.3 -.2 -.6 -.9 -.5 -.6 15 -.9 -2.1 -2.1 -3.5 -2.0 -.2 -.4 -.3 -.8 -1.1 -.6 -.8 16 -3.5 -2.0 -.2 -.4 -.3 -.8 -1.1 -.5 -.7 -.7 -.7 -2.0 17 -2.7 -1.6 -.2 -.3 -.2 -.6 -.9 -.4 -.5 -.6 -.5 -1.6 18 -2.7 -1.6 -.2 -.3 -.2 -.6 -.9 -.4 -.5 -.6 -.5 -1.6 19 -2.7 -1.7 -.3 -.3 -.2 -.6 -.9 -.4 -.5 -.6 -.5 -1.7 20 -.9 -.6 -.2 -.3 -.3 -1.6 -2.7 -1.6 -.5 -.6 -.5 -.4 21 -.9 -.6 -.2 -.3 -.2 -1.6 -2.7 -1.6 -.5 -.6 -.5 -.4 22 -.9 -.6 -.2 -.3 -.2 -1.5 -2.7 -1.5 -.5 -.6 -.5 -.4 23 -1.1 -.8 -.3 -.4 -.2 -2.0 -3.5 -2.0 -.7 -.7 -.7 -.5 24 -.4 -.3 -.8 -1.1 -.6 -.8 -.9 -2.1 -2.1 -3.5 -2.0 -.2 25 -.3 -.2 -.6 -.9 -.5 -.6 -.7 -1.3 -1.6 -2.7 -1.6 -.2 26 -.3 -.2 -.6 -.9 -.5 -.6 -.7 -1.0 -1.6 -2.7 -1.6 -.2 27 -.3 -.2 -.6 -.9 -.5 -.6 -.7 -.8 -1.7 -2.7 -1.7 -.3 28 -.3 -.2 -.6 -.9 -.5 -.6 -.7 -.7 -1.7 -2.7 -1.7 -.3 29 -.3 -.2 -.6 -.9 -.5 -.6 -.7 -.6 -1.8 -2.7 -1.8 -.4 30 -.3 -.2 -.6 -.9 -.5 -.6 -.7 -.6 -1.8 -2.7 -1.8 -.4 31 -.3 -.2 -.6 -.9 -.5 -.6 -.7 -.6 -1.9 -2.7 -1.9 -.5 32 -.3 -.4 -1.8 -2.7 -1.8 -.6 -.7 -.6 -.5 -.9 -.6 -.2 33 -.3 -.4 -1.8 -2.7 -1.8 -.6 -.7 -.6 -.5 -.9 -.6 -.2 34 -.3 -.3 -1.7 -2.7 -1.7 -.7 -.7 -.6 -.5 -.9 -.6 -.2 35 -.3 -.3 -1.7 -2.7 -1.7 -.8 -.7 -.6 -.5 -.9 -.6 -.2 36 -.3 -.2 -1.6 -2.7 -1.6 -1.0 -.7 -.6 -.5 -.9 -.6 -.2 37 -.3 -.2 -1.6 -2.7 -1.6 -1.3 -.7 -.6 -.5 -.9 -.6 -.2 38 -.4 -.2 -2.0 -3.5 -2.1 -2.1 -.9 -.8 -.6 -1.1 -.8 -.3 39 -3.5 -2.0 -.7 -.7 -.7 -.5 -1.1 -.8 -.3 -.4 -.2 -2.0 40 -2.7 -1.6 -.5 -.6 -.5 -.4 -.9 -.6 -.2 -.3 -.2 -1.6 41 -2.7 -1.6 -.5 -.6 -.5 -.4 -.9 -.6 -.2 -.3 -.2 -1.6 42 -2.7 -1.7 -.5 -.6 -.5 -.4 -.9 -.6 -.2 -.3 -.3 -1.7 43 -.9 -.4 -.5 -.6 -.5 -1.6 -2.7 -1.6 -.3 -.3 -.2 -.6 44 -.9 -.4 -.5 -.6 -.5 -1.6 -2.7 -1.6 -.2 -.3 -.2 -.6 45 -.9 -.4 -.5 -.6 -.5 -1.5 -2.7 -1.5 -.2 -.3 -.2 -.6 46 -1.1 -.5 -.7 -.7 -.7 -2.0 -3.5 -2.0 -.2 -.4 -.3 -.8 4-7 Hazus-MH Technical Manual Figure 4.2. Locations of Pressure Estimates on Rectangular Building as Presented in Tables 4.5 and 4.6 (Plan View). performed with the coefficients referenced to the mean hourly wind speed at the mean roof height. Tables 4.7 through 4.9 present comparisons of the various coefficients. Again, as in the case of wall pressures, the effect of the directionality factor has been removed from the coefficients given in the SBCCI Code and the NBCC. The pressure zones associated with each of the codes and standards are given in Figure 4.5. Comparisons of the peak coefficients prescribed in each of the above noted standards to those produced by Meecham (1988), shown in Figure 4.3, suggest that the coefficients prescribed in ASCE-7 are generally too high along the roof ridge and eaves, whereas those prescribed by the NBCC and the SBCCI tend to be low along the roof edge and eaves. All of the above noted codes/standards appear to underestimate the wind-induced loads at the ridge/gable end corner, and this underestimation of the loads in this region is also supported in the pressure coefficient data given in Case (1996). A comparison of the SBCCI loads and the ASCE loads for hip and gable roofs suggests that the average of the two sets of pressure coefficients would yield results that most closely reproduce those obtained from the wind tunnel (except at the gable ridge). For the estimation of wind loads and resulting damage, both the SBCCI loads and the ASCE loads are investigated in the damage/loss studies. Effect of Wind Direction. The effect of wind direction on the estimated pressure coefficients on the roofs of low-rise buildings was determined independently of the building code/standard information using the results of wind tunnel test data given in Stathopolous (1978); Meecham (1988); Ho (1993); Vickery (1984); Surry and Davenport and Mikituk (1993). This wind tunnel information was supplemented by the directional pressure coefficient data given in the United Kingdom Building Code, CP3. 4-8 Chapter 4. Wind Loads Rectangular Building - Open Terrain -ASCE-7 Based Negative Pressures y = 0.9204x R2 = 0.4883 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 Measured Peak Pressures Modeled Peak Pressures Rectangular Building - Open Terrain - ASCE-7 Based Positive Pressures y = 0.9906x R2 = 0.8999 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Measured Peak Pressures Modeled Peak Pressures Figure 4.3. Comparison of Measured and Modeled Wall Pressure Coefficients on a Flat Roof Building in Open Terrain (z0 = 0.1 m). 4-9 Hazus-MH Technical Manual Rectangular Building - Suburban Terrain - ASCE-7 Based Positive Pressures y = 0.9812x R2 = 0.896 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Measured Peak Pressures Modeled Peak Pressures Rectangular Building - Suburban Terrain -ASCE-7 Based Negative Pressures y = 0.9645x R2 = 0.4472 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 Measured Peak Pressures Modeled Peak Pressures Figure 4.4. Comparison of Measured and Modeled Wall Pressure Coefficients on a Flat Roof Building in Suburban Terrain (z0 = 0.3 m). 4-10 Chapter 4. Wind Loads Table 4.7. Comparison of Negative Pressure Coefficients on Flat Roofs Pressure Zone Pressure Coefficient NBCC SBCCI ASCE-7-95 NBCC SBCCI ASCE-7-95 c c 3 6.8 5.6 6.9 s si 2 3.1 3.1 4.5 r re 1 2.3 2.3 2.5 Table 4.8. Comparison of Negative Pressure Coefficients on Gable Roofs Pressure Zone Pressure Coefficient NBCC SBCCI ASCE-7-95 NBCC SBCCI ASCE-7-95 c c 3 5.1 5.2 5.2 s si 2 2.5 2.5 5.2 s’ se 2 3.9 4.0 5.2 r re 1 2.0 2.1 2.1 Table 4.9. Comparison of Negative Pressure Coefficients on Hip Roofs Pressure Zone Pressure Coefficient NBCC SBCCI ASCE-7-95 NBCC SBCCI ASCE-7-95 c c 3 5.1 5.2 5.2 s si 2 2.5 2.5 5.2 s’ se 2 2.5 4.0 5.2 r re 1 2.0 2.1 2.1 In the development of the wind loads as a function of direction, a zone-based approach was used for the hip and gable roofs using the data noted above. In the case of the gable roof, the zones are based on those given in the SBCCI where, because more zones exist here than in either the ASCE-7 provisions or the NBCCI provisions, the effect of wind directionality can be better modeled. For example, the largest loads on eave zone occur when the wind is blowing perpendicular to the eave or ridge), whereas the largest loads in the corner zones tend to occur when the wind is approaching from an oblique angle, and the largest loads in the center of the gable end occur when the wind is approaching in a direction which is approximately parallel to the ridge line. In the case of the hip roof buildings, the zones (or sub-zones) used to incorporate the effect of directionality are based primarily on the UK wind loading code, CP3 as shown in Figure 4.7. Effect of Terrain. A key assumption in the use of pressure coefficients for estimating wind loads, is that the pressure coefficients, normalized with respect to the peak gust wind speed at roof height, do not change with changes in the flow characteristics (e.g., turbulence intensity). This assumption is important because most pressure coefficient data derived from wind tunnel tests given in the literature are presented as coefficients normalized by the mean wind speed at roof height. To adjust these coefficients referenced 4-11 Hazus-MH Technical Manual Figure 4.5. Zones used for Defining Pressure Coefficients for Gable and Hip Roofs for the SBCCI (Top Drawings), the NBCC (Middle Drawings) and ASCE-7-95 (Bottom Drawings). 4-12 Chapter 4. Wind Loads Figure 4.6. Peak Pressure Coefficients on Hip and Gable on Hip and Gable Roofs in Open Terrain (taken from Meecham, 1988). to the mean wind speed to coefficients referenced to the peak gust speed, information on the flow characteristics used in the wind tunnel tests must be known. If the key flow parameters needed to convert the reference wind speed from mean hourly to peak gust are known (i.e., mean velocity and longitudinal turbulence intensity profiles), then the wind tunnel pressure coefficient data referenced to the mean dynamic pressure can be readily converted to a coefficient normalized to the peak gust velocity pressure. In instances when wind tunnel tests have been performed on the same building in different terrain conditions (e.g., typical open terrain and typical suburban terrain), one would expect the pressure coefficients normalized by the peak gust velocity pressure at roof height to collapse to the same value. 4-13 Hazus-MH Technical Manual Figure 4.7. Pressure Coefficient Zones Used in the UK Wind Loading Code for Hip Roof Buildings. Using wind tunnel data given in Monroe (1996), Ho (1992), Meecham(1988), Case (1996), Stathopolous (1978), and Lin and Surry (1997), all of which present roof pressure coefficients normalized by the mean dynamic pressure at roof height for more than one terrain condition, the coefficients were adjusted to be to be normalized with respect to the peak gust velocity pressure at roof height. The degree to which the pressure coefficients normalized by the local gust velocity pressure (at mean roof height) collapsed to yield the same negative pressure coefficient varied from study to study and building to building. In general, it was found that the peak gust pressure coefficients in the rougher terrain (normalized to the local gust velocity pressure) were higher than those at the same location in the smoother terrain. For example, Monroe (1996) measured roof suctions on a model building with a 1:12 roof slope having an eave height of 4.9 m (full scale) in flow conditions having turbulence intensities at roof height of 12.5% and 19%. On average, the peak roof suction coefficients (normalized with respect to the mean velocity pressure at roof height) obtained in the rougher flow conditions were 75% higher than those obtained in the smoother flow conditions. By normalizing the pressures by the peak gust velocity pressure at roof height (defined as the mean wind speed plus three standard deviations of the fluctuating wind speed), the difference reduces so that the pressure coefficients in the rougher terrain are about 35% higher than those obtained in the smooth terrain. These higher coefficients suggest that using the peak gust velocity pressure to normalize the pressure coefficients is not sufficient to explain the differences in the measured pressure coefficients associated with changes in the flow characteristics. 4-14 Chapter 4. Wind Loads In the case of Ho (1992), the negative pressures in the suburban terrain case do not collapse to a constant value, with the peak suction coefficients referenced to the peak gust velocity pressure being higher in suburban terrain than in open terrain. For example, converting a roof corner pressure in suburban terrain to be referenced to the peak gust velocity pressure yields a coefficient which is 15% higher than the open country value referenced to the local peak gust velocity pressure. Similar observations were made using the Lin and Surry pressure data, the Case (1996) pressure data and a large portion of the Stathopolous (1978) data. The observation that the pressure coefficients in the rougher terrains, even when normalized with respect to the local peak gust wind, are larger (in magnitude) than those in open terrain is apparently recognized in ASCE-7-95 where the wind loads on buildings in suburban terrain (Exposure B) are limited to be no less than 85% of the value that would be computed if the building were in open terrain. To take into account this apparent increase in the peak pressure coefficients, the basic pressure coefficient referenced to the peak gust wind speed is increased by a factor equal to the square root of the ratio of the turbulence intensity at roof height in the local terrain to the turbulence at roof height in the reference open terrain. This empirical adjustment in the pressure coefficients helps collapse the pressure coefficient data noted above, but is clearly a subject requiring more research. The use of this factor does yield estimates of pressures in low buildings in a standard suburban terrain (z0 = 0.3 m) which are much closer to those required by ASCE-7 than if the adjustment were not made. As an illustration of the effect of the turbulence intensity, consider the following example of a building located in suburban terrain having a mean roof height of 5 m. Using the ESDU representation of the gust velocity profile, the ratio of the 5 m gust wind speed in suburban terrain to the 5 m gust wind speed in open terrain is 0.787, implying a wind load equal to 62% of the open terrain wind load. The roof height turbulence intensities in the open and suburban terrains (from ESDU, 1992) are 18% and 29%, respectively, resulting in a 27% increase in the pressure coefficient (i.e., 100 0.29/ 0.18 ). The net effect of the reduction in the peak gust velocity combined with the increase in the pressure coefficient associated with the turbulence intensity adjustment is a wind load equal to 79% of the open terrain wind load, which is comparable to the 85% factor given in ASCE-7-98. Comparison of ASCE-7 Roof Pressure Loads to Wind Tunnel Tests. Figure 4.8 shows a comparison of the ASCE-7 based roof pressure loads to those obtained from wind tunnel tests for a relatively open terrain case and a suburban terrain case. Note that the surface roughness associated with the nominal open terrain case is described by a z0 value of 0.1 m, which is larger than the value of about 0.03 m which is typically associated with open terrain conditions. The suburban terrain case is characterized by a roughness length of about 0.30 m. The modeled pressures (based on the ASCE-7 loads) presented in Figure 4.8 were produced using the actual values of z0 as derived from the wind tunnel tests. 4-15 Hazus-MH Technical Manual Rectangular Building - Suburban Terrain - ASCE-7 Based Pressures y = 0.9877x + 0.3772 R2 = 0.7365 -12 -10 -8 -6 -4 -2 0 -12 -10 -8 -6 -4 -2 0 Measured Peak Pressures Modeled Peak Pressures Rectangular Building - Open Terrain ASCE-7 Based Pressures y = 1.0536x + 0.1374 R2 = 0.7025 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -10 -8 -6 -4 -2 0 Measured Peak Pressure Coefficient Modeled Pressure Coefficient Figure 4.8. Comparison of Modeled and Measured Peak Roof Pressure Coefficients on a Flat Roof Low-Rise Building. 4-16 Chapter 4. Wind Loads The comparisons of the modeled and measured wind loads suggests that the ASCE-7 based loads with the directional models and the empirical turbulence intensity adjustment factors reproduce the wind tunnel results reasonably well. Summary. A directional pressure coefficient model has been developed using code based loads to define the maximum pressure coefficients. The roof slopes considered are in the range of 3:12 to 5:12. The effect of directionality is taken into account using available wind tunnel data, scaled (or truncated) to ensure the maximum values of the pressures are equivalent to the code specified values. The reduction in the roof loads associated with decreased wind speeds caused by increasing surface roughness is lessened through the use of a turbulence intensity adjustment factor, which yields a final reduction in wind loads comparable to that specified in ASCE-7-95. 4.4 Wind Loads on Low-Rise Buildings – Effect of Nearby Buildings The preceding discussion of wind loads on the roofs and walls of low-rise buildings was applicable to isolated structures located within a homogeneous open or suburban terrain. In the case of real buildings situated in real environments surrounded by buildings of like size, on average there is a reduction in the loads experienced by these buildings. The reduction in load is clearly a function of both the spacing and size of the near by buildings as indicated in Holmes (1994). Comprehensive wind tunnel test data showing the effects of nearby buildings on the wind loads experienced by the test building is limited. The wind tunnel test results given in Ho (1992) are probably the most widely quoted results. In Ho (1992), low-rise, flat roofed buildings were tested in both open and suburban terrain conditions with and without the existence of nearby buildings. For the cases where nearby buildings were in place, a total of 16 different representations of surrounding buildings were modeled. The results of the Ho (1992) study indicate that the average reduction in the wind loads on the roofs is about 25% compared to the isolated building case, although the amount of the reduction varied with the location on the roof. The coefficient of variation of the reduction in wind loads was about 20%, but this value also varied with location on the roof. The reduction in the wind loads on the walls of the test building was shown to be somewhat lower, ranging between about a minimum of a 10% reduction up to a maximum of a 25% reduction in load. The coefficient of variation was about 20%. Ho made no attempt so separately examine the effects of nearby buildings on the positive and negative pressures. In Case (1996), models of a gable roof building with a 4:12 roof slope were tested as isolated buildings and then tested for three different representations of the building surrounded by other buildings. Case found that the reduction in the negative roof and wall loads was similar to that found by Ho (1999) (i.e., a 25% reduction), but found no mean reduction in the peak positive wall pressures. Case found that the positive roof pressures actually increased in the presence of nearby buildings. In the simulation of wind loads on low-rise buildings for the prediction of damage and loss, the effects of nearby buildings are taken into account by reducing the peak negative pressures by a mean value of 25%. No decrease in the positive wall pressures is taken. 4-17 Hazus-MH Technical Manual 4.5 Integrated (Overall) Wind Loads on Low-Rise Buildings The prime thrust of this effort with respect to wind-induced damage and loss estimation is directed towards the prediction of damage to the relatively small building envelope components. Overall (large area) loads are important for the prediction of overturning and uplifting of manufactured homes, whole roof failures on residential and small commercial buildings, and failures of structural systems such as those that exist in metal buildings, roof systems, etc. The estimates of the overall loads must take into account the fact that the peak pressures which act on the exterior of buildings and other structures are not fully correlated, and as the area over which the pressures are averaged increases, the effective loading coefficient decreases. This relationship of decreasing loading coefficient with increasing area is reflected in the pressure coefficients given in wind loading codes and standards such as the SBCCI and ASCE-7, but not in the main wind force resisting calculations as defined in ASCE-7-95. The reduction in the effective pressures given in these codes/standards are based on limited wind tunnel test data. In the development of the overall loading model, a model for the prediction of the mean exterior pressures was developed using the code based wind loading model developed for components and cladding as described earlier. This mean pressure model did not exist prior to the development of the overall load model as the loading and damage models were directed towards envelope component loads and failures only. To estimate overall loads for the prediction of overturning moments, uplift forces, etc., the modeled local pressures described earlier for the hip and gable roof buildings were integrated over the area of interest with the lack of correlation taken into account using a correlation coefficient approach similar to that originally developed by Davenport (1961). The major differences between the approach developed by Davenport and the approach used herein are: (1) Davenport properly uses the mean and standard deviations of the fluctuating pressures, whereas the present approach uses the mean and peak values (since these are estimated using the empirical pressure model) and (2) Davenport’s approach was developed for line-like structures, whereas the present methodology is applied to three dimensional structures. To estimate the peak integrated loads acting on a structure the pressures are integrated using: 1 2 2 2 1 / A j i p j p i dA dA ) / r exp( Cˆ I Cˆ I V Rˆ j i .. . .. . . . .. .. . (4.1) where Rˆ is a peak force, moment or structural action, i p Cˆ is the peak pressure coefficient (minus the mean value) at location i, Ii is an influence coefficient converting the pressure at location i to a global force, .r is the distance between locations i and j, and . is a length scale which can be considered a measure of the extent over which the fluctuating pressures are correlated. In the modeling approach used for negative pressures here, the length scale decreases with increasing magnitude of the negative pressures (i.e., the very high local negative pressures are correlated over relatively small areas), and the basic value of . is a function of the building height. 4-18 Chapter 4. Wind Loads Roof Uplift Loads. Using the integration methodology described above, the code based component and cladding loads were integrated over the roof surface of a hip roof and gable roof residence. The roof slopes in both cases are 4:12, the plan dimensions of the buildings are 30..60. and the eave height is 9.. As indicated in Figure 4.9, predictions of integrated loads for uplift have been compared to the results of Meecham (1988) for the uplift loads on hip and gable roofs with 4:12 roof slopes. Comparisons the uplift load estimates to those obtained from Figure 6-3 of ASCE-7-95 are also given in Figure 4.9. Hip Roof 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 10 20 30 40 50 60 70 80 90 Wind Direction Uplift Coefficient Model Meecham ASCE-7-95 Gable Roof 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 10 20 30 40 50 60 70 80 90 Wind Direction Uplift Coefficient ASCE-7-95 Model Meecham Figure 4.9. Comparisons of Modeled (Integrated) Uplift Loads on Hip and Gable Roofs to those Obtained from Wind Tunnel Experiments. Uplift Coefficients are Defined with Respect to the Mean Dynamic Pressure at Roof Height. The comparisons of the total uplift forces given in Figure 4.9 indicate that the modeled uplift loads are in general agreement with the results given in Meecham (1988), although the variation of the uplift coefficients with wind direction is less evident in the model results. 4-19 Hazus-MH Technical Manual ASCE-7 allows for the computation of overall uplift for gable and flat roofs using Figure 6-3 of the standard. The methodology allows for computation of the uplift loads for wind approaching normal to the roof ridge and parallel to the roof ridge only. The uplift loads computed for these two directions are shown in Figure 4.9, where it is seen that for winds approaching normal to the roof ridge, the ASCE-7 uplift loads obtained from Figure 6-3 of ASCE-7 agree well with the uplift loads computed by integrating the component and cladding loads discussed earlier. In the case of the hip roof, the ASCE-7 uplift loads presented in Figure 4.9 are the same as the gable values since ASCE-7 does not provide a means to compute uplift loads on roof shapes that are hip shaped. For winds approaching parallel to the roof ridge (90. as shown in Figure 4.9) the ASCE-7 uplift values are lower than either the Meecham data or the integrated uplift data. For the prediction of roof uplift failure, the integrated loading approach is used since the methodology is based on code type loads, it produces values of uplift (for the 0. case) that are very similar to those predicted using ASCE-7. The approach allows the effect of directionality (however small in this case) to be incorporated in the damage model, consistent with the approach used throughout model development. Integrated Roof and Wall Loads on Low-Rise Buildings with Flat Roofs. In order to further validate the pressure integration loading model, comparisons were made with integrated loads obtained directly from wind tunnel tests. The integrated wind tunnel loads were obtained by integrating the time series of wind induced pressures obtained from the wind tunnel tests of the 100. by 200. buildings described in Section 4.3. The individual measured pressures acting on the roof were integrated over a number of different areas as indicated in Figure 4.10. Note that in the case of the integrated wall loads, panels 1, 2 and 3 are located on the back side of the building, but are shown in Figure 4.10 as being on the front side for clarity. Comparisons of the modeled and measured force coefficients for the wall and roof sections are given in Figures 4.11 through 4.13. All force coefficients are expressed as the total wind induced force acting on the element divided by the mean dynamic pressure at roof height times the area of the element. The model results are seen to agree reasonably well with the measured results, reproducing both the reduction in the force coefficient with increasing area, and the directional characteristics of the loads. Overall Loads on Manufactured Homes. Using Equation 4.1, the code based roof and wall loads were integrated over the surface of a manufactured home in order to evaluate the effectiveness of the approach in estimating the lift, drag and overturning moments on manufactured homes. The results of the integration are compared to the full scale measurements described in Marshall (1977) as well as Roy (1983) and the estimates of lift, drag and overturning obtained from ASCE-7. Figure 4.14 presents the comparisons of lift, drag and overturning coefficients. 4-20 Chapter 4. Wind Loads Figure 4.10. Integration Areas Used for Comparison of Overall Roof and Wall Loads. 1/2 Wall (Panels 1, 2 and 3) -3 -2 -1 0 1 2 3 0 90 180 270 360 Wind Direction Wall Force Coefficient Measured Modeled 1/3 Wall (Panels 1 and 2) -3 -2 -1 0 1 2 3 0 90 180 270 360 Wind Direction Wall Force Coefficient Measured Modeled 1/6 Wall (Panel A) -3 -2 -1 0 1 2 3 4 0 90 180 270 360 Wind Direction Wall Force Coefficient Measured Modeled Figure 4.11. Comparison of Modeled and Measured Wall Forces on Rectangular Building in Suburban Terrain. 4-21 Hazus-MH Technical Manual 1/4 Roof Area (Panels A, B and C) 0 0.5 1 1.5 2 2.5 3 0 90 180 270 360 Wind Direction Uplift Coefficient Measured Modeled 1/6 Roof Area (Panels A and B) 0 0.5 1 1.5 2 2.5 3 0 90 180 270 360 Wind Direction Uplift Coefficient Measured Modeled 1/12 Roof Area (Panel A) 0 0.5 1 1.5 2 2.5 3 0 90 180 270 360 Wind Direction Uplift Coefficient Measured Modeled Figure 4.12. Comparison of Modeled and Observed Measured Uplift Coefficients on a Rectangular Building in Open Terrain. Roof Areas Indicated on the Graphs are Shown in Figure 4.10. 1/2 Roof Area (Panels A, B, C, D, E and F) 0 0.5 1 1.5 2 2.5 3 0 90 180 270 360 Wind Direction Uplift Coefficient Measured Modeled 1/3 Roof Area (Panels A, B, D and E) 0 0.5 1 1.5 2 2.5 3 0 90 180 270 360 Wind Direction Uplift Coefficient Measured Modeled 1/6 Roof Area (Panels A and D) 0 0.5 1 1.5 2 2.5 3 0 90 180 270 360 Wind Direction Uplift Coefficient Measured Modeled Figure 4.13. Comparison of Modeled and Observed Measured Uplift Coefficients on a Rectangular Building in Suburban Terrain. Roof Areas Indicated on the Graphs are Shown in Figure 4.11. 4-22 Chapter 4. Wind Loads 0 0.5 1 1.5 2 2.5 3 3.5 0 10 20 30 40 50 60 70 80 90 Wind Direction Drag Coefficient Model - Drag Full Scale Drag (No Skirt) Wind Tunnel Drag Full Scale Drag - With Skirt ASCE_7 0 0.5 1 1.5 2 2.5 3 3.5 0 10 20 30 40 50 60 70 80 90 Wind Direction Lift Coefficient Model - Lift Lift - Wind Tunnel - No Skirt Lift - Full Scale - No Skirt Lift - Full Scale Average ASCE-7 0 2 4 6 8 10 12 0 10 20 30 40 50 60 70 80 90 Wind Direction Moment Coefficient Model - Moment Wind Tunnel - Moment ASCE-7 Figure 4.14. Comparison of Modeled, Wind Tunnel Measured, Full Scale Measured and ASCE-7 Estimated Drag, Lift and Moment Coefficients on a Manufactured Home. The results given in Figure 4.14 show the modeled load estimates to be in general agreement with the limited full scale lift and drag data, as well as the wind tunnel measured lift and moment data. The drag and moment coefficients for the zero wind direction case (winds approaching the long side of a manufactured home) obtained from the model are about 20% to 30% lower than the values estimated using ASCE-7. For use in damage prediction, the modeled lift and drag forces are increased by 10% for all wind directions examined, yielding loading estimates that have maxima closer to the values 4-23 Hazus-MH Technical Manual produced by ASCE-7 than indicated in Figure 4.14, but limiting the overestimate of the loads as compared to the bulk of the full scale and model scale data. This approach retains a reasonable representation of the effect of wind direction on the loads and strikes a balance between the ASCE-7-98 loads obtained using Figure 6-3 in the standard and the loads obtained from full scale and wind tunnel experiments. Wind Loads on Long Span Roof Elements. To compute the wind induced uplift loads and bending moments acting on long span roof elements (such as trusses, open web steel joists, pre-cast concrete Tees, etc.) an influence line approach is used. Using this methodology, influence functions describing a specific structural action associated with the application of a load at a given point on the member, are used in conjunction with Equation 4.1 to produce estimates of the wind loads acting on the structural element. The influence function methodology was evaluated through comparisons of modeled and measured uplift coefficients for simply supported joists used as the primary roof system in a low-rise school building. The uplift loads at the joist supports were determined from wind tunnel tests performed at the University of Western Ontario using a 1:100 scale model of the building. Details of the wind tunnel tests and results are given in Young and Vickery (1994). Figures 4.15 and 4.16 show photographs of the model in the wind tunnel. Figure 4.15. Close-up View of Model of School Building Used in Wind Tunnel Tests. 4-24 Chapter 4. Wind Loads Figure 4.16. View of Model in Wind Tunnel Showing Upstream Terrain. The roof system of the structure is comprised of open web steel joists (OWSJ) spanning the school in the North-South direction. Three trusses are used in the complete span, each supported by a masonry wall. The two longest OWSJs, spanning the classrooms (span of 25.) are supported by the outer walls and the inner hall way walls, while one shorter OWSJ truss spans the hallway. The joist layout is shown in Figure 4.17. Figure 4.17. Layout of OWSJs as Modeled in Wind Tunnel Tests. The location of the supports as modeled in the wind tunnel are shown in Figure 4.18, and Figure 4.19 shows the locations of all pressure taps used in the modeling. Comparing the layout of pressure taps to the locations of the computed up-lift points, it is evident that a total of four pressure taps are positioned along each main joist. The pressures measured at the locations of the four individual pressure taps located along the line of each main joist were combined instantaneously with pre-computed influence coefficients to obtain estimates of the uplift loads acting at the ends of each OWSJ. The uplift loads were computed for winds approaching the building for the full 360. azimuth range at intervals of 10.. 4-25 Hazus-MH Technical Manual Figure 4.18. Plan View of School Showing Location of Truss Uplift Loads (North is towards top of page). Figure 4.19. Plan View of School Showing Location of all Pressure Taps Used in the Wind Tunnel Tests (North is towards top of page). To validate the model used to estimate OWSJ loads, comparisons of modeled and measured uplift loads were made for the uplift reactions at the points designated by the numbers 2007 through 2016, and 2101 through 2112. The measured uplift loads are compared to the modeled uplift (or reaction) loads in coefficient form, where both the wind tunnel and modeled coefficients are presented in the form: U L C R H R 2 2 1 . . (4.5-2) where L is the length (or span) of the joist, R is the uplift load per unit width, . is the density of air and UH is the mean wind speed at roof height. Figure 4.20 shows comparisons of the simulated and measured uplift coefficients as a function of wind direction for a total of 11 joists (22 reactions). 4-26 Chapter 4. Wind Loads 2008 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2007 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2012 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2011 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2009 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2010 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient Figure 4.20. Comparison of Wind Tunnel Measured (open squares) and Simulated (solid squares) Joist Uplift Coefficients as a Function of Wind Direction. As indicated in the comparisons between modeled and measured uplift coefficients, the agreement between the two data sets is generally quite good, particularly for OWSJs located on the north side of the building, away from the corners. The model tends to overestimate the maximum uplift loads acting on the OWSJs located on the south side of the building (denoted as 2012, 2016, 2104, 2108 and 2112) by as much as 30% (see location 2012) but this overestimate varies from joist to joist, and considering the geometry of the building, it is expected that the peak loads experienced by these joists would be nominally the same suggesting that some of the differences can be attributed to experimental variability. In the case of the OWSJs located on the north side of the building, the agreement between the measured and modeled uplift coefficients is better than for those located on the south side of the building, with the model both slightly overestimating and underestimating the magnitudes of the peak uplift coefficients at the locations of the individual joists. 4-27 Hazus-MH Technical Manual 2015 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2016 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 90 180 270 360 Wind Direction Uplift Coefficient 2102 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2101 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2014 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2013 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2104 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2103 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient Figure 4.20. Comparison of Wind Tunnel Measured (open squares) and Simulated (solid squares) Joist Uplift Coefficients as a Function of Wind Direction (continued). The overestimate of the wind uplift loads for joists located on the south side of the building is thought to be a result of the low buildings located to the south of the building as indicated in Figure 4.12 interfering with the flow. The net reduction in wind loads produced by these upstream buildings is consistent with the load reduction factor applied to buildings located in “real” environments as described earlier in Section 4.3. 4-28 Chapter 4. Wind Loads 2110 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2109 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2108 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2107 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2106 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2105 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient 2112 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 0 90 180 270 360 Wind Direction Uplift Coefficient 2111 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 90 180 270 360 Wind Direction Uplift Coefficient Figure 4.20. Comparison of Wind Tunnel Measured (open squares) and Simulated (solid squares) Joist Uplift Coefficients as a Function of Wind Direction (concluded). 4.6 Wind Loads on High-Rise Buildings In the case of high-rise buildings, overall structural loads are not modeled. Wind induced damage to high-rise buildings is modeled as being associated with wind induced failure of components (i.e., windows) and damage to windows caused by windborne debris. The maximum magnitudes of the directionally dependent exterior cladding pressure load 4-29 Hazus-MH Technical Manual model are set equal to the peak values given in ASCE-7-02, and information on directionality was derived using data given in Djakovich (1985) and the 1995 Version of the British Wind Loading Standard, CP3. Example directional plots of modeled wind induced pressures and suctions have been developed for a rectangular building and a square building. The rectangular building has a length of 100. and a width of 40.. The square building has a width of 40.. The exterior pressures are given along a ring around the building spaced a 5. apart, with the first location positioned 2.5. from the edge. Figures 4.21 and 4.22 indicate the locations on the model buildings for which the pressure coefficients apply. Figure 4.21. Location of Pressures Points for 2.5:1 High-Rise Building. Figure 4.22. Location of Pressures Points for 1:1 High-Rise Building. 4-30 Chapter 4. Wind Loads Plots of the pressure coefficients as a function of wind direction are given in Figures 4.23 and 4.24 for the buildings having length to width ratios of 2.5:1 (rectangular) and 1:1 (square), respectively. Note that in the case of the building having an aspect ratio of 2.5:1, locations on the short face experience large peak negative pressures for winds approaching from both 0. and 180., reflecting the fact that the flow does not reattach to the short wall. In the case of winds approaching perpendicular to the short wall, the peak negative pressures on the long wall occur for one direction only, owing to the fact that the flow reattaches to the long wall. 4-31 Hazus-MH Technical Manual Wall Location = 1 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 2 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 3 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =4 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 5 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 6 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 7 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =8 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Figure 4.23. Maximum and Minimum Pressure Coefficients vs. Wind Direction Used in Modeling of a Rectangular High-Rise Building Having a Length to Width Ratio of 2.5. 4-32 Chapter 4. Wind Loads Wall Location =9 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 10 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 11 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =12 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =13 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 14 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 15 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =16 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Figure 4.23. Maximum and Minimum Pressure Coefficients vs. Wind Direction Used in Modeling of a Rectangular High-Rise Building Having a Length to Width Ratio of 2.5 (continued). 4-33 Hazus-MH Technical Manual Wall Location =17 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 18 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 19 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =20 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =21 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 22 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 23 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =24 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Figure 4.23. Maximum and Minimum Pressure Coefficients vs. Wind Direction Used in Modeling of a Rectangular High-Rise Building Having a Length to Width Ratio of 2.5 (continued). 4-34 Chapter 4. Wind Loads Wall Location =29 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 30 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 31 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =32 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =25 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 26 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 27 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =28 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Figure 4.23. Maximum and Minimum Pressure Coefficients vs. Wind Direction Used in Modeling of a Rectangular High-Rise Building Having a Length to width Ratio of 2.5 (continued). 4-35 Hazus-MH Technical Manual Wall Location =33 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 34 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 35 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =36 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =37 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 38 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 39 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =40 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Figure 4.23. Maximum and Minimum Pressure Coefficients vs. Wind Direction Used in Modeling of a Rectangular High-Rise Building Having a Length to Width Ratio of 2.5 (continued). 4-36 Chapter 4. Wind Loads Wall Location =41 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 42 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 43 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 44 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =45 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 46 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =47 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =48 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Figure 4.23. Maximum and Minimum Pressure Coefficients vs. Wind Direction Used in Modeling of a Rectangular High-Rise Building Having a Length to Width Ratio of 2.5 (continued). 4-37 Hazus-MH Technical Manual Wall Location =49 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 50 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 51 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 52 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =53 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 54 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 55 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =56 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Figure 4.23. Maximum and Minimum Pressure Coefficients vs. Wind Direction Used in Modeling of a Rectangular High-Rise Building Having a Length to Width Ratio of 2.5 (concluded). 4-38 Chapter 4. Wind Loads Wall Location = 1 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 2 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 3 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =4 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 5 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 6 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 7 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =8 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Figure 4.24. Maximum and Minimum Pressure Coefficients vs. Wind Direction Used in Modeling of a Square High-Rise Building. 4-39 Hazus-MH Technical Manual Wall Location =9 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 10 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 11 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =12 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =13 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 14 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 15 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =16 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Figure 4.24. Maximum and Minimum Pressure Coefficients vs. Wind Direction Used in Modeling of a Square High-Rise Building (continued). 4-40 Chapter 4. Wind Loads Wall Location =17 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 18 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 19 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =20 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =21 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 22 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 23 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =24 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Figure 4.24. Maximum and Minimum Pressure Coefficients vs. Wind Direction Use d in Modeling of a Square High-Rise Building (continued). 4-41 Hazus-MH Technical Manual Wall Location =25 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 26 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 27 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =28 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =29 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 30 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location = 31 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Wall Location =32 -2 -1.5 -1 -0.5 0 0.5 1 0 90 180 270 360 Wind Direction (Degrees) Pressure Coefficient Figure 4.24. Maximum and Minimum Pressure Coefficients vs. Wind Direction Used in Modeling of a Square High-Rise Building (concluded). 4-42 Chapter 4. Wind Loads 5-1 Hazus-MH Technical Manual Chapter 5. Windborne Debris A significant amount of the damage to structures associated with hurricane winds is produced by windborne debris impacting the buildings and damaging the building exterior, including roof covering, windows, doors, and other openings. Two windborne debris models are used in the model. The first applies to residential environments and the second is a commercial building model for predicting the damage produced by windborne gravel. The windborne debris model used to estimate impact risk in residential environments is based on the model described in Twisdale, et al. (2000a, 2000b). The residential windborne debris model uses an explicit damage and missile transport approach. A description of the residential windborne debris model and its simplified implementation in damage simulations is provided in Section 5.1. The gravel missile model, developed to predict the damage to buildings from roof gravel missiles, is described in Section 5.2. 5.1 Windborne Debris – Residential Missile Model Windborne Debris Simulation and Analysis. The windborne debris model developed by Twisdale, et al. (2000a, 2000b), is used to quantify the windborne debris risk in typical residential environments. The residential missile model focuses on debris produced from the roofs of residential structures since, as observed in the field after severe wind events, most of the impact damage is caused by debris that is generated from the roofs of nearby buildings. The debris types modeled include roof tiles, shingles, sheathing panels, planks (structural members) and whole roofs. The model represents the first to attempt to quantify, using physically-based models, the risk of impact damage to buildings in a residential environment. The approach used in the residential model consists of modeling typical subdivisions, as shown for example in Figure 5.1, and impacting the buildings with debris generated from within the model subdivision. Through simulations of hurricane winds striking the subdivision, the roof components fail when the modeled wind loads exceed the component capacity. Once a component fails, it is released into the turbulent hurricane wind field, where the trajectory is computed until the component strikes either the ground or another structure. If a missile strikes the wall of another building, the impact velocity, energy and momentum are recorded. In the trajectory model, the turbulence within the hurricane wind field is modeled using an approach in which both the longitudinal and vertical components of the turbulent wind field are simulated. The missile risk simulations were performed for the subdivisions located in three different surrounding terrain environments. For each terrain case examined, a total of 36 hurricanes were simulated for four maximum peak gust speeds of 110 mph, 130 mph, 150 mph and 170 mph, in open terrain conditions (i.e., z0 = 0.03 m). A total of 9 different representative hurricane tracks relative to the subdivision site were simulated for each wind speed case. Typical terrain 5-2 Chapter 5. Windborne Debris Figure 5.1. Example Model Subdivision Used in the Missile Risk Study. conditions representative of open, suburban and treed terrain, were modeled for the wind simulation. The open terrain case was representative of the wind conditions that would be expected to be experienced on barrier islands. The suburban terrain (i.e., z0 = 0.3 m) is representative of a residential area with relatively few tall trees to reduce the wind speeds (such as South Florida), and the treed terrain (i.e., z0 = 1.0 m) is representative of a terrain with trees having heights greater than the heights of the buildings. This last terrain type is representative of many suburban locations along the US hurricane coastline, away from barrier islands. Examples of the turbulent wind traces generated for open country conditions at a height of 10 m above ground are given in Figure 5.2. Also shown, in Figure 5.2, is the “gust speed envelope” represented by the solid line. This envelope is defined as the mean wind speed multiplied by the three second gust factor. A comparison of the turbulent wind trace and the theoretical envelope shows that the peak gusts produced by the turbulent model equal or slightly exceed the envelope value about three to four times per hour. Upon completing the wind speed simulations (i.e., nine hurricanes), information on the total number of hits and associated energy and momentum levels are available. Given the information on the expected number of missile impacts on the walls of a structure, the risk of damage to an opening, PV(D) for a given wind speed, V can be obtained from: PV .D. . 1. exp...q.1. P.. ..d ... (5.1) 5-3 Hazus-MH Technical Manual Wind Speed at H=10m in Open Terrain, 150mph-Hurricane #1 0 20 40 60 80 100 120 140 160 0 3600 7200 10800 14400 18000 21600 Time (sec) Wind Speed (mph) Wind Speed at H=10m in Open Terrain, 150mph-Hurricane #2 0 20 40 60 80 100 120 140 160 0 3600 7200 10800 14400 18000 21600 Time (sec) Wind Speed (mph) Figure 5.2. Example Hurricane Wind Speed Traces Used for the 150 mph Case. 5-4 Chapter 5. Windborne Debris Wind Speed at H=10m in Open Terrain, 150mph-Hurricane #3 0 20 40 60 80 100 120 140 160 0 3600 7200 10800 14400 18000 Time (sec) Wind Speed (mph) Figure 5.2 . Example Hurricane Wind Speed Traces Used for the 150 mph Case (concluded). where .d is the energy or momentum level assumed to produce damage, q is the fraction of the building surface occupied by windows and glass doors, and . represents the mean number of missile impacts per building. P(. < .d) is the probability for the impact energy or momentum (.) to be less than the damage threshold value (.d) given an impact. The probability of no damage, R is expressed in Equation 5.2: R.1.PV .D..exp...q.1.P.. ..d ... . (5.2) Using Equation 5.2, probability curves for R vs. wind speed were developed, which indicate the energy or momentum level a window/door must be able to withstand in order to achieve a given probability level of no damage. Figure 5.3 shows an example of the reliability curves generated for one of the cases examined in the windborne debris risk study. The example in Figure 5.3 presents reliability curves for several impact energies and a q value of 0.2. Implementation of the Windborne Debris Model. In the development of the damage and loss functions described herein, it is not possible to explicitly model the windborne debris on a storm-by-storm basis using the detailed first principles based trajectory and impact model described above because of computer run-time limitations. The simplified windborne debris model makes use of the results of the explicit study using an analytical model which yields results similar to those obtained from the explicit model. 5-5 Hazus-MH Technical Manual (b) Reliability vs Gust Speed for Various Design Equivalent Impact Energy, Eg 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 110 120 130 140 150 160 170 W, Peak Gust (mph) R, Reliability 20000 10000 5000 2000 1000 500 200 100 50 20 0 Eg (lb-ft) Figure 5.3. Example Energy Reliability Curves Derived for a Subdivision Comprised of Single Story Homes with Asphalt Shingle Roofs. Using the simplified debris modeling approach, at each time step in a hurricane simulation, the number of missiles impacting the wall is given as Nw . a.P1.v.N2.v. (5.3) where a is a constant, . is a constant representing the number, density and size of the missile source buildings in a 45. sector, P1(.) is the fraction of missiles that hit the wall for the wind speed v, and N2(.) represents the number of missiles generated at each time step. Using a value of . equal to unity for the eight 45. sectors represents a missile environment similar to that used in the explicit study. Increasing or decreasing . has the effect of changing the density of the surrounding homes. The function P1(.) is obtained directly from the explicit missile simulation, whereas the function N2(.) is obtained by performing roof damage simulations using the same damage model used in the missile study, but for a larger number of wind speeds. The fraction of missiles generated that impact another building is a linear function of wind speed, whereas the number of missiles generated at each time step increases more rapidly. Given that the building is impacted by a missile at a given time step, the impact energy is determined by sampling from Weibull distribution in the form: . . . . .k . Pe e . E . 1. exp . E / C (5.4) 5-6 Chapter 5. Windborne Debris where the Weibull parameters C and k were determined by fitting the energy exceedance data derived from the physically-based debris model. Both of the Weibull parameters are functions of the peak gust wind speed. Note that the building can only be impacted by missiles generated from within a 90. sector, centered on a vector normal to the wall surface, and the wind must be approaching from within this sector. These criteria ensure that walls can be impacted by missiles only when the wind is blowing towards the wall, and only when there are missile sources upwind of the structure. Figure 5.4 shows a comparison of the reliability curves generated from the physicallybased model to those derived using the simplified model. In this figure, the points shown without lines connecting the data points represent those derived from the simplified model, whereas those shown with lines connecting the data points represent the original data as produced by the explicit missile simulation. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 110 120 130 140 150 160 170 W, Peak Gust (mph) R, Reliability 20000 10000 5000 2000 1000 500 200 100 50 20 0 0 20 50 100 200 500 1000 Eg (lb-ft) Figure 5.4. Comparison of Reliability Curves Derived from the Explicit Missile (lines) Simulation to Those Obtained from the Simplified Model (points only). The comparisons of the two sets of reliability curves show reasonable agreement, for all impact energy levels for wind speeds less than 130 mph. In the 150 mph case, the simplified model tends to slightly underestimate the reliability (i.e., overestimate the probability of missile impact), and at a wind speed of 170 mph, the reverse is true. In general, for missile impact energies less than 500 ft-lbs, the simplified model satisfactorily reproduces the results obtained from the explicit model. For very high 5-7 Hazus-MH Technical Manual impact energies (~1000 ft-lbs), the simplified model underestimates the frequency of impact, as indicated by the overestimate in the computed reliability levels. This underestimate of the frequency of very high energy impacts is not of great concern, since damage to window protection (discussed later) occurs at energies much lower than 1000 ft-lbs. In summary, a simplified, fast running missile impact model is used which approximates the results derived with an explicit modeling approach. The simplified model, which yields reasonable estimates of the windborne debris risk, is used in the building damage model to develop the fast-running Hazus damage and loss functions. 5.2 Windborne Debris – Commercial Missile Model The study on the risk of damage to commercial buildings by windborne gravel debris consists of two components. The first component is a mathematical simulation of the debris generation, transport and impact on building envelopes during a hurricane passage. This windborne gravel debris model simulates the characteristic layout of the gravel layers, the turbulent hurricane wind trace, local wind fields on the roof, wind action on gravel stones, gravel scour and transport, and the eventual interception of its trajectory with a building’s envelope (or with the ground). Throughout a hurricane, the simulation provides detailed records of individual gravel missiles generated, their origin location, transport distance, impact location and impact momentum, as well as the characteristic layout of the gravel remaining on the roof. This model is a stand-alone program, and can be used for specific case studies or used to derive information for gravel debris risk assessment for generic settings. The development of this model, along with its validation against three field-observed cases, is described in detail in Section 5.2.1. It is demonstrated that the model agrees with field observations reasonably well. The second component of the study aims at constructing a fast-running risk model to estimate the probability of damage to building envelope by windborne gravel debris given the impact resistance capacity of the target surfaces. The fast-running debris risk model estimates the expected number and location of fenestration elements breached by debris within each short time interval in order to interactively account for the rainwater penetration and internal pressure change in a building. The model utilizes the previous analytical formulation on debris risk (Twisdale, et. al, 2000a, 2000b) and the above physical modeling on generic configurations to provide inputs (for example, the expected number of impacts and impact momentum) required by the analytical risk formulation. From the simulation records, the number of impacts per unit area within a time interval and the impact momentum distribution for a target surface element, such as a window, with specified location and orientation relative to the source are derived. The derived number of impacts and momentum distribution are functions of the reference wind speed, wind direction, terrain, height and area of gravel source roof, depth of the gravel ballast layer and gravel size. Based on this information, a set of simplified expressions describing the relationships between the variables yields a fast-running debris module suitable for incorporation into the damage model. This second part of the model is described in Section 5.2.2. 5-8 Chapter 5. Windborne Debris 5.2.1 Windborne Gravel Debris Simulation and Case Studies Flat, built-up roofs and ballasted membrane roofs are commonly seen on high-rise and low-rise commercial buildings in urban and suburban areas. Gravel used on these roofs often becomes windborne missiles during high winds. This problem has been observed and reported by many field investigators (e.g., Minor, et al., 1978; Minor, 1994; Minor and Behr, 1993a, 1993b; and Behr and Minor, 1994). This section describes the computer modeling of gravel missile generation (scour and blow-off), transport trajectory and physical impact on surfaces. Three case studies are presented along with comparisons against field observations. Scope of the Simulation. The problem of debris generation, transport and impact involves many variables. The present model includes the effects of the mean hurricane wind trace (speed and direction variation with time), correlated three-dimensional turbulence components, building geometry and street layout, roof gravel configuration (diameter distribution and thickness), as well as upstream terrain influences. Local wind velocity fields over the roof and in the wake behind the buildings are also approximated. The gravel scour pattern, trajectories and impact statistics are used to compute the information required for model calibration and for risk prediction. Missile Generation from Roof Gravel. Within an assembly of gravel stones of nearly spherical shape and variable diameters loosely lying on a flat bed, an individual stone on the top layer will be subject to a drag, an uplift, and an overturning moment caused by the wind blowing over the surface. Gravity and the constraint of other stones balance these wind forces; however, when the wind speed increases and exceeds some threshold value, the wind forces overcome these constraints. At this point, the stone starts to intermittently rotate and shift horizontally. At another slightly higher threshold wind speed, the stone will be lifted and blown away. Both the first and second threshold wind speeds have been shown to be proportional to the square root of the stone diameter (Kind and Wardlaw, 1984). The model developed here considers the second threshold wind speed, since only at this higher wind speed is the stone released into the wind field. In determining the local wind speeds on the roof surface, the flow separation and vortex induced velocity field is included in the model as a function of building geometry and the free stream wind speed and direction. An example of the horizontal component of the mean wind velocity on the roof surface of a cube-shaped building is shown in Figure 5.5 for an oblique on-coming wind. Figure 5.5 also shows a photograph of stream lines obtained from a flow visualization test given for comparison. The streamline patterns are in a good agreement. The resulting scour pattern is illustrated in Figure 5.6 and compared with qualitative wind tunnel and field observations (Kind and Wardlaw, 1984). It is seen that the computer model reproduces the typical two-lobed scour pattern under oblique winds. Note that the wind tunnel model of Kind and Wardlaw has a low parapet so that the scour pattern shifts slightly downstream. Moreover, their model represents a low-rise building such that the high turbulence in the lower part of the simulated boundary layer flow reduces the sharpness of the two-lobed pattern compared to the field observation and the computer model results which are both for multi-story buildings (low turbulence intensity). 5-9 Hazus-MH Technical Manual 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 X Y Wind Tunnel Computer Surface Flow Pattern Comparison (Courtesy of Mr. Bengt G. Wiren, Swedish Royal Institute of Technology) Figure 5.5. Example of Computer-Modeled Surface Flow Pattern Compared with Wind Tunnel Observation. Missile Transport in the Wind Field. When gravel is released into the three-dimensional wind field, it is transported by the turbulent wind. This is modeled by numerically solving the equation of motion for a particle of mass, with the wind force acting on the gravel updated as a function of location and time. The influence of the vortex flow over the rooftop and the wake flow downstream of the buildings are incorporated with the oncoming turbulent wind to obtain a resultant wind field. As an example, the computed trajectory for a sample gravel missile generated from the roof of a cube-shaped building is illustrated in Figure 5.7 for a 45. oblique wind. The gravel missile is first moved sideways toward one of the upstream roof edges by the spiral vortex flow near the roof surface. Kind and Wardlaw’s (1984) wind tunnel experiments on gravel scour and blow-off also indicate that gravel missiles generated from the front portion of the roof would leave the roof over the upstream edges. After it leaves the roof, the trajectory starts to gradually bend into the on-coming wind. The gravel missiles generated from the downstream portion of the roof would have less curved trajectories since the spiral vortex flow will be weakened downstream. Missile Impact on Building Envelopes. The trajectory of the gravel missile will eventually intersect with a surface, either the ground or a building envelope, which are geometrically defined on a global coordinate frame. The impact location and velocity are recorded. The impact momentum and energy are then calculated for each gravel missile of a given mass. This information can be used to derive statistical distributions of impact 5-10 Chapter 5. Windborne Debris Gravel Scour Pattern Figure 5.6. Example of Gravel Scour Pattern Compared with Field and Experimental Observations. location, momentum or energy, and number of impacts on a specific area of the building envelope, which are subsequently used to predict the risk of building envelope breach during a storm. The recorded impact results for specific building complexes can also be used to perform model calibration and validation studies by comparing them with the field observed data for the same buildings and environments. Case Study 1 . Kendall, Florida, Hurricane Andrew. During Hurricane Andrew, the downstream buildings in a high-rise complex in Kendall, Florida (Figure 5.8), suffered severe windborne debris impact damage to the windows, which has been investigated and documented by several researchers (e.g., Smith, 1999; Behr and Minor, 1994; and Minor, 1994). This case provides a basis for examining the results obtained with the windborne debris model. 5-11 Hazus-MH Technical Manual 0 5 10 15 20 25 30 35 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 Y Z -15 -10 -5 0 5 10 15 20 25 30 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 Y X Elevation View Plan View WIND Figure 5.7. Example of Gravel Missile Trajectory. The plan of the complex is shown in Figure 5.9. The missile source is the Marriott Hotel roof gravel ballast. The gravel missiles were generated from the two penthouse roofs only, since the other parts of the roof have tall parapets that prevented gravel from leaving the roof. For the case study, a Hurricane Andrew mean wind trace was re-created for the site using the hurricane model described in Chapter 2. The mean wind direction changed from northerly to southeasterly in a time period of about 2.5 hours during which 5-12 Chapter 5. Windborne Debris Figure 5.8. The Marriott-Datran Complex in Kendall, Florida. open terrain 10 m-height peak gust winds are above 90 mph. The largest peak gusts reached 140 mph when the mean wind direction was approximately normal to the northeast walls of the buildings. Typical 3-dimensional turbulence components for a terrain roughness length of 0.5 m (slightly rougher than standard suburban) were simulated. The mean diameter of the roof gravel was determined to be 12 mm from survey records reported in Behr and Minor (1994) and Smith (1999) with a distribution given in ASTM Standards, Designation D1863-93 (Re-approved 1996) for Size # 67A. The depth of the gravel ballast layer on the roof was 76 mm (Behr and Minor, 1994). The window glass on the downstream buildings is 6 mm thick fully tempered monolithic glass (Behr and Minor, 1994) that provides an estimated threshold average breakage momentum of 0.1 kg-m/s (Minor, 1994). The impact results obtained with the computer model are shown in Figure 5.10 for the northeast walls of the two downstream buildings, where each dot represents a damaging hit. A damaging hit is an impact by a gravel missile with its momentum’s component normal to the wall being larger than the 0.1 kg-m/s threshold. The coordinate grid approximately corresponds to the window grid, one cell containing one window. One or more damaging hits within a cell yield one count of damaged window. Note that, for the case where windows occupy only a percentage of the wall area such as these buildings, only the corresponding percentage of generated gravel missiles that are randomly sampled is used for damage counts. The results shown in Figure 5.10 are these sampled hits. The photographs (Minor, 1994; Smith, 1999) documenting the window breaches are shown in Figure 5.11. For the northeast wall of Datran Tower I, the simulation yields a window failure rate of 96.7% for the upper 10 floors, in good agreement with the observed value of 97.4% as counted from Figure 5.10(a) for the same part of the wall.