В качестве общего примера, представленного в нашей статье, будет использована трехмерная деревянная конструкция от криволинейной деревянной кровли, доходящей до фундамента. The clear span of a single timber arch is 64 ft, and the height from the base to the crown of the arch is 16 ft.
Snow Loads from ASCE 7-16
Примером того, каким образом следует загружать криволинейные кровли при сбалансированных и несбалансированных снеговых нагрузках, служит в рамках данной нормы Рисунок 7.4-2 [1]. The downward snow load application varies along the arch length dependent upon the roof's slope at a specific location. Therefore, it is necessary to determine the slope in degrees along the entire arch length.
Determining Roof Slope
Converting the elevation view of the arch roof into a simple line element and projecting onto an x and y coordinate system, the x coordinate points are determined at a 1-foot increment along the base of the structure. Knowing the arch from the structure example is only a portion of a larger circle, the equation for a circle can be utilized to determine additional info about the arch length.
где
x = coordinate of arch along the x axis
y = coordinate of arch along the y axis
h = x coordinate of circle center
k = y coordinate of circle center
r = radius or circle
Rearranging the above equation, since all values are given other than the y coordinate of the arch, the equation becomes:
To find the slope of a point anywhere along the arch, implicit differentiation must be applied to the equation of the circle with respect to x.
При решении дифференцирования неявной функции, является рост/пробег наклона, который обозначается dx/dy, следующим.
To determine the slope in degrees, the inverse tangent function is applied.
Additionally, the equation above for "y" can be substituted in the slope equation, since this value may not be readily known when comparing to the known x coordinate point. It is now possible to determine the slope in degrees along every x location for the structure arch.
Snow Load Magnitude
According to Fig. 7.4-2, there are three different cases depending on the curved roof geometry at the roof edge or eave.
- Arc slope at the eaves < 30°
- Arc slope at the eaves 30° to 70°
- Arc slope at the eaves > 70°
For each case, both a balanced and an unbalanced loading are given along the arch length. Snow load acting on a sloping surface is applied in the horizontal projection of the surface. Рис. 7.4-2 данные значения нагрузки обобщаются путем умножения снеговой нагрузки на плоскую кровлю pf на коэффициент уклона кровли Cs. Cs accounts for the varying slope along the arch length and is dependent on several factors indicated in Figure 7.4-1 [1], including the Thermal Factor Ct found in Table 7.3-2 [1], the surface type (that is, unobstructed slippery surfaces versus all other surface types), and the roof slope in degrees, which was determined in the Slope equation above.
Для сценариев несбалансированных нагрузок требуется у величины снеговой нагрузки в тех местах, где скос дуги колеблется между 30° и 70°, дополнительное применение коэффициента экспозиции Ce. 7.4-2 for the unbalanced load scenarios only. Данное значение можно определить из таблицы 7.3-1 [1] в зависимости от категории рельефа и условий внешних воздействий на кровлю.
The flat roof snow load is determined from Eqn. 7.3-1 [1] shown below.
pf = 0.7 ⋅ Ce ⋅ Ct ⋅ Is ⋅ pg
Where Ce and Ct are discussed above and found in Tables 7.3-1 and 7.3-2, respectively. The Importance Factor Is is found in Table 1.5-2 [1], which is further dependent on the Risk Category from Table 1.5-1 [1]. Снеговая нагрузка на грунт pg отображена на Рис. 7.2-1 [1] и в Таблице 7.2-1 [1].
Dlubal Software has integrated the ground snow load maps found directly in ASCE 7-16 with Google Maps Technology to create the Geo Zone Tool available on the Dlubal website. This tool allows the user to set the address of the project location or to click directly on the map. In return, the Geo-Zone Tool will automatically display the snow, wind, and seismic data based on ASCE 7-16 for the specified location. This provides a more efficient and simpler alternative in comparison to manually locating this info from the standard to determine ground snow loads for various locations within the United States.
- More info on the Geo-Zone Tool for Snow, Wind, and Seismic Zoning Maps as per ASCE 7-16:
Snow Load Location
For all three snow load cases for curved roofs, the magnitude varies along the arch length depending on the roof slope shown in the loading diagrams in Fig. 7.4-2. The major locations needed for any of the three cases are 70°, 30°, and the crown. With the Slope equation above, these specific points can easily be determined along the arch length. The magnitudes vary linearly between these specific location points, so it is unnecessary to evaluate the snow load magnitude at each slope point.
For the balanced load scenarios, the magnitude of the arch to the left and right of the crown is set as Cs ⋅ pf, where Cs = 1.0. Потому требуется, чтобы пользователь сначала на основе рисунка 7.4-1 определил, в каком месте ската кровли будет коэффициент Cs равен 1,0. Once this roof slope is determined, the point along the arch length can be found based on the information from the Slope equation.
For unbalanced load scenarios, the windward side is considered free from snow. Snow load will only be applied to the arch along the leeward side, as indicated in the loading diagrams. If another roof abuts to the current roof, the diagrams also indicate how to consider these special cases in the unbalanced load cases for both load magnitude and location.
Применение в программе RFEM
Complex loading scenarios are easily handled in RFEM with the available tools. Самым простым способом расчета наклона кровли во всех местах дуги, полученными с помощью вышеприведенных исходных уравнений, является использование программы для работы с электронными таблицами, такой как Microsoft Excel.
With the calculated roof slope and the steps above taken to determine the snow load magnitude from ASCE 7-16, the loads can be simplified in Excel to a few extreme locations, where applicable, such as the roof eaves, 70°, 30°, and the crown. This information can be set up in table format defined in a single spreadsheet with the x location defined along the projected x axis of the arch and the corresponding snow load magnitude.
Сначала задайте в программе RFEM «новую нагрузку на стержень» и определите, будет ли она применяться к отдельным стержням или к блокам стержней. «Переменное» распределение нагрузки используется в направлении Z проекции ZP. Кроме того, нажав на кнопку «Изменить переменную нагрузку» будет в программе активирована и соответствующая таблица нагрузок. Затем, с помощью всего одного щелчка мыши, можно всю информацию, определенную в текущем листе Excel, легко импортировать в общую таблицу программы RFEM.
Для применения несбалансированной снеговой нагрузки, позволяет программа RFEM использовать данный сценарий также в случае отдельного загружения.
Возможность импорта различных нагрузок непосредственно из таблиц Excel чрезвычайно полезна в случаях применения нагрузки на несколько стержней, а также при значительном изменении величины нагрузки вдоль стержня.