A barra é de pinho do Sul nº 2, 2x4 nominal, 90 cm de comprimento e foi utilizada como barra treliçada. O apoio lateral é fornecido apenas nas extremidades da barra e são consideradas articuladas. As cargas de permanente (DL), de neve (SL) e de vento (WL) são aplicadas no ponto superior e central da viga-pilar, como apresentado abaixo.
As propriedades da barra são exibidas após selecionar a secção e o material apropriados no programa.
Fatores de ajuste na Tabela 4.3.1 da NDS 2018 para dimensionamento de ASD
Os valores de dimensionamento de referência (Fb, Fc e Emin) são multiplicados pelos fatores de ajuste para determinar os valores de dimensionamento ajustados. Para madeira serrada, estes fatores são dados na Tabela 4.3.1 {%>#Refer [1]]]. Existem onze fatores de ajuste diferentes para o dimensionamento de acordo com ASD. Many of these factors are equal to 1.0 in the NDS example [2]. No entanto, de seguida é descrito de forma breve como o RF-/TIMBER AWC considera os fatores individuais.
Factors Calculated by Program
CL – Beam Stability Factor
It depends on the geometry and lateral support of the member as described in Section 3.3.3 [1]. Este fator é calculado automaticamente no RF-/TIMBER.
Note: the effective length, le, used to calculate CL is defined by the user in the "Effective Length" section of RF-/TIMBER AWC. The "Acc. to Table 3.3.3" option with the appropriate loading case must be selected.
A figura abaixo apresenta o caso de carga que se aplica a este exemplo.
CF – Size Factor
It depends on the depth and thickness of the member as specified in Section 4.3.6 [1]. Este fator é determinado automaticamente no RF-/TIMBER AWC.
Cfu – Flat Use Factor
It accounts for weak axis bending of the member as specified in Section 4.3.7 [1]. Este fator é calculado automaticamente no RF-/TIMBER AWC.
CP – Column Stability Factor
It depends on the geometry, end fixity conditions, and lateral support of the member as described in Section 3.7.1 [1]. When a compression member is fully supported throughout its length, CP = 1.0. This factor is automatically calculated in RF-/TIMBER AWC for both strong and weak axis directions.
Fatores definidos pela entrada do utilizador
CD – Load Duration Factor
It accounts for various loading periods based on the load case, such as dead, snow, and wind, based on Section 4.3.2 [1]. Selecionar "ASCE 7-16 NDS (Madeira)" como norma no RFEM ativa a opção de duração da carga na caixa de diálogo Casos de carga. The load duration class (Permanent, Ten Years, and so on) default setting is based on the "Action Category" of the load case. Esta configuração pode ser ajustada pelo utilizador no RFEM ou no RF-TIMBER AWC. The value selected by the program is based on Table 2.3.2 [1].
CM – Wet Service Factor
It accounts for the moisture service conditions of the member as specified in Section 4.1.4 [1]. O utilizador pode selecionar "molhado" ou "seco" na secção 'Condições de utilização' do RF-/TIMBER AWC.
Ct – Temperature Factor
It accounts for exposure to elevated temperatures of up to 100 degrees F, 100 to 125, and 125 to 150 as described in Section 2.3.3 [1]. The user can select between the three temperature ranges in the "In-Service Conditions" section of RF-/TIMBER AWC. The value selected by the program is based on Table 2.3.3 of [1].
Ci – Incising Factor
It accounts for the loss of the area from the small incisions made in the member to receive preservative treatment for decay prevention as described in Section 4.3.8 [1]. The user can select "Not Incised" or "Incised" in the "Additional Design Parameters" section of RF-/TIMBER AWC.
Cr – Repetitive Member Factor
It is used when multiple members act compositely to properly distribute a load amongst themselves as described in Section 4.3.9 [1]. Cr = 1.15 for members that meet the criteria of being closely spaced and connected by a sheathing or equivalent. The user can select "Not Repetitive" or "Repetitive" in the "Additional Design Parameters" section of RF-/TIMBER AWC.
Atenção: If necessary, code-based values of the user input adjustment factors can be changed in the "Standard" option.
Factors Excluded in Program
CT – Buckling Stiffness Factor
It accounts for the contribution of plywood sheathing to the buckling resistance of compression truss chords as specified in Section 4.4.2 [1]. Este fator é utilizado para aumentar a Emín da barra. CT can be manually calculated as per <nobr>Equation 4.4-1 [1]</nobr> or conservatively taken as 1.0.
Cb – Bearing Area Factor
It is used to increase the compression design values (Fcp) for concentrated loads applied perpendicular to the grain as specified in Section 3.10.4 [1]. Cb can be manually calculated per equation 3.10-2 [1] or conservatively taken as 1.0.
Actual Stress in Beam-Column
Neste exemplo, a combinação de cargas foi simplificada para CO1: DL + SL + WL.
- Tensão de compressão de cargas de permanente e neve, fc = 171 psi
- Tensão de flexão no eixo forte da carga de vento, fbx = fb1 = 353 psi
- Tensão de flexão no eixo fraco de cargas permanentes e de neve, fby = fb2 = 1029 psi
Determination of Adjusted Design Values as per NDS 2018 Table 4.3.1 ASD Method
- Critical Buckling Design Value for Compression Member in Strong Axis, FcEx:
FcEx
Critical buckling design value for the compression member in the major axis, psi
Emin'
= Emin ⋅ CM ⋅ CT ⋅ Ci = 510,000 psi
le1
Effective length = 36.0 in
d1
Member depth = 3.5 in
- Critical Buckling Design Value for Compression Member in Weak Axis, FcEy:
FcEy
Critical buckling design value for the compression member in the minor axis, psi
Emin'
= Emin ⋅ CM ⋅ CT ⋅ Ci = 510,000 psi
le2
Effective length = 36.0 in
d2
Member thickness = 1.5 in
- Adjusted Compressive Design Value Parallel to Grain, Fc':
Fc'
Adjusted compressive design value parallel to the grain, psi
Fc
Reference compressive design values parallel to the grain, psi
CD
Load duration factor
CM
Wet service factor
Ct
Temperature factor
CF
Size factor
Ci
Incising factor
CP
Column stability factor
- Critical Buckling Design Value for Bending Member, FbE:
FbE
Critical buckling design value for the bending member, psi
Emin'
= Emin ⋅ CM ⋅ CT ⋅ Ci = 510,000 psi
RB
Slenderness ratio = 9.65 < 50 (NDS Equation 3.3-5)
- Adjusted Strong Axis Bending Design Value, Fbx':
Fbx'
Adjusted major axis bending design value, psi
Fb
Reference bending design value, psi
CD
Load duration factor
CM
Wet service factor
CL
Beam stability factor
Ct
Temperature factor
CF
Size factor
Ci
Incising factor
Cr
Repetitive member factor
- Adjusted Weak Axis Bending Design Value, Fby':
Fby'
Adjusted minor axis bending design value, psi
Fb
Reference bending design value, psi
CD
Load duration factor
CM
Wet service factor
CL
Beam stability factor
Ct
Temperature factor
Cfu
Flat use factor
CF
Size factor
Ci
Incising factor
Cr
Repetitive member factor
- Relação de cálculo combinada de flexão biaxial e compressão axial
Inserting the actual stresses and limiting design values presented above into NDS equation 3.9-3 [1], the final design ratio is shown below.
fc |
Compression stress due to the dead and snow load |
Fc' |
Adjusted compressive design value parallel to the grain |
fbx |
Major-axis bending stress due to the wind load |
Fbx' |
Adjusted major axis bending design value |
FcEx |
Critical buckling design value for the compression member in the major axis |
fby |
Minor-axis bending stress due to the dead and snow load |
Fby' |
Adjusted minor axis bending design value |
FcEy |
Critical buckling design value for the compression member in the minor axis |
FbE |
Critical buckling design value for the bending member |
And NDS equation 3.9-4 [1],
fc |
Compression stress due to the dead and snow load |
FcEy |
Critical buckling design value for the compression member in the minor axis |
fbx |
Major-axis bending stress due to the wind load |
FbE |
Critical buckling design value for the bending member |
Resultados no RF-/TIMBER AWC
O utilizador pode comparar cada fator de ajuste e valor de cálculo ajustado do método de cálculo manual analítico com o resumo de resultados no RF-/TIMBER AWC. Como apresentado, os resultados são idênticos. The controlling final design ratio = 0.98 is based on the geometrically linear analysis (1st degree) calculation method. Keep in mind that the default setting in RFEM for the load combination is set to the second-order analysis. This will result in a slightly larger design ratio = 1.03. The user has the option to choose which method listed in the "Calculation Parameters" is best for the structure.