Diseño de vigas y pilares de madera según NDS 2018 utilizando el módulo RF-/TIMBER AWC

La barra es un pino del sur núm. 2, 2x4 nominal, 3 pies de largo y se usa como una barra de cercha. Lateral support is provided only at the member ends, and they are considered pinned. The dead (DL), snow (SL), and wind (WL) loads are applied at the top and midpoint of the beam-column, as shown below.

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Columna de madera

The member properties are shown after selecting the appropriate cross-section and material in the program.

Propiedades de la sección de madera aserrada 2x4

Propiedades del material del pino meridional

Adjustment Factors Listed in Table 4.3.1 of NDS 2018 for ASD Design

The reference design values (F_b, F_c, and E_min) are multiplied by the applicable adjustment factors to determine the adjusted design values. For sawn lumber, these factors are found in Table 4.3.1 [1]. There are eleven different adjustment factors for the ASD design. Many of these factors are equal to 1.0 in the NDS example [2]. However, brief description and how RF-/TIMBER AWC accounts for each factor is given below.

Factors Calculated by Program

C_L – Beam Stability Factor

It depends on the geometry and lateral support of the member as described in Section 3.3.3 [1]. This factor is automatically calculated in RF-/TIMBER.

Note: the effective length, le, used to calculate C_L 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.

The image below shows the applicable loading case for this example.

Longitud eficaz para el factorC L

C_F – Size Factor

It depends on the depth and thickness of the member as specified in Section 4.3.6 [1]. This factor is automatically determined in RF-/TIMBER AWC.

C_fu – Flat Use Factor

It accounts for weak axis bending of the member as specified in Section 4.3.7 [1]. This factor is automatically calculated in RF-/TIMBER AWC.

C_P – 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, C_P = 1.0. This factor is automatically calculated in RF-/TIMBER AWC for both strong and weak axis directions.

Factors Defined by User Input

C_D – 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]. Selecting "ASCE 7-16 NDS (Wood)" as the standard in RFEM activates the load duration option in the Load Cases dialog box. The load duration class (Permanent, Ten Years, and so on) default setting is based on the "Action Category" of the load case. This setting can be adjusted by the user in RFEM or RF-/TIMBER AWC. The value selected by the program is based on Table 2.3.2 [1].

C_M – Wet Service Factor

It accounts for the moisture service conditions of the member as specified in Section 4.1.4 [1]. The user can select "wet" or "dry" in the 'In-Service Conditions' section of RF-/TIMBER AWC.

C_t – 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].

C_i – 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.

C_r – 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]. C_r = 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.

Nota: If necessary, code-based values of the user input adjustment factors can be changed in the "Standard" option.

Opción para factores de ajuste

Factors Excluded in Program

C_T – 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]. This factor is used to increase E_min of the member. C_T can be manually calculated as per <nobr>Equation 4.4-1 [1]</nobr> or conservatively taken as 1.0.

C_b – Bearing Area Factor

It is used to increase the compression design values (F_cp) for concentrated loads applied perpendicular to the grain as specified in Section 3.10.4 [1]. C_b can be manually calculated per equation 3.10-2 [1] or conservatively taken as 1.0.

Actual Stress in Beam-Column

In this example, the load combination has been simplified to CO1: DL + SL + WL.

• Compression stress from dead and snow loads, f_c = 171 psi
• Strong-axis bending stress from wind load, f_bx = f_b1 = 353 psi
• Weak-axis bending stress from dead and snow loads, f_by = f_b2 = 1,029 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, F_cEx:
  $${\mathrm{F}}_{\mathrm{cEx}} = {\mathrm{F}}_{\mathrm{cE}1} = \frac{0.822 · {\mathrm{E}}_{\min }\text{'}}{{\left[{\displaystyle \frac{{\mathrm{l}}_{\mathrm{e}1}}{{\mathrm{d}}_1}}\right]}^2}$$

  $${\mathrm{F}}_{\mathrm{cEx}} = {\mathrm{F}}_{\mathrm{cE}1} = \frac{0.822 · 510,000 \mathrm{psi}}{{\left[{\displaystyle \frac{36.0 \mathrm{in}}{3.5 \mathrm{in}}}\right]}^2}$$

  $${\mathrm{F}}_{\mathrm{cEx}} = {\mathrm{F}}_{\mathrm{cE}1} = 3,963 \mathrm{psi}$$

  FcEx	Valor de cálculo de pandeo crítico para la barra comprimida en el eje mayor, psi
  Emín.'	= Emín ⋅ CM ⋅ CT ⋅ Ci = 510 000 psi
  le1	Longitud eficaz = 36,0 in
  d1	Canto de la barra = 3,5 in

  Valor de cálculo de pandeo crítico para una barra comprimida en el eje mayor, FcEx
• Critical Buckling Design Value for Compression Member in Weak Axis, F_cEy:
  $${\mathrm{F}}_{\mathrm{cEy}} = {\mathrm{F}}_{\mathrm{cE}2} = \frac{0.822 · {\mathrm{E}}_{\min }\text{'}}{{\left[{\displaystyle \frac{{\mathrm{l}}_{\mathrm{e}2}}{{\mathrm{d}}_2}}\right]}^2}$$

  $${\mathrm{F}}_{\mathrm{cEy}} = {\mathrm{F}}_{\mathrm{cE}2} = \frac{0.822 · 510,000 \mathrm{psi}}{{\left[{\displaystyle \frac{36.0 \mathrm{in}}{1.5 \mathrm{in}}}\right]}^2}$$

  $${\mathrm{F}}_{\mathrm{cEy}} = {\mathrm{F}}_{\mathrm{cE}2} = 728 \mathrm{psi}$$

  FcEy	Valor de cálculo de pandeo crítico para la barra comprimida en el eje menor, psi
  Emín.'	= Emín ⋅ CM ⋅ CT ⋅ Ci = 510 000 psi
  le2	Longitud eficaz = 36,0 in
  d2	Espesor de la barra = 1,5 in

  Valor de cálculo de pandeo crítico para una barra comprimida en el eje menor, FcEy
• Adjusted Compressive Design Value Parallel to Grain, F_c':
  $${\mathrm{F}}_{\mathrm{c}}\text{'} = {\mathrm{F}}_{\mathrm{cy}}\text{'} = {\mathrm{F}}_{\mathrm{c}} · {\mathrm{C}}_{\mathrm{D}} · {\mathrm{C}}_{\mathrm{M}} · {\mathrm{C}}_{\mathrm{t}} · {\mathrm{C}}_{\mathrm{F}} · {\mathrm{C}}_{\mathrm{i}} · {\mathrm{C}}_{\mathrm{P}}$$

  $${\mathrm{F}}_{\mathrm{c}}\text{'} = {\mathrm{F}}_{\mathrm{cy}}\text{'} = 1,450 \mathrm{psi} · 1.6 · 1.0 · 1.0 · 1.0 · 1.0 · 0.29$$

  $${\mathrm{F}}_{\mathrm{c}}\text{'} = {\mathrm{F}}_{\mathrm{cy}}\text{'} = 673 \mathrm{psi}$$

  Fc'	Valor de cálculo a compresión ajustado paralelo a la fibra, psi
  fc	Valores de cálculo a compresión de referencia paralelos a la fibra, psi
  CD	Factor de duración de carga
  CM	Factor de humedad en servicio
  Ct	Coeficiente de temperatura
  CF	Factor de tamaño
  Ci	Factor de corte
  CP	Factor de estabilidad del pilar

  Valor de cálculo de compresión ajustado en la dirección de la fibra, Fc '
• Critical Buckling Design Value for Bending Member, F_bE:
  $${\mathrm{F}}_{\mathrm{bE}} = \frac{1.20 · {\mathrm{E}}_{\min }\text{'}}{{{\mathrm{R}}_{\mathrm{B}}}^2}$$

  $${\mathrm{F}}_{\mathrm{bE}} = \frac{1.20 · 510,000 \mathrm{psi}}{{9.65}^2}$$

  $${\mathrm{F}}_{\mathrm{bE}} = 6,577 \mathrm{psi}$$

  FbE	Valor de cálculo de pandeo crítico para la barra flectada, psi
  Emín.'	= Emín ⋅ CM ⋅ CT ⋅ Ci = 510 000 psi
  RB	Relación de esbeltez = 9.65 < 50 (ecuación NDS 3.3-5)

  Valor crítico de cálculo del pandeo para la barra a flexión, FbE
• Adjusted Strong Axis Bending Design Value, F_bx':
  $${\mathrm{F}}_{\mathrm{bx}}\text{'}= {\mathrm{F}}_{\mathrm{b}1} = {\mathrm{F}}_{\mathrm{b}} · {\mathrm{C}}_{\mathrm{D}} · {\mathrm{C}}_{\mathrm{M}} · {\mathrm{C}}_{\mathrm{L}} · {\mathrm{C}}_{\mathrm{t}} · {\mathrm{C}}_{\mathrm{F}} · {\mathrm{C}}_{\mathrm{i}} · {\mathrm{C}}_{\mathrm{r}}$$

  $${\mathrm{F}}_{\mathrm{bx}}\text{'}= {\mathrm{F}}_{\mathrm{b}1} = 1,100 \mathrm{psi} · 1.6 · 1.0 · 0.982 · 1.0 · 1.0 · 1.0 · 1.0$$

  $${\mathrm{F}}_{\mathrm{bx}}\text{'}= {\mathrm{F}}_{\mathrm{b}1} = 1,729 \mathrm{psi}$$

  fbx'	Valor de cálculo a flexión del eje mayor ajustado, psi
  Fb	Valor de cálculo de referencia de flexión, psi
  CD	Factor de duración de carga
  CM	Factor de humedad en servicio
  CL	Factor de estabilidad de la viga
  Ct	Coeficiente de temperatura
  CF	Factor de tamaño
  Ci	Factor de corte
  Cr	Factor de barra repetitiva

  Valor de cálculo de flexión mayor ajustado, Fbx'
• Adjusted Weak Axis Bending Design Value, F_by':
  $${\mathrm{F}}_{\mathrm{by}}\text{'} = {\mathrm{F}}_{\mathrm{b}2} = {\mathrm{F}}_{\mathrm{b}} · {\mathrm{C}}_{\mathrm{D}} · {\mathrm{C}}_{\mathrm{M}} · {\mathrm{C}}_{\mathrm{L}} · {\mathrm{C}}_{\mathrm{t}} · {\mathrm{C}}_{\mathrm{fu}} · {\mathrm{C}}_{\mathrm{F}} · {\mathrm{C}}_{\mathrm{i}} · {\mathrm{C}}_{\mathrm{r}}$$

  $${\mathrm{F}}_{\mathrm{by}}\text{'} = {\mathrm{F}}_{\mathrm{b}2} = 1,100 \mathrm{psi} · 1.6 · 1.0 · 1.0 · 1.0 · 1.1 · 1.0 · 1.0 · 1.0$$

  $${\mathrm{F}}_{\mathrm{by}}\text{'} = {\mathrm{F}}_{\mathrm{b}2} = 1,936 \mathrm{psi}$$

  fby'	Valor de cálculo a flexión del eje menor ajustado, psi
  Fb	Valor de cálculo de referencia de flexión, psi
  CD	Factor de duración de carga
  CM	Factor de humedad en servicio
  CL	Factor de estabilidad de la viga
  Ct	Coeficiente de temperatura
  Cfu	Factor de uso para piezas planas
  CF	Factor de tamaño
  Ci	Factor de corte
  Cr	Factor de barra repetitiva

  Valor de cálculo de flexión respecto al eje menor ajustado, Fby'
• Combined Biaxial Bending and Axial Compression Design Ratio

Inserting the actual stresses and limiting design values presented above into NDS equation 3.9-3 [1], the final design ratio is shown below.

And NDS equation 3.9-4 [1],

Result in RF-/TIMBER AWC

The user can compare each adjustment factor and adjusted design value from the analytical hand calculation method to the result summary in RF-/TIMBER AWC. As shown, the results are identical. The controlling final design ratio = 0.98 is based on the geometrically linear analysis (1^st 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.

razón de tensiones

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Pilar de viga de madera

Base de datos de conocimientos

KB 001714 | Diseño de vigas y pilares de madera según NDS 2018 utilizando el módulo RF-/TIMBER AWC