Progettazione di pilastri in legno secondo NDS 2018 utilizzando il modulo AWC RF-/TIMBER

L'asta è un pino del sud nr. 2, 2x4 nominale, lungo 3 piedi e utilizzato come asta di travatura reticolare. 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.

• 3D Viewer | Google
• 3D Viewer | Babylon
• Realtà virtuale

Colonna di legno

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

Proprietà della sezione trasversale del legno segato 2x4

Proprietà del materiale del pino meridionale

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.

Lunghezza efficace per il coefficienteC 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.

Opzione per i coefficienti di aggiustamento

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	Valore critico di progetto per l'instabilità per l'asta compressa nell'asse maggiore, psi
  Emin'	= Emin ⋅ CM ⋅ CT ⋅ Ci = 510.000 psi
  le1	Lunghezza efficace = 36,0 pollici
  d1	Altezza dell'asta = 3,5 pollici

  Valore di progetto di instabilità critica per l'asta compressa nell'asse maggiore, 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	Valore critico di progetto per l'instabilità per l'asta compressa nell'asse minore, psi
  Emin'	= Emin ⋅ CM ⋅ CT ⋅ Ci = 510.000 psi
  le2	Lunghezza efficace = 36,0 pollici
  d2	Spessore dell'asta = 1,5 pollici

  Valore di progetto di instabilità critica per l'asta compressa nell'asse minore, FcEy
• Adjusted Compressive Design Value Parallel to Grain, F_c':
  $${\mathrm{F}}_{\mathrm{c}}\text{'} = {\mathrm{F}}_{\mathrm{cy}}\text{'} = {\mathrm{F}}_{\mathrm{c}} · {\mathrm{C}}_{\mathrm{D}} · {\mathrm{C}}_{\mathrm{M}} · {\mathrm{C}}_{\mathrm{t}} · {\mathrm{C}}_{\mathrm{F}} · {\mathrm{C}}_{\mathrm{i}} · {\mathrm{C}}_{\mathrm{P}}$$

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

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

  [F9]c'	Valore di progetto della compressione regolato parallelo alla fibratura, psi
  fC	Valori di progetto di compressione di riferimento paralleli alla fibratura, psi
  CD	Coefficiente di durata del carico
  CM	Coefficiente di umidità di esercizio
  Ct	Coefficiente di temperatura
  CF	Coefficente dimensionale
  Ci	Coefficiente di incisione
  CP	Coefficiente di stabilità della colonna

  Valore di progetto della compressione modificato in direzione della fibratura, 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	Valore critico di progetto per l'instabilità per l'asta flettente, psi
  Emin'	= Emin ⋅ CM ⋅ CT ⋅ Ci = 510.000 psi
  RB	Rapporto di snellezza = 9.65 < 50 (equazione NDS 3.3-5)

  Valore critico di progetto dell'instabilità per asta flettente, 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'	Valore di progetto della flessione dell'asse maggiore modificato, psi
  Fb	Valore di riferimento del progetto di piegatura, psi
  CD	Coefficiente di durata del carico
  CM	Coefficiente di umidità di esercizio
  CL	Coefficiente di stabilità della trave
  Ct	Coefficiente di temperatura
  CF	Coefficente dimensionale
  Ci	Coefficiente di incisione
  Cr	Coefficiente dell'asta ripetitiva

  Valore di progetto di flessione dell'asse maggiore modificato, 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'	Valore di progetto della flessione dell'asse minore modificato, psi
  Fb	Valore di riferimento del progetto di piegatura, psi
  CD	Coefficiente di durata del carico
  CM	Coefficiente di umidità di esercizio
  CL	Coefficiente di stabilità della trave
  Ct	Coefficiente di temperatura
  Cfu	Coefficiente di sbandamento laterale
  CF	Coefficente dimensionale
  Ci	Coefficiente di incisione
  Cr	Coefficiente dell'asta ripetitiva

  Valore di progetto di flessione dell'asse minore modificato, 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.

rapporto di verifica

• 3D Viewer | Google
• 3D Viewer | Babylon
• Realtà virtuale

Colonna in trave di legno

Knowledge Base

KB 001714 | Progettazione di colonne di legno secondo NDS 2018 utilizzando il modulo AWC RF-/TIMBER