Wymiarowanie drewnianych belek i słupów zgodnie z NDS 2018 przy użyciu modułu RF-/TIMBER AWC

Pręt to sosna południowa nr 2, nominalna 2x4 i długości 3 stóp, użyta jako pręt kratownicowy. 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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Słup drewniany

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

Właściwości przekroju poprzecznego tarcicy 2x4

Właściwości materiałowe sosny południowej

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.

Długość efektywna dla współczynnikaC 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.

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

Możliwość zastosowania współczynników korygujących

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	Wartość obliczeniowa wyboczenia krytycznego dla pręta ściskanego względem osi mocnej, psi
  Emin'	= Emin ⋅ CM ⋅ CT ⋅ Ci = 510000 psi
  le1	Długość efektywna = 36,0 cali
  d1	Głębokość pręta = 3.5 in

  Krytyczna wartość obliczeniowa wyboczenia dla pręta ściskanego w osi mocnej, 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	Wartość obliczeniowa wyboczenia krytycznego dla pręta ściskanego w osi słabej, psi
  Emin'	= Emin ⋅ CM ⋅ CT ⋅ Ci = 510000 psi
  le2	Długość efektywna = 36,0 cali
  d2	Grubość pręta = 1,5 in

  Krytyczna wartość obliczeniowa wyboczenia dla pręta ściskanego względem osi słabej, 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'	Skorygowana obliczeniowa nośność na ściskanie równolegle do włókien, psi
  fC	Referencyjne wartości obliczeniowe na ściskanie równolegle do włókien, psi
  CD	Współczynnik czasu trwania obciążenia
  CM	Współczynnik użytkowania w warunkach mokrych
  Ct	Współczynnik temperaturowy
  CF	Współczynnik rozmiaru
  Ci	Współczynnik nacinania
  CP	Współczynnik stateczności słupa

  Skorygowana wartość obliczeniowa ściskania w kierunku włókien, 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	Wartość obliczeniowa wyboczenia krytycznego dla zginanego pręta, psi
  Emin'	= Emin ⋅ CM ⋅ CT ⋅ Ci = 510000 psi
  RB	Smukłość = 9,65 < 50 (równanie NDS 3.3-5)

  Krytyczna obliczeniowa wartość wyboczenia dla pręta zginanego, 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'	Skorygowana wartość obliczeniowa zginania względem osi mocnej, psi
  Fb	Obliczeniowa wartość odniesienia zginania, psi
  CD	Współczynnik czasu trwania obciążenia
  CM	Współczynnik użytkowania w warunkach mokrych
  CL	Współczynnik stateczności belki
  Ct	Współczynnik temperaturowy
  CF	Współczynnik rozmiaru
  Ci	Współczynnik nacinania
  Cr	Współczynnik dla działania ciągłego

  Skorygowana wartość obliczeniowa zginania względem osi mocnej, 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'	Skorygowana wartość obliczeniowa zginania osi słabej, psi
  Fb	Obliczeniowa wartość odniesienia zginania, psi
  CD	Współczynnik czasu trwania obciążenia
  CM	Współczynnik użytkowania w warunkach mokrych
  CL	Współczynnik stateczności belki
  Ct	Współczynnik temperaturowy
  Cfu	Współczynnik stosowania na płasko
  CF	Współczynnik rozmiaru
  Ci	Współczynnik nacinania
  Cr	Powtarzający się współczynnik pręta

  Skorygowana wartość obliczeniowa zginania względem osi słabej, 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.

Stopień wykorzystania

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Słup z drewnianej belki

Baza informacji

KB 001714 | Wymiarowanie belek drewnianych zgodnie z NDS 2018 z wykorzystaniem modułu RF-/TIMBER AWC