木结构梁柱设计按照 NDS 2018 使用 RF-/TIMBER AWC 模块

The member is a No. 2 Southern Pine, 2x4 nominal, 3 feet long and used as a truss member. 只在杆件末端提供侧向支座，并且认为它们是固定的。 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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木柱

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

锯材2x4的截面属性

南部松木的材料属性

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.

有效长度CL系数

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.

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

调整系数选项

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:
  $${\mathrm{F}}_{\mathrm{cEx}} = {\mathrm{F}}_{\mathrm{cE}1} = \frac{0.822 · {\mathrm{E}}_{\min }\text{'}}{{\left[{\displaystyle \frac{{\mathrm{l}}_{\mathrm{e}1}}{{\mathrm{d}}_1}}\right]}^2}$$

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

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

  [F12] F cEx	受压杆件沿强轴的临界屈曲设计值, psi
  Emin'	= E分钟⋅CM⋅（CT）⋅CI = 510000磅
  le1	有效长度= 36.0 in
  [SCHOOLTRAINING.NUMBEROFSTUDENTS]1	杆件深度 = 3.5"

  受压杆件强轴临界屈曲设计值 FcEx
• Critical Buckling Design Value for Compression Member in Weak Axis, F_cEy:
  $${\mathrm{F}}_{\mathrm{cEy}} = {\mathrm{F}}_{\mathrm{cE}2} = \frac{0.822 · {\mathrm{E}}_{\min }\text{'}}{{\left[{\displaystyle \frac{{\mathrm{l}}_{\mathrm{e}2}}{{\mathrm{d}}_2}}\right]}^2}$$

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

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

  [F12] F	受压杆件弱轴临界屈曲设计值, psi
  Emin'	= E分钟⋅CM⋅（CT）⋅CI = 510000磅
  le2	有效长度= 36.0 in
  d2	杆件厚度 = 1.5"

  受压杆件弱轴临界屈曲设计值, FcEy
• Adjusted Compressive Design Value Parallel to Grain, F_c':
  $${\mathrm{F}}_{\mathrm{c}}\text{'} = {\mathrm{F}}_{\mathrm{cy}}\text{'} = {\mathrm{F}}_{\mathrm{c}} · {\mathrm{C}}_{\mathrm{D}} · {\mathrm{C}}_{\mathrm{M}} · {\mathrm{C}}_{\mathrm{t}} · {\mathrm{C}}_{\mathrm{F}} · {\mathrm{C}}_{\mathrm{i}} · {\mathrm{C}}_{\mathrm{P}}$$

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

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

  [F7]c'	调整的顺纹抗压设计值, psi
  Fc	顺纹方向抗压设计值, psi
  CD	荷载作用持续时间系数
  CM	湿度系数
  Ct	温度系数
  CF	尺寸系数
  Ci	切入系数
  CP	柱子稳定系数

  调整后的竖向抗压设计值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	受弯杆件的临界屈曲设计值, psi
  Emin'	= E分钟⋅CM⋅（CT）⋅CI = 510000磅
  RB	长细比 = 9.65 < 50（NDS 公式 3.3-5）

  弯曲杆件屈曲临界设计值FbE
• Adjusted Strong Axis Bending Design Value, F_bx':
  $${\mathrm{F}}_{\mathrm{bx}}\text{'}= {\mathrm{F}}_{\mathrm{b}1} = {\mathrm{F}}_{\mathrm{b}} · {\mathrm{C}}_{\mathrm{D}} · {\mathrm{C}}_{\mathrm{M}} · {\mathrm{C}}_{\mathrm{L}} · {\mathrm{C}}_{\mathrm{t}} · {\mathrm{C}}_{\mathrm{F}} · {\mathrm{C}}_{\mathrm{i}} · {\mathrm{C}}_{\mathrm{r}}$$

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

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

  [F7]bx'	调整的长轴弯曲设计值，psi
  Fb	折弯参照设计值psi
  CD	荷载作用持续时间系数
  CM	湿度系数
  CL	梁稳定性系数
  Ct	温度系数
  CF	尺寸系数
  Ci	切入系数
  Cr	杆件均布作用系数

  调整的强轴弯矩设计值 Fbx'
• Adjusted Weak Axis Bending Design Value, F_by':
  $${\mathrm{F}}_{\mathrm{by}}\text{'} = {\mathrm{F}}_{\mathrm{b}2} = {\mathrm{F}}_{\mathrm{b}} · {\mathrm{C}}_{\mathrm{D}} · {\mathrm{C}}_{\mathrm{M}} · {\mathrm{C}}_{\mathrm{L}} · {\mathrm{C}}_{\mathrm{t}} · {\mathrm{C}}_{\mathrm{fu}} · {\mathrm{C}}_{\mathrm{F}} · {\mathrm{C}}_{\mathrm{i}} · {\mathrm{C}}_{\mathrm{r}}$$

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

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

  [F7]by'	调整的弱轴弯曲设计值，psi
  Fb	折弯参照设计值psi
  CD	荷载作用持续时间系数
  CM	湿度系数
  CL	梁稳定性系数
  Ct	温度系数
  Cfu	平整系数
  CF	尺寸系数
  Ci	切入系数
  Cr	杆件均布作用系数

  ' 调整的弱轴弯矩设计值 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.

设计利用率

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木结构梁柱

知识库

KB 001714 | 使用RF-/TIMBER AWC模块按照NDS 2018木木柱设计