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001848

Alex Bacon, EIT

2024-02-14

RFEM 6 中的 2018 NDS 木柱柱设计

使用“木结构设计”模块，可以按照 2018 NDS 标准 ASD 方法进行木柱设计。准确计算木杆件的抗压承载力和调整系数对于安全考虑和设计非常重要。下面的文章将按照 NDS 2018 标准，使用逐步的解析方程验证“木结构设计”模块计算的最大临界屈曲强度，包括受压调整系数、调整后的抗压设计值和最终设计比率。

A 10 foot, nominal 8 inch ⋅ 8 inch Alaska Cedar Select Structural column with an axial load of 30.00 kips will be designed. 这种分析的目的是确定调整后的柱子的压缩系数和抗压设计值。 A normal load duration and pinned supports at each end of the member are assumed. The loading criteria are simplified for this example. Normal loading criteria can be referenced in Sec. 1.4.4 [1]. In Image 01 and 02 is a diagram of the simple column and section properties respectfully.

知识库 001848 | 在 RFEM 6 中按照 2018 NDS 标准进行木柱设计

木柱模型

截面属性

Column Properties

The cross-section used in this example is an 8 inch square post. The cross-section properties of the timber column are shown below:

b = 7.50 in, d = 7.50 in, L = 10.00 ft

Gross cross-section area:

A_g = b ⋅ d = 7.50 in ⋅ 7.50 in = 56.25 in²

截面模量:

$S_{x} = \frac{b \cdot d^{2}}{6} = \frac{(7.50 in) \cdot {(7.50 in)}^{2}}{6} = 70.30 {in}^{3}$

截面模量

Moment of inertia:

$I_{x} = \frac{b \cdot d^{3}}{12} = \frac{(7.50 in) \cdot {(7.50 in)}^{3}}{12} = 263.70 {in}^{4}$

惯性矩

The material used is "Alaska Cedar, 5"x5" and Larger, Beam and Stringer, Select Structural". The material properties are as follows:

Reference compression design value:

F_c = 925 psi

Minimum modulus of elasticity:

E_min = 440 ksi

Column Adjustment Factors

For the design per the 2018 NDS standard and the ASD method, stability factors (or adjustment factors) must be applied to the compressive design value (f_c). This will ultimately provide the adjusted compressive design value (F'_c). The factor F'_c is calculated with the following equation, highly dependent on the listed adjustment factors from Table 4.3.1 [1]:

F'_c = F_c ⋅ C_D ⋅ C_M ⋅ C_t ⋅ C_f ⋅ C_i ⋅ C_P

Below, each adjustment factor is determined:

C_D – The load duration factor is implemented to take into account different periods of loading. Snow, wind, and earthquakes are taken into account with C_D. This factor must be multiplied by all reference design values except for the modulus of elasticity (E), modulus of elasticity for beam and column stability (E_min), and the compression forces perpendicular to the grain (F_c) based on Sec. 4.3.2 [1]. C_D in this case is set to 1.00 as per Sec. 2.3.2 [1] assuming a load duration of 10 years.

C_M – The wet service factor references design values for structural sawn lumber based on moisture service conditions specified in Sec. 4.1.4 [1]. In this case, based on Sec. 4.3.3 [1], C_M is set to 0.910.

C_t – The temperature factor is controlled by a member's sustained exposure to elevated temperatures up to 150 degrees Fahrenheit. All reference design values will be multiplied by Ct. Utilizing Table 2.3.3 [1], C_t is set to 1.00 for all reference design values, assuming temperatures are equal to or lesser than 100 degrees Fahrenheit.

C_F – The size factor for sawn lumber does not consider wood as a homogeneous material. The size of the column and type of wood are taken into account. For this example, our column has a depth lesser than or equal to 12 inches. Referencing Table 4D based on the size of the column, a factor of 1.00 is applied. This info can be found in Sec. 4.3.6.2 [1].

C_i – The incising factor considers the preservation treatment applied to the wood to resist decay and avoid fungal growth. Most of the time this involves pressure treatment, but in some cases requires the wood to be incised increasing the surface area for chemical coverage. For this example, we will be assuming the wood is incised. Referencing Table 4.3.8 [1], an overview of the factors by which each member property must be multiplied is shown.

Adjusted Modulus of Elasticity

The reference modulus of elasticity values (E and E_min) must also be adjusted. The adjusted modulus of elasticity (E' and E'_min) are determined from Table 4.3.1 [1] and the incising factor C_i is equal to 0.95 from Table 4.3.8 [1].

E' = E ⋅ C_M ⋅ C_t ⋅ C_i = 1,140,000.00 psi

E'_min = E_min ⋅ C_M ⋅ C_t ⋅ C_i = 418,000.00 psi

Column Stability Factor (C_P)
The column stability factor (C_P) is needed in order to calculate the column's adjusted compressive design value and the compressive design ratio. The following steps will include the necessary equations and values to find C_P.

The equation used to calculate C_P is Eqn. (3.7-1) referenced in Section 3.7.1.5. The reference compression design value parallel to grain (F_c) is required and calculated below:

F'_c = F_c ⋅ C_D ⋅ C_M ⋅ C_t ⋅ C_F ⋅ C_i = 673.40 psi

The next value that needs to be calculated in Eqn. (3.7-1) is the critical buckling design value for compression members (F_cE).

$F_{cE} = \frac{0.822 E'_{\min}}{{(\frac{l_{e}}{d})}^{2}}$

受压杆件的临界屈曲设计值

The slenderness ratio is calculated as so:

$\frac{l_{e}}{d} = 16$

长细比

The slenderness ratio is applied to the equation for F_cE and the following value is calculated:

F_cE = 1342.17 psi

The last variable needed is (c), which is equal to 0.8 for sawn lumber. All of the variables can be applied to Eqn. (3.7-1) and the following value is calculated for C_P.

$C_{P} = \frac{1 (\frac{F_{cE}}{F_{c} *})}{2 c} - \sqrt{{[\frac{1 (\frac{F_{cE}}{F_{c} *})}{2 c}]}^{2} - \frac{(\frac{F_{cE}}{F_{c} *})}{c}} = 0.866$

柱子稳定系数

Now, all adjustment factors have been determined from Table 4.3.1 [1]. Therefore, the adjusted compressive design value parallel to grain (F'_c) can be calculated.

F'_c = F_c ⋅ C_D ⋅ C_M ⋅ C_t ⋅ C_F ⋅ C_i ⋅ C_P = 583.602 psi

Column Design Ratio

The ultimate goal of this example is to obtain the design ratio for this simple column. This will determine if the member size is adequate under the given load or if it should be further optimized. Calculating the design ratio requires the adjusted compressive design value parallel to the grain about both axes (F'_c) and actual compressive stress parallel to the grain (f_c). In this case, the cross-section is symmetrical, so F'_c is equivalent for both the x- and the y-axis.

The actual compressive stress (f_c) is calculated below:

$f_{c} = \frac{P}{A} = \frac{30 kip}{56.25 in ²} = 533.33 psi$

顺纹方向压应力

The adjusted compressive design value parallel to the grain (F'_c) and the actual compressive stress (f_c) are used to compile the design ratio (η) as per Sec. 3.6.3.

$η = \frac{f_{c}}{F'_{c}} \cdot η = \frac{533.33 psi}{583.602 psi} \cdot η = 0.913$

柱子利用率

RFEM 6 Verification

When designing timber per the 2018 NDS standard in RFEM 6, the Timber Design Add-on analyzes and optimizes cross-sections based on loading criteria and member capacity for a single member or a set of members. This is available for either LRFD or ASD design methods. The results between the analytical example and RFEM 6 are compared and verified below.

Editing the Member is where the Design Properties like the Effective Lengths, Service Conditions, Design Configurations and Design Supports can be adjusted for design. The material and cross-section are defined here as well. The moisture service condition is set to Wet and the temperature is equal to or less than 100 degrees Fahrenheit. Lateral-Torsional Buckling is defined according to Table 3.3.3 [1]. The material is set to "User-Defined" and considered "Incised".

Adjusted Compression Design Value Parallel to Grain:

F'_c = 1.000

Design Ratio:

η = 1.000

RFEM 6 – 木结构设计计算结果

作者

Alex 负责北美市场的客户培训、技术支持和持续的程序开发。

参考

National Design Specification (NDS) for Wood Construction 2018 Edition

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