N D S 2018 3 7 Solid Column
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NDS 2018 3.7 Solid column

The scope of this module is to calculate the sawn lumber nominal column compression capacity. The building code subsections required include:

  • NDS 2018 Section 3.7 Solid Columns
  • NDS 2018 Section 3.10 Design for Bearing
  • NDS 2018 Section 4 Sawn Lumber.
  • NDS 2018 Supplement Table 4B and 4D Adjustment Factors and Reference Design Values

Assumptions and limitations

  • ASD method
  • Douglas Fir No 2 Grade
  • Compression only with no eccentricity
  • Compression and bearing parallel to the grain
  • Column unbraced along entire height ie, interior column (posts)
  • Column end condition pin-pin (effective length factor Ke = 1.0)
  • Square or rectangular column without taper along the length of the section
  • No notching in the section
  • Column slenderness ratio KeL/d <= 50

Design Codes

Inputs parameters

Design Geometry Input

  • L = length of the post in ft. This is usually the story height of the building.
  • b[in]: Rectangular dimension 1.
  • a[in]: Rectangular dimension 2.

Material Properties Input

Take these parameters from NDS_2018/4_2_ReferenceDesignValues

Compression parallel to grain reference design value

  • \(F_c\) : Compression parallel to Grain, recommended for Douglas Fir Larch = 850 psi (2018 NDS Supplement, 2021).

  • Emin: Minimum modulus of Elasticity, recommended for Douglas Fir Larch = 510000 psi (2018 NDS Supplement, 2021).

Wood adjustment factors

Take these parameters from: NDS_2018/4_3_AdjustmentOfReferenceDesignValues.md

  • \(C_D \) : Load duration factor. Recommended value: 1 for D+L combination. Refer to (2018 NDS, 2018) - Section 2.3.2 for more information.

  • \(C_M \) : Wet service factor. Recommended value: 1 for moisture content less than 19% for an extended time period. Refer to (2018 NDS, 2018) - Section 4.3.3 for more information.

  • \(C_t \) : Temperature factor. Recommended value: 1 for not exposed to temperatures larger than 150 F. Refer to (2018 NDS, 2018) - Section 4.3.4 for more information.

  • \(C_F \) : Size factor. Recommended value: 1 to be conservative. Refer to (2018 NDS, 2018) - Section 4.3.6 for more information.

  • \(C_i \) : Incising factor. Recommended value: 1 for not incised. Refer to (2018 NDS, 2018) - Table 4.3.8 for more information.

  • \(C_T \) :Buckling stiffness factor. Recommended value: 1 to be conservative because it is only required for 2x4s or smaller members of wood trusses.

  • \(c \) : c factor to compute stability factor. Refer to (2018 NDS, 2018) - Section 3.7.1.5 for more information.

Calculations

Calculate the sectional area

  • \(A_g \) = a * b

Calculate maximum slenderness

  • \({(\frac{l_e}{d})} \) = min [L/min (a,b), 50]

Column Stability factor

  • \(CP = \left(\frac{{1+\frac{{F_{\text{cE}}}}{{F*_{\text{c}}}}}}{{2 \cdot c}}\right) - \sqrt{\left(\left(\frac{{1+\frac{{F_{\text{cE}}}}{{F*_{\text{c}}}}}}{{2 \cdot c}}\right)^2 - \frac{{\frac{{F_{\text{cE}}}}{{F*_{\text{c}}}}}}{{c}}\right)} \) : column stability factor, (2018 NDS, 2018) - Eq. 3.7.1,

Where:

  • \(F_{\text{cE}} = \frac{0.822 \cdot E'_{\text{min}}}{(\frac{l_e}{d})^2} \)
  • \(F*_{\text{c}} = F_{\text{c}} \cdot C_D \cdot C_M \cdot C_t \cdot C_F \cdot C_i \) [lb/in²] adjusted ASD compressive design value parallel to grain without Cp.

Maximum axial bearing stress

  • \(Fbearing_{\text{c}} = 0.75 F*_{\text{c}} \)

Adjusted compressive stress parallel to grain

  • \(F'_{\text{c}} = F_{\text{c}} \cdot C_D \cdot C_M \cdot C_t \cdot C_F \cdot C_P \cdot C_i \) [lb/in²] adjusted ASD compressive design value parallel to grain.

Maximum axial stress allowed for the column

  • \(MaxAxialStress = min(Fbearing_{\text{c}},F'_{\text{c}}) \)

Compression Capacity

  • \(Pc = {A_g} * {MaxAxialStress} \) [in²] actual compressive capacity parallel to grain on center.

Output Results

  • Compression Capacity

References

2018 NDS. (2018). American Wood Council. https://awc.org/publications/2018-nds/

2018 NDS Supplement. (2021). American Wood Council. https://awc.org/publications/2018-nds-supplement/

ASCE 7-22. (2021). https://www.asce.org/publications-and-news/civil-engineering-source/article/2021/12/02/updated-asce-7-22-standard-now-available

Breyer, D. E., Cobeen, K. E., & Martin, Z. (2017). Design of Wood Structures ASD/LRFD Eighth Edition. https://shop.iccsafe.org/design-of-wood-structures-asd-lrfd-eighth-edition.html

Validation

Several validations were performed: