N D S 2018 3 5 Bending Members Deflection
  2. Spreadsheets
  3. Beams
  4. N D S 2018 3 5 Bending Members Deflection

NDS 2018 Section 3.5 Bending Member - Deflection

The scope of this module is to calculate the sawn lumber beam deflection capacity. The building code subsections required include:

  • NDS 2018 Section 3.2 Bending Members - General
  • NDS 2018 Section 3.5 Bending Members - Deflection
  • 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 only
  • Rectangular section, not notched or tapered
  • Supported beam with uniformly distributed load
  • Beam stability requirements in NDS 2018 Section 4.4.1.2 must be met
  • Beam sizes limited to 6”, 8”, 10”, 12”, 14”
  • Time-dependent deformation (creep) factor, Kcr, assumed to be 2.0.

Design Codes

  • AWC-NDS (2018), National Design Specification (NDS) for Wood Construction 2018 Edition. American Wood Council, Leesburg, VA.
  • AWC-NDS (2021), National Design Specification (NDS) Supplement: Design Values for Wood Construction 2018 Edition. American Wood Council, Leesburg, VA.

Inputs parameters

Design Loads

  • \( M [kip-ft] \) : Maximum Moment acting on the beam per structural analysis using ASD combinations.

Design Geometry Input

  • b[in]: Rectangular dimension 1.
  • d[in]: Rectangular dimension 2.
  • L[ft]: Clear span length

Material Properties Input

Modulus of elasticity

Take these values from Reference Design Values

  • \(E [psi]\) : Modulus of elasticity value

Wood adjustment factors

TTake these parameters from Adjustment Values

  • \(C_M \) : 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.

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

Calculations

Calculate the section modulus

\( S [in3] \) is calculated below:

\[ S = \frac{b \cdot d^2}{6} \]

Adjusted shear capacity

Adjusted elastic modulus capacity \( E' [psi] \) is calculated as below:

\[ E' = E \cdot C_M \cdot C_t \cdot C_i \]

Deflection Check

Deflection demand \( Def_{a} [in] \)

\[ Def_{a} = \frac{1.2 \cdot 5 \cdot M \cdot L^2}{24E' \cdot S \cdot d}\]

Output Results

  • Deflection demand, [in]

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/

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: