Webinar Slides | Wood Beam Design to NDS 2018 | ClearCalcs

Designing a Wood Beam per the
NDS 2018
Discovering different wood products and their
design process
Laurent Gérin, EIT
laurent.gerin@clearcalcs.com
Brooks H. Smith, PE, CPEng, MIEAust, NER
brooks.smith@clearcalcs.com

Outline
• Introduction
• Wood Products
• Adjustment Factors
• Designing a Wood Beam
• Flexural Capacity
• Shear Capacity
• Bearing Capacity
• Deflection
• Example Beam Calculations
• Conclusion & Questions
218 March 2020 ClearCalcs.com | FEA Structural Design in the Cloud

• Structural Lead in North America for ClearCalcs
• Responsible for development of design
calculators in United States and Canada
• Previous experience in:
• Structural diagnostics & restoration engineering
• Structural aluminum design
• Bridge repair and construction
• Currently pursuing a Masters in structural
engineering at the University of Waterloo
ClearCalcs.com | FEA Structural Design in the Cloud 3
Introduction – About the Presenters
Laurent Gérin
18 March 2020
• Currently the Engineering Development
Lead for ClearCalcs
• Chartered Professional Engineer
• MCivE, MIEAust, NER, P.E. (USA)
• 8 years of previous experience in:
• Structural engineering R&D consulting,
specialising in cold-formed steel
• Research fellowship in system behaviour of
thin-walled steel
• Forensic structural engineering, specialising
in reinforced and PT concrete
Brooks H. Smith

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Intro Video Hyperlink
18 March 2020

Introduction – Today’s Goals
• To be able to design a wood beam to NDS 2018
• Different product types (lumber, glulam, SCL)
• Understand various adjustment factors for design
• The design process with wood
• We’ll distribute this slide deck and video after the webinar
• Please ask quick questions as we go – best to answer while on
the topic
• Please ask using the “Q&A” feature, NOT the chat/messaging feature
• We’ll save involved questions until the end

Outline
• Introduction
• Wood Products
• Shear Capacity
• Deflection

Wood
• High strength to weight ratio
• Very low ductility – rely on steel connections and redundancy
• Sustainable and environmentally friendly
• Bigger and bigger buildings using it
ThinkwoodWikipedia – Wood Framing
18 March 2020

Wood Products
• We’ll cover 3 common types of wood products
• Sawn lumber
• Glulam
• Structural Composite Lumber (SCL)
• Other products exist!
• Prefabricated wood I-joists
• Prefabricated trusses
• Structural panels (e.g. plywood)
• Cross-laminated timber (CLT)
ClearCalcs.com | FEA Structural Design in the Cloud 818 March 2020
Boise Cascade

Sawn Lumber
• Most common wood product
• Visually graded between Select Structural, No.1, No.2, Stud
• Can also get machine graded lumber
• Comes in many different species with varying properties
• Inexpensive, but comes with high variability of properties
Secret Life of the Forest – Richard M. Ketchum
Menards

Glulam
• Made from multiple sawn lumber laminations glued together
• Allows using lower grade laminations in low stress areas
• Weaker in negative moment, unless balanced section is specified
• No limit on size and depth
• Can be cambered and bent to create arches
American Laminators
18 March 2020
Boise Glulam

Structural Composite Lumber (SCL)
• Often seen as laminated veneer lumber (LVL), parallel strand
lumber (PSL) or laminated strand lumber (LSL)
• Non-standardized, data available from manufacturers
• Very high strength and low variability
LVL PSL LSL
APA – Engineered Wood Association
18 March 2020

The NDS 2018 Code
• Used for most wood design in buildings
• Includes provisions for sawn lumber, glulam, structural
composite panels (SCL)
• Includes ASD and LRFD provisions
• The NDS 2018 Supplement provides design values
• Lateral load systems covered in separate standard
(Special Design Provisions for Wind and Seismic)
• Available for free online
• https://www.awc.org/codes-
standards/publications/nds-2018 (click on free view-
only download)

Outline
• Introduction
• Wood Products
• Shear Capacity
• Deflection

Designing a Wood Beam
• Calculate your demands with ASCE 7 / local building code
• ASD vs LRFD
• Determine material and design conditions
• Limit states which must be checked:
• Flexural capacity
• Shear capacity
• Bearing capacity
• Deflection

Design Philosophy
• Applied stresses should be less than adjusted allowable stresses
• E.g. in shear (ASD): 𝑓𝑓𝑣𝑣 = 1.5
𝑉𝑉
𝐴𝐴
≤ 𝐹𝐹𝑣𝑣
′
= 𝐹𝐹𝑣𝑣 𝐶𝐶𝐷𝐷 𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡 𝐶𝐶𝑖𝑖
• In LRFD design, typically expressed in terms of loads and
adjusted capacities
• E.g. for shear: 𝑉𝑉𝑢𝑢 ≤ 𝜙𝜙𝑉𝑉𝑛𝑛 =
2
3
� 𝜙𝜙𝑣𝑣 𝐹𝐹𝑣𝑣 𝐾𝐾𝐹𝐹 𝜆𝜆𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡 𝐶𝐶𝑖𝑖 � 𝐴𝐴
• Different products have different factors – respective chapters
in NDS 2018 have tables to guide what factors to apply

Load Duration Factor (𝑪𝑪𝑫𝑫 or 𝝀𝝀)
• Wood strength increases significantly when load has a short
duration, and decreases for sustained loads
• Can usually divide demands from respective load combination by
load duration factor – except for bending and compression
• This factor varies between ASD and LRFD
• ASD (𝐶𝐶𝐷𝐷): based on duration of shortest load in load combination
• LRFD (𝜆𝜆): directly based on load combination

Wet Service and Temperature factors
• Wood weakens when it is wet or at high temperature
• Wet service factor (𝐶𝐶𝑀𝑀) depends on wood product type
• Can take away significant strength (up to 50% reduction!)
• Definition of “wet” depends on product type!
• Usually, SCL is not used in wet conditions
• Temperature factor is universal for all product types, depends on
moisture conditions

Size, Volume, and Flat Use Factors
• Size factor (𝐶𝐶𝐹𝐹) is used in visually graded dimension lumber and
timbers
• Accounts for the size effect, where larger-sized members typically
exhibit lower strength
• Specified in the NDS 2018 Supplement
• Volume factor (𝐶𝐶𝑉𝑉) is the equivalent of the size factor for glulam
and SCL members
• Considers total volume of member instead of just cross-section shape
• Flat use factor (𝐶𝐶𝑓𝑓𝑓𝑓) increases the strength of dimension lumber
and glulam, and decreases the strength of timbers
• Specified in the NDS 2018 Supplement

LRFD Factors
• Values in the NDS 2018 Supplement are for ASD and already
include safety factors
• Format conversion factor 𝐾𝐾𝐹𝐹 brings strengths back to nominal
values
• Varies between 1.67 (bearing) and 2.88 (shear)
• Resistance factor 𝜙𝜙 is similar to other materials
• Accounts for variability of strength, assumptions, failure mode, etc.
• Varies between 0.75 (shear) and 0.90 (compression)

Other Factors
• Repetitive member factor (𝐶𝐶𝑟𝑟)
• Accounts for load distribution and higher redundancy in typical
structural systems with dimension lumber
• Incising factor (𝐶𝐶𝑖𝑖)
• Some wood species are harder to treat and incisions are made to
increase the depth of preservative, which affects strength
• Buckling stiffness factor (𝐶𝐶𝑇𝑇)
• Applies to truss members – not covered in this webinar
• Curvature and stress interaction factors (𝐶𝐶𝑐𝑐 and 𝐶𝐶𝐼𝐼)
• Used in curved or tapered glulam members – not covered in this
webinar

Bending
• Based on the basic bending equation
• Not based on plastic modulus!
• Lateral-torsional buckling must be considered
𝑆𝑆 =
𝑏𝑏ℎ2
6
ASD LRFD
𝑓𝑓𝑏𝑏 ≤ 𝐹𝐹𝑏𝑏
′
𝑀𝑀𝑢𝑢 ≤ 𝜙𝜙𝑀𝑀𝑛𝑛
𝑓𝑓𝑏𝑏 = 𝑀𝑀/𝑆𝑆 𝜙𝜙𝑀𝑀𝑛𝑛 = 𝐹𝐹𝑏𝑏
′
𝑆𝑆
𝐹𝐹𝑏𝑏
′
= 𝐹𝐹𝑏𝑏 𝐶𝐶𝐷𝐷 𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡 𝐶𝐶𝐿𝐿 𝐶𝐶𝐹𝐹 𝐶𝐶𝑓𝑓𝑓𝑓 𝐶𝐶𝑖𝑖 𝐶𝐶𝑟𝑟 (sawn lumber)
𝐹𝐹𝑏𝑏
′
= 𝐹𝐹𝑏𝑏 𝐶𝐶𝐷𝐷 𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡(𝐶𝐶𝐿𝐿 𝑜𝑜𝑜𝑜 𝐶𝐶𝑣𝑣) (glulam and SCL)
𝐹𝐹𝑏𝑏
′
= 𝜙𝜙𝑏𝑏 𝐾𝐾𝐹𝐹 𝐹𝐹𝑏𝑏 𝜆𝜆𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡 𝐶𝐶𝐿𝐿 𝐶𝐶𝐹𝐹 𝐶𝐶𝑓𝑓𝑓𝑓 𝐶𝐶𝑖𝑖 𝐶𝐶𝑟𝑟 (sawn lumber)
𝐹𝐹𝑏𝑏
′
= 𝜙𝜙𝑏𝑏 𝐾𝐾𝐹𝐹 𝐹𝐹𝑏𝑏 𝜆𝜆𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡(𝐶𝐶𝐿𝐿 𝑜𝑜𝑜𝑜 𝐶𝐶𝑣𝑣) (glulam and SCL)

Bending – Lateral Stability
• One more factor! Beam stability factor 𝐶𝐶𝐿𝐿
• Accounts for lateral-torsional buckling
• Effective length method is used in code
• Works for most typical situations
• Very conservative for nonstandard loading conditions
• No guidance for continuous beams
• Alternative solution is detailed in AWC TR14
• Essentially, same LTB calculations as in steel code
• Used by ClearCalcs
• https://www.awc.org/pdf/codes-standards/publications/tr/AWC-TR14-0312.pdf
http://alohonyai.blogspot.com/2018/04/geometry-of-joist-bridging.html

• Get effective length from Table 3.3.3
• Based on loading conditions and unbraced length
• Find slenderness ratio: 𝑅𝑅𝐵𝐵 =
ℓ𝑒𝑒 𝑑𝑑
𝑏𝑏2
• Must be less than 50

• Find elastic buckling stress 𝐹𝐹𝑏𝑏𝑏𝑏 =
1.20𝐸𝐸min
′
𝑅𝑅𝐵𝐵
2
• 𝐸𝐸min
′
is also adjusted!
• Find the nominal section strength 𝐹𝐹𝑏𝑏
∗
using every factor except
the beam stability factor (and 𝐶𝐶𝑉𝑉 for glulam)
• Use equation 3.3-6 to find factor:
𝐶𝐶𝐿𝐿 =
1 +
𝐹𝐹𝑏𝑏𝑏𝑏
𝐹𝐹𝑏𝑏
∗
1.9
−
1 +
𝐹𝐹𝑏𝑏
∗
1.9
2
−
𝐹𝐹𝑏𝑏
∗
0.95

Bending – Volume Factor
• Glulam beams have a volume factor 𝐶𝐶𝑉𝑉
• Not applied at the same time as 𝐶𝐶𝐿𝐿
• 𝐶𝐶𝑉𝑉 accounts for size effects in tension, 𝐶𝐶𝐿𝐿 for stability effects in
compression
• The lower of 𝐶𝐶𝐿𝐿 and 𝐶𝐶𝑉𝑉 should be applied

Bending – Duration Factor
• Can’t simply divide moment demands by 𝐶𝐶𝐷𝐷 (ASD) or 𝜆𝜆 (LRFD)
• Stiffness does not vary with duration – so duration factor has
less effect at high slenderness
• Must check every load case to see which controls
• Some cases will be obvious, but be wary of wind / seismic LCs

Shear
• Wood is typically much weaker in shear (~1/10th of max bending
stress)
• Can take shear at distance d from supports with UDLs
• Can’t use average stress, must use actual distribution
• For rectangular sections, 50% increase over average stress
ASD LRFD
𝑓𝑓𝑣𝑣 ≤ 𝐹𝐹𝑣𝑣
′
𝑉𝑉𝑢𝑢 ≤ 𝜙𝜙𝑉𝑉𝑛𝑛
𝑓𝑓𝑣𝑣 =
3
2
𝑉𝑉/𝐴𝐴 𝜙𝜙𝑉𝑉𝑛𝑛 =
2
3
𝐹𝐹𝑣𝑣
′
𝐴𝐴
𝐹𝐹𝑣𝑣
′
= 𝐹𝐹𝑣𝑣 𝐶𝐶𝐷𝐷 𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡 𝐶𝐶𝑖𝑖 (sawn lumber)
𝐹𝐹𝑣𝑣
′
= 𝐹𝐹𝑣𝑣 𝐶𝐶𝐷𝐷 𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡 (glulam and SCL)
𝐹𝐹𝑣𝑣
′
= 𝜙𝜙𝑣𝑣 𝐾𝐾𝐹𝐹 𝐹𝐹𝑣𝑣 𝜆𝜆𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡 𝐶𝐶𝑖𝑖 (sawn lumber)
𝐹𝐹𝑣𝑣
′
= 𝜙𝜙𝑣𝑣 𝐾𝐾𝐹𝐹 𝐹𝐹𝑣𝑣 𝜆𝜆𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡 (glulam and SCL)

Bearing
• Compression loads perpendicular to grain of wood
• Low bearing strength (~1/3rd of max bending stress)
• No duration factor applied!
• Allowed to increase bearing strength with factor 𝐶𝐶𝑏𝑏 when bearing
length (ℓ𝑏𝑏) is less than 6”
• Except at ends of beams
𝐶𝐶𝑏𝑏 =
ℓ𝑏𝑏 + 0.375
ℓ𝑏𝑏
AWC DCA6 Fig. 8B
ASD LRFD
𝑓𝑓𝑐𝑐⊥ ≤ 𝐹𝐹𝑐𝑐⊥
′
𝑅𝑅𝑢𝑢 ≤ 𝜙𝜙𝑅𝑅𝑛𝑛
𝑓𝑓𝑐𝑐⊥ = 𝑅𝑅/𝐴𝐴𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝜙𝜙𝑅𝑅𝑛𝑛 = 𝐹𝐹𝑐𝑐⊥
′
𝐴𝐴𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏
𝐹𝐹𝑐𝑐⊥
′
= 𝐹𝐹𝑐𝑐⊥ 𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡 𝐶𝐶𝑖𝑖 (sawn lumber)
𝐹𝐹𝑐𝑐⊥
′
= 𝐹𝐹𝑐𝑐⊥ 𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡 (glulam and SCL)
𝐹𝐹𝑐𝑐⊥
′
= 𝜙𝜙𝑐𝑐⊥ 𝐾𝐾𝐹𝐹 𝐹𝐹𝑐𝑐⊥ 𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡 𝐶𝐶𝑖𝑖 (sawn lumber)
𝐹𝐹𝑐𝑐⊥
′
= 𝜙𝜙𝑐𝑐⊥ 𝐾𝐾𝐹𝐹 𝐹𝐹𝑐𝑐⊥ 𝐶𝐶𝑀𝑀 𝐶𝐶𝑡𝑡 (glulam and SCL)

Deflection
• Wood creeps - need to check short term and long term deflection
• Short term: usually live load, snow or wind
• Long term: usually dead load (adjusted for creep) + short term load
• Deflection usually limited to L/360 for short term and L/240 for
long term in floor beams
• Stiffness must be adjusted!
• 𝐶𝐶𝑀𝑀, 𝐶𝐶𝑡𝑡, 𝐶𝐶𝑖𝑖, 𝐶𝐶𝑓𝑓𝑓𝑓 must be applied to nominal elastic modulus
• In IBC, only the “creep” deflection is counted for long term, not
the immediate dead load deflection
• For dry conditions, can use 0.5D+L for long term, wet conditions use D+L

Outline
• Introduction
• Wood Products
• Shear Capacity
• Deflection

Example Beam #1 – Simply Supported
31
10’
• Floor joist in small house
• 16” joist spacing
• Fully supported laterally
• Bearing on 2x4 top plate
• Design per ASD provisions
L = 50 psf
D = 25 psf
Showing methods and formulas
using ClearCalcs’s wood calculator
Find smallest adequate No.1
Southern Pine “2-by” section

Example Beam #2 – Complex Beam
32
• Find adequate 24F-V8 DF Glulam section,
width of 5-1/2”
• 43’ total length
• Cantilevered beam supporting a gym floor
• Beam spacing at 6’
• Braced only at supports
• Bearing on 8x8 posts (7.25” bearing length)
• Design per LRFD provisions
Anthony Forest Co.
LL = 100 psf
DL = 25 psf
15’ 20’ 8’

Outline
• Introduction
• Wood Products
• Shear Capacity
• Deflection

Summing It Up
• Wood is an efficient, cost-effective, sustainable solution
• Multiple products exist, each with their pros & cons
• Beams must be checked in:
• Bending: Considering stability effects
• Shear: Weak in shear - may govern for longer spans than expected
• Bearing: Wood connections mean that this often governs
• Deflection: Creep must be considered
• All strengths must be adjusted based on project conditions

Other resources
• Online resources by American Wood Council
• Manual for Engineered Wood Construction
• https://www.awc.org/pdf/codes-standards/publications/archives/AWC-2018-
Manual-1810.pdf
• Structural Wood Design Examples
• https://www.awc.org/pdf/codes-standards/publications/nds/AWC-NDS2015-
StructuralWoodDesignExamples-ViewOnly-190821.pdf
• Textbooks
• AITC Timber Construction Manual
• Design of Wood Structures ASD/LRFD (Breyer et al.)

Questions?
3618 March 2020
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And watch for more free webinars
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members and connections!
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Appendix
About ClearCalcs
ClearCalcs Pty Ltd 3718 March 2020

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18 March 2020

Webinar Slides | Wood Beam Design to NDS 2018 | ClearCalcs

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