Architecture 324
Structures II
Wood Beam Analysis
and Design
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Properties of Wood
ASD approach
NDS criteria
Examples using Wood
2012 NDS
University of Michigan, TCAUP
Structures II
Slide 1/35
Wood Properties that affect Strength
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Species
Growth Characteristics
Moisture Content
Temperature
Application Factors (stability, repetitive)
Load Duration
University of Michigan, TCAUP
Structures II
Slide 2/35
Adjustment Factors
Sawn Lumber - 4
2012 NDS
University of Michigan, TCAUP
Structures II
Moisture Content
Slide 3/35
Living tree
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MC = %water to oven dry wood
In a living tree, MC can be 200%
“free water” is contained in cell cavity
“bound water” is within the cell wall
Fiber Saturation Point (FSP) is the
MC at 0% free and 100% bound water
FSP is about 30%
• Equilibrium Moisture Content (EMC) is
reached in service
FSP
Shrinkage
• Shrinkage begins once MC<FSP
• Shrinkage is not the same in each
direction
• Uncontrolled shrinkage results in splits
EMC
University of Michigan, TCAUP
Structures II
Slide 4/35
Shrinkage
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Is different in different directions
Longitudinal is the least
Across the grain is more
Circumferential is greatest
Cut
• Plain Sawn – most economical and
common
• Quarter Sawn – less warping
• Rift Sawn – least warping but more waste
University of Michigan, TCAUP
Structures II
Slide 5/35
Yard Dry
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Initial free water is removed
Air dried outdoors or under cover
Dry rate depends on humidity and circulation
Coating ends reduces splitting
Takes ~ some weeks to months
Kiln Dry
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Enclosed in humidity controlled chamber
Introduction of controlled heat
Air circulation
Dried to < %18
University of Michigan, TCAUP
Structures II
Slide 6/35
Engineered Wood Products
Glulam
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Glue laminated lumber
Stress rated and graded
Parallel grain
Different finish grades
Standard widths and lams
Straight or curved
Size limit by transportation
Stock or custom dimensions
2012 NDS
University of Michigan, TCAUP
Structures II
Slide 7/35
Engineered Wood Products
Prefabricated Wood I-Joists
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ASTM D 5055
Standard dimensions
Specifications per manufacturer
University of Michigan, TCAUP
Structures II
Slide 8/35
Engineered Wood Products
Structural Composite Lumber
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Laminated Veneer Lumber (LVL)
Veneer ≤ ¼”
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Parallel Strand Lumber (PSL)
Strand thickness ≤ ¼”
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Specifications per manufacturer
University of Michigan, TCAUP
Structures II
Slide 9/35
Engineered Wood Products
Wood Structural Panels
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Plywood – cross laminated wood veneer panels
pressed and glued.
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Oriented Strand Board (OSB) – cross
laminated layers of wood strands or wafers,
compressed and glued
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Composite Panel – wood veneer and
reconstituted wood based material
University of Michigan, TCAUP
Structures II
Slide 10/35
Engineered Wood Products
Cross Laminated Timber (CLT)
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Developed in early 1990 in Switzerland and
Austria – Kreuzlagenholz (KLH).
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Multiple cross laminated layers of solid wood
lumber, glued to make solid plates or panels
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Suited for CNC finishing off site
University of Michigan, TCAUP
Structures II
Slide 11/35
ASD Approach - Flexure
Fb’ ≥ fb
Allowable Flexure Stress
Fb from tables determined by species and grade
Fb’ = Fb (usage factors)
usage factors for flexure:
CD Load Duration Factor
CM Moisture Factor
CL Beam Stability Factor
CF Size Factor
Cfu Flat Use
Cr Repetitive Member Factor
Actual Flexure Stress
fb = Mc/I = M/S
M = Moment force
c = the distance to the extreme fibers
I = the Moment of Inertia
S = Section Modulus, I/c = bd2/6, for rectangle
2012 NDS
University of Michigan, TCAUP
Structures II
Slide 12/35
ASD Approach – Shear
Fv’ ≥ fv
Allowable Shear Stress
Fv from tables determined by species and grade
Fv’ = Fv (usage factors)
usage factors for shear:
CD Load Duration Factor
CM Moisture Factor
Actual Shear Stress
fv = VQ / I b = 1.5 V/A
V = Shear force
Q = Static Moment
I = Moment of Inertia
b = width
2012 NDS
Can use V at d from support as maximum
University of Michigan, TCAUP
Structures II
Slide 13/35
Tabulated Allowable Stress
NDS Table 4 A-F
By species and grade
Table 4A – Visually Graded for Dimensioned Lumber
Table 4B – Visually Graded Southern Pine
Table 4C - Mechanically Graded
Table 4D – Timbers (5”x5” and larger)
Table 4E – Decking
Table 4F – Non-North American species
2012 NDS
University of Michigan, TCAUP
Structures II
Slide 14/35
Adjustment Factors
Sawn Lumber - 4
2012 NDS
University of Michigan, TCAUP
Structures II
Slide 15/35
Structures II
Slide 16/35
Adjustment Factors
Allowable Flexure Stress Fb’
Fb from tables determined by species and grade
Fb’ = Fb (CD CM Ct CL CF Cfu Ci Cr )
Usage factors for flexure:
CD Load Duration Factor
Ct Temperature Factor
2012 NDS
University of Michigan, TCAUP
Adjustment Factors
Allowable Flexure Stress Fb’
Fb from NDS tables
Fb’ = Fb (CD CM Ct CL CF Cfu Ci Cr )
Usage factors for flexure:
CM Moisture Factor
CF Size Factor
Cfu Flat Use
Cr Repetitive Member Factor
2012 NDS
University of Michigan, TCAUP
Structures II
Slide 17/35
Adjustment Factors
Allowable Flexure Stress Fb’
Fb from tables determined by species and grade
Fb’ = Fb (CD CM Ct CL CF Cfu Ci Cr )
Usage factors for flexure:
Ci Insizing Factor
2012 NDS
University of Michigan, TCAUP
Structures II
Slide 18/35
Adjustment Factors
Allowable Flexure Stress Fb’
Fb from tables determined by species and grade
Fb’ = Fb (CD CM Ct CL CF Cfu Ci Cr )
Usage factors for flexure:
CL Beam Stability Factor
2012 NDS
University of Michigan, TCAUP
Structures II
Slide 19/35
Structures II
Slide 20/35
CL
CL = 1.0
for depth/width ratio in
4.4.1 CL = 1.0
Otherwise
CL < 1.0
calculate factor using
section 3.3.3
University of Michigan, TCAUP
CL Beam Stability Factor
In the case bracing provisions of 4.4.1 cannot be met,
CL is calculated using equation 3.3-6
The maximum allowable slenderness, RB is 50
2012 NDS
University of Michigan, TCAUP
Structures II
Slide 21/35
Adjustment Factors for Shear
Allowable Flexure Stress Fv’
Fv from tables determined by species and grade
Fv’ = Fv (usage factors)
Usage factors for flexure:
CD Load Duration Factor
CM Moisture Factor
Ct Temperature Factor
Ci Insizing Factor
University of Michigan, TCAUP
2012 NDS
Structures II
Slide 22/35
Analysis Procedure
Given: loading, member size, material and span.
Req’d: Safe or Unsafe
1. Find Max Shear & Moment
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Simple case – equations
Complex case - diagrams
2. Determine actual stresses
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fb = M/S
fv = 1.5 V/A
3. Determine allowable stresses
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Fb and Fv (from NDS)
Fb’ = Fb (usage factors)
Fv’ = Fv (usage factors)
4. Check that actual ≤ allowable
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fb ≤ F’b
fv ≤ F’v
5. Check deflection
6. Check bearing (Fb = Reaction/Abearing )
University of Michigan, TCAUP
from NDS 2012
Structures II
Slide 23/35
Structures II
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Analysis Procedure
Example
Given: loading, member size, material
and span.
Req’d: Safe or Unsafe?
University of Michigan, TCAUP
Species and Grade
S-P-F
No.2
Fb = 875 psi
Fv = 135 psi
2012 NDS
University of Michigan, TCAUP
Structures II
Slide 25/35
Structures II
Slide 26/35
Analysis Procedure
1.
Find Max Shear & Moment
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Simple cases – equations
Complex cases - diagrams
University of Michigan, TCAUP
Analysis Procedure
2.
Determine actual stresses
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3.
fb = M/S
fv = 1.5 V/A
Determine allowable stresses
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Fb = 875 psi
Fv = 135 psi
Determine factors:
CD = ?
CM = 1
Ct = 1
CL = 1
CF = ?
Cfu = 1
Ci = 1
Cr = 1
2012 NDS
University of Michigan, TCAUP
Structures II
Slide 27/35
Structures II
Slide 28/35
Analysis Procedure
CD Load duration factor
Use 1.6 (10 minutes)
CF Size factor
2x4
use 1.5
2012 NDS
University of Michigan, TCAUP
Analysis Procedure
3.
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Determine allowable stresses
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Fb’ = Fb (CD)(CF)
Fb’ = 875 (1.6)(1.5) = 2100 psi
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Fv’ = Fv (CF)
Fv’ = 135 (1.6) = 216 psi
Check that actual ≤ allowable
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5.
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fb < F’b
fv < F’v
Check deflection
Check bearing (Fcp = R/Ab )
University of Michigan, TCAUP
Structures II
Slide 29/35
Analysis Procedure
Given: member size, material and span.
Req’d: Max. Safe Load (capacity)
1.
Assume f = F
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Solve stress equations for force
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M = Fb S
V = 0.66 Fv A
Use maximum forces to find loads
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4.
5.
Maximum actual = allowable stress
Back calculate a load from forces
Assume moment controls
Check shear
Check deflection
Check bearing
from NDS 2012
University of Michigan, TCAUP
Structures II
Slide 30/35
Analysis Procedure
Given: member size, material and span.
Req’d: Max. Safe Load (capacity)
1.
Assume f = F’
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Solve stress equation for moment
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3.
Maximum actual = allowable stress
M = F’b S (i.e. moment capacity)
Use maximum forces to find loads
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Back calculate a maximum load from
moment capacity
University of Michigan, TCAUP
Structures II
Slide 31/35
Structures II
Slide 32/35
Analysis Procedure (cont.)
4.
Use maximum forces to find loads
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5.
6.
Check shear for load capacity from
step 3.
Use P from moment to find Vmax
Check that fv < Fv’
Check deflection (serviceability)
Check bearing (serviceability)
University of Michigan, TCAUP
Design Procedure
Given: load, wood, span
Req’d: member size
1.
Find Max Shear & Moment
• Simple case – equations
• Complex case - diagrams
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Determine allowable stresses
Solve S=M/Fb’
Choose a section from Table 1B
5.
Check shear stress
• Revise DL and Fb’
• First for V max (easier)
• If that fails try V at d distance
from support
• If the section still fails, choose a
new section with A=1.5V/Fv’
6.
7.
Check deflection
Check bearing
from NDS 2012
University of Michigan, TCAUP
Structures II
Slide 33/35
Structures II
Slide 34/35
Design Procedure
Given: load, wood, span
Req’d: member size
1.
Find Max Shear & Moment
• Simple case – equations
• Complex case - diagrams
University of Michigan, TCAUP
Design Procedure
2.
Determine allowable stresses
(given in this example)
F’b = 1000 psi
F’v = 100 psi
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Solve S=M/Fb’
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Choose a section from S table
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Check shear stress
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7.
Revise DL and Fb’
First for V max (easier)
If that fails try V at d distance
(remove load d from support)
If the section still fails, choose a
new section with A=1.5V/Fv’
Check deflection
Check bearing
University of Michigan, TCAUP
Structures II
Slide 35/35