Design of Bending Members in Timber What can go wrong

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Design of Bending Members in Timber
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An Example of Timber Beams
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What can go wrong ?

• TIMBER BEAMS
• Bending failure
• Lateral torsional buckling
• Shear failure
• Notch failure
• Bearing failure
• Excessive deflections

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Bending Strength

• Linear elastic stresses

y
M
Design Equation
Where Fb is the characteristic bending
strength For timber it is Fb fb (KDKHKSbKT)
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Bending failure in compression

• Only likely for very high grade material
• Benign failure mode

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Logging bridge near Pemberton, BC Glulam I-beam
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Bending failure in tension

• Most likely failure mode
• Brittle
• Combination of tension and shear, although
  tension fracture is the initiating mode

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Bending capacity
Mr f Fb S KZb KL where f 0.9 and Fb
fb (KD KH KSb KT )
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Glulam beams in a Gerber system
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Glued-laminated beams
better laminations
20f-E and 24f-E grades
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Glued-laminated beams
20f-EX and 24f-EX grades
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Lateral torsional buckling of timber beams
Le
Note The warping stiffness for rectangular
shapes is small compared to the torsional and
bending stiffness
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Lateral torsional buckling of deep I-joists
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Capacity of a timber beam subject to lateral
torsional buckling
Mr
Le
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Lateral torsional buckling factor KL
KL
1.0
KL 1
KL 1 1/3 (CB / CK)4
0.67
practical limit
0.5
KL (0.65 E KSE KT) / (CB2 Fb KX)
CK ( 0.97 E KSE KT / Fb )0.5
0
CB
10
30
40
20
50
0
Slenderness ratio CB ( Le d / b2 )0.5
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Deep glulam beam
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Prevention of lateral torsional buckling
lt 610 mm
KL 1.0 when lateral support is provided as
shown
lt 610 mm
lt 8d
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Bridging for floor joists
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Shear stress in a beam
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Shear in a timber beam
As
sv(max)
Vr f Fv 2/3 A KZv where f 0.9 and Fv
fv (KD KH KSv KT )
sv(avg)
sv(max) 1.5 sv(avg) 1.5 V / A
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UNBC Prince George, BC
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Shear failures

• One of the very weak properties of wood
• Shrinkage cracks often occur at the ends of beams
  in the zone of maximum shear stress

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Shear design of glulam beams

• A simple approach for beams where the volume lt
  2.0 m3

Vr f Fv 2/3 A KN where f 0.9 and Fv
fv (KD KH KSv KT ) KN notch factor (see
next section)
For larger beams this is usually quite
conservative and a more sophisticated approach
is used (see clause 6.5.7.3)
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Notch factor for Glulam beams
dn
d
dn
e
KN ( 1 dn/d )2
For e gt d KN ( 1 dn/d ) For e lt d KN
1 dne/d(d dn)
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Notch effect in sawn lumber

• For notches on the tension side of supports (sawn
  lumber)
• In new code Reaction calculation

NEW !!
Fr ? Ft A KN ? 0.9 Ft ft (KD KH KSt KT)
where ft specified reaction force strength
0.5 MPa for sawn lumber KSt 1.0 for dry and 0.7
for wet service conditions A gross
cross-section area KN notch factor
Area A
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Notch factorKN
Based on Fracture Mechanics theory
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Bearing failure in a timber beam

• The soft property of wood
• Often governs

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Bearing resistance
Ab

• Qr ? Fcp Ab KZcp KB
• ? 0.8
• Fcp fcp (KScp KT)

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Critical bearing areas in woodframe construction
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Bearing resistance (double bearing)
Ab2
Abavg 0.5(Ab1 Ab2) but 1.5 Ab1
Ab1
45 deg

• Qr (2/3) ? Fcp Abavg KZcp KB
• ? 0.8
• Fcp fcp (KD KScp KT)

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Bearing factor KB
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Deflections

• A serviceability criterion
• Avoid damage to cladding etc. (? L/180)
• Avoid vibrations (? L/360)
• Aesthetics (? L/240)
• Use unfactored loads
• Typically not part of the code

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