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Design of Bending Members in Timber. An Example of Timber Beams. What can go wrong ?. TIMBER BEAMS: Bending failure Lateral torsional buckling Shear failure Notch failure Bearing failure Excessive deflections. Bending Strength . Linear elastic stresses. y. M. Design Equation:.

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what can go wrong
What can go wrong ?

TIMBER BEAMS:

  • Bending failure
  • Lateral torsional buckling
  • Shear failure
  • Notch failure
  • Bearing failure
  • Excessive deflections
bending strength
Bending Strength

Linear elastic stresses

y

M

Design Equation:

Where Fb is the characteristic bending strength

For timber it is Fb = fb (KDKHKSbKT)

bending failure in compression
Bending failure in compression
  • Only likely for very high grade material
  • Benign failure mode
slide6

Logging bridge

near Pemberton, BC

Glulam I-beam

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

Lateral torsional buckling

Bending capacity

Mr = φ Fb S KZb KL

where φ = 0.9

and Fb = fb (KD KH KSb KT )

glued laminated beams
Glued-laminated beams

better laminations

20f-E and 24f-E grades

lateral torsional buckling of timber beams

Elastic buckling:

Mcr = π / Le √(G J E Iy )

Lateral bending stiffness

Torsional stiffness

y

y

Δx

x

Δy

θ

x

x

y

y

Lateral torsional buckling of timber beams

Le

Note: The warping stiffness for rectangular shapes is small compared to the torsional and bending stiffness

capacity of a timber beam subject to lateral torsional buckling

Mu

Mr = φ Fb S KZb

Mr = φ Fb S KZb KL

material failure

combination of material failure and lateral torsional buckling

elastic lateral torsional buckling

Capacity of a timber beam subject to lateral torsional buckling

Mr

Le

lateral torsional buckling factor k l
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

0

10

20

30

40

50

Slenderness ratio CB = ( Le d / b2 )0.5

prevention of lateral torsional buckling

d

b

Prevention of lateral torsional buckling

< 610 mm

KL = 1.0 when lateral support is provided as shown

< 610 mm

< 8d

shear stress in a beam

A

τ

y

d

τmax

= V(0.5A)(d/4)

(bd3/12)b

=1.5 V/A

N.A.

b

Shear stress in a beam
shear in a timber beam
Shear in a timber beam

As

σv(max)

Vr = φ Fv 2/3 A KZv

where φ = 0.9

and Fv = fv (KD KH KSv KT )

σv(avg)

σv(max) = 1.5 σv(avg)

= 1.5 V / A

slide23

UNBC

Prince George, BC

shear failures

This part of the load transferred in direct compression

  • Direct compression transfer of loads in the end zones reduces the total shear force to be carried.

45o

critical section

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
shear design of glulam beams
Shear design of glulam beams

A simple approach for beams where the volume < 2.0 m3:

Vr = φ Fv 2/3 A KN

where φ = 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)

notch factor for glulam beams
Notch factor for Glulam beams

dn

d

dn

e

KN = ( 1 – dn/d )2

For e > d :

KN = ( 1 – dn/d )

For e < d :

KN = 1 – dne/[d(d – dn)]

notch effect in sawn lumber
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

notch factor k n

d1

e

d

dn

Notch factorKN

Based on Fracture Mechanics theory

bearing failure in a timber beam

Not only compression perpendicular to grain but also tension of the fibres along edges

compression perpendicular to grain

tension of fibres along the edges

Bearing failure in a timber beam
  • The “soft” property of wood
  • Often governs
bearing resistance

< 150mm

no high bending stress

> 75mm

Bearing factor

Bearing resistance

Ab

Qr =  Fcp Ab KZcp KB

= 0.8

Fcp = fcp (KScp KT)

bearing resistance double bearing
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)

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