Henrik Danielsson Division of Structural Mechanics, Lund ......Henrik Danielsson Division of...
Transcript of Henrik Danielsson Division of Structural Mechanics, Lund ......Henrik Danielsson Division of...
CLT – Design and use
Henrik Danielsson
Division of Structural Mechanics, Lund University, Sweden
CLT – Design and use slide 2
CLT (Cross Laminated Timber) – Design and use
• Favourable mechanical properties
+ strength
+ stiffness
• Environmental friendly
• Pre-fabrication, rapid on-site erection
CLT – Design and use slide 3
Outline
Introduction• Production• Typical dimensions and layups• Out-of-plane and in-plane loading• Basic mechanical behavior
Modelling• Beam models• Plate/shell models
Design• Ultimate Limit state design• Serviceability Limit state design
Use of CLT – two examples
CLT – Design and use slide 4
Production
CLT – Design and use slide 5
Typical dimensions
CLT – Design and use slide 6
Typical Layups
3 layers
5 layers
7 layers
Gaps Grooves
Flat side bonding Edge-bonding?
CLT – Design and use slide 7
Out-of-plane loading
Line supported – bending in one dir. Line supported – bending in two dirs.
Point supported Openings, cantilever
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In-plane loading
Line supported
Point supported Openings, cantilever
CLT – Design and use slide 9
Definitions and basic assumptions
Stiffness properties
Assumptions
CLT – Design and use slide 10
The issue of rolling shear
Shear stiffness
Shear strength
Low strength! Low stiffness!
The low rolling shear stiffness and strength need to be considered.
CLT – Design and use slide 11
Timoshenko beam deformation
Timoshenko beam
Total deformation
Bending deformation
Shear deformation
=
+
CLT – Design and use slide 12
Deformation in CLT
Bending deformation
Shear deformation
Significant contribution to shear deformations due to rolling shear in transverse layers.
CLT – Design and use slide 13
Outline
Introduction• Production• Typical dimensions and layups• Out-of-plane and in-plane loading• Basic mechanical behavior
Modelling• Beam models• Plate/shell models
Design• Ultimate Limit state design• Serviceability Limit state design
Use of CLT – two examples
CLT – Design and use slide 14
Structural analysis - modelling approaches
Beam modelling approaches
• Gamma-method• Timoshenko theory (shear correction factor)
• Shear analogy method
Plate/Shell modelling approaches
• “Beam grillage”• Orthotropic plate/shell
effective element thicknesses
• Orthotropic plate/shellwith correction factors
• Orthotropic plate/shell based on laminate theory
Full 3D FE-analysis
CLT – Design and use slide 15
Gamma-method
Calculation of beam deflection according to Bernoulli-Euler theory using an effective bending stiffness (second moment of inertia)
Approximate method for consideration of shear flexibility of the transverse layers.
(Analogy: Mechanically jointed beams acc. to EC5, Annex B)
Reduction of Steiner partg
CLT – Design and use slide 16
Gamma-method
Effective bending stiffness (second moment of inertia)
Thickness of transversal layers
Rolling shear stiffness
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Gamma-method
Effective bending stiffness (second moment of inertia)
Reference length
Simply supported beam:
Continuous beam:
Cantilever beam:
CLT – Design and use slide 18
Gamma-method
Ratio of effective to net stiffness as influenced by span length L
CLT 3s 120 mm(40-40-40)
CLT 5s 100 mm (20-20-20-20-20)
CLT 5s 200 mm(40-40-40-40-40)
CLT – Design and use slide 19
Gamma-method
+ Calculation of beam deflection using Bernoulli-Euler beam theory
Approximate method for consideration of shear flexibility of the transverse layers.
- Bending stiffness depends of structural system (effective beam length)
SUMMARY
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Timoshenko theory with shear correction factor
Consideration of shear flexibility of a composite beam.
Bending stiffness:second moment of inertia of net cross section
Shear stiffness:Timoshenko theory - shear correction factor
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Timoshenko theory with shear correction factor
Shear stiffness:Timoshenko theory - shear correction factor
One layer only (= homogeneous rect. beam):
Typical CLT layups:
CLT – Design and use slide 22
Timoshenko theory with shear correction factor
SUMMARY
Consideration of shear flexibility of a composite beam.
+ Shear stiffness as cross sectional property
- Shear deformations (Timoshenko theory) need to be considered
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Plate/shell modelling approaches
Orthotropic plate with effective thicknesses
Z
XY
Isometric“Beam grillage” model
Simplified modelling approaches for out-of-plane (plate bending) loading situations
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Plate/shell modelling approaches
Orthotropic shell
• Mindlin-Reissner plate theory
• Shear correction factors
• … and other (“CLT-specific”) correction factors.
Enables analysis of 3D structures exposed to a combination ofout-of-plane and in-plane loading.
(Plate bending and membrane action)
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Plate/shell modelling approaches
Orthotropic shell
Bending and twisting
Out-of-plane shear
In-plane (membrane) actions
CLT – Design and use slide 26
Plate/shell modelling approaches
Orthotropic shell
Reduction factors relating to:
• Gaps (no edge-bonding) or cracks
• Shear correction (rolling shear)
0.65
0.25
0.75
CLT – Design and use slide 27
Outline
Introduction• Production• Typical dimensions and layups• Out-of-plane and in-plane loading• Basic mechanical behavior
Modelling• Beam models• Plate/shell models
Design• Ultimate Limit state design• Serviceability Limit state design
Use of CLT – two examples
CLT – Design and use slide 28
Design of CLT elements
Current status of CLT in relation to standards
CLT is not yet included in European standards, e.g. Eurocode 5 (EN 1995-1-1), with the exception of German and Austrian National Applications Documents.
Design according to producers specific European Technical Assessments (ETAs).
Design handbooks are also available, e.g.
• “BSPHandbuch – Holz-massivbauweise in Brettsperrholz” (in German)Schickhofer, Bogensperger, Moosbrugger, TU Graz, 2010.
• “CLT Handbook” (in English)Gagnon, Pirvu, FP Innovations, Canada, 2011.
• “Cross Laminated Timber Structural Designs” (in German and English)Wallner-Novak, Koppelhuber, Pock, ProHolz Austria, 2014.
• “KL-trähandbok” (in Swedish)Svenskt trä, to be published in 2017.
CLT – Design and use slide 29
Design of CLT elements - ULS
Verification of capacity on cross sectional level:
sor material point level:
NOTE: Notation (indices) for cross sectional forces/moments, stresses and strengths are not consistent in literature
bending moment around y-axis
bending moment giving normal stress in x-direction
Example
CLT – Design and use slide 30
Design of CLT elements - ULS
Overview of design w.r.t. to: Bending mx and my
Out-of-plane shear vxz and vyz
In-plane axial loading nx and ny
(In-plane shear nxy)
Combined loading and buckling
In-plane beam loading
CLT – Design and use slide 31
Design of CLT elements - ULS
Typical characteristic strengths found in ETAs (C24) [CrossTimberSystems]
Bending strengthTensile strength – along grain
Compression strength – along grainTensile strength – perp-to-grain
Compressive strength – perp-to-grainShear strength – longitudinal shear
Shear strength – rolling shear
Design strength
Partial factor for material Modification factor
Sweden
Austria
Germany
According to GLT for SC 1 and 2
(CLT not allowed in SC 3)
CLT – Design and use slide 32
Design of CLT elements - ULS
Out-of-plane loading - Bending moment
Bending in strong direction – 5s Bending in weak direction – 5s
General format
CLT – Design and use slide 33
Design of CLT elements - ULS
Out-of-plane loading - Bending moment (cont.)
Bending in strong direction – 5s Bending in weak direction – 5s
Bending in strong direction – 3s Bending in weak direction – 3s
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Design of CLT elements - ULS
Out-of-plane loading - Bending moment (cont.)
General format
System factor
Width of uniformly stressed element [m]
CLT – Design and use slide 35
Design of CLT elements - ULS
Out-of-plane loading - Bending moment (cont.)
Bending around the x- and the y-axis give
normal stress in different directions
and
normal stress in different layers.
Verification of strength can be carried out separately for the two directions.
CLT – Design and use slide 36
Design of CLT elements - ULS
Out-of-plane loading – Shear force
Shear force strong direction – 5s Shear force weak direction – 5s
General formatRolling shear
Longitudinal shear
CLT – Design and use slide 37
Design of CLT elements - ULS
Out-of-plane loading – Shear force (cont.)
Shear force strong direction – 5s Shear force weak direction – 5s
Shear force strong direction – 3s Shear force weak direction – 3s
Due to interaction of shear and perp-to-grain tension, rolling shear strength should be reduced for laminations with:
• grooves
• aspect ratio
CLT – Design and use slide 38
Design of CLT elements - ULS
Out-of-plane loading – Shear force (cont.)
Shear force strong direction – 5s Shear force weak direction – 5s
Grooves
CLT – Design and use slide 39
Design of CLT elements - ULS
Out-of-plane loading – Shear force (cont.)
Shear forces vxz and vyz give
shear stress in different directions,
but in the same plane
and
within the same layer.
Interaction of longitudinal and rolling shear.
Recommendation [ProHolz Handbook]: “Verification of strength can with sufficient accuracy be carried out separately for the two shear stress components.”
CLT – Design and use slide 40
Design of CLT elements - ULS
In-plane loading – Axial force
Axial force in strong direction – 5s Axial force in weak direction – 5s
General format
Considering layers with grain direction in direction of loading
CLT – Design and use slide 41
Design of CLT elements - ULS
In-plane loading – Axial force (cont.)
Axial force in strong direction – 5s Axial force in weak direction – 5s
Axial force in strong direction – 3s Axial force in weak direction – 3s
CLT – Design and use slide 42
Design of CLT elements - ULS
In-plane loading – Axial force (cont.)
Axial force along the x- and the y-axis give
normal stress in different directions
and
normal stress in different layers.
Verification of strength can be carried out separately for the two directions.
CLT – Design and use slide 43
Design of CLT elements - ULS
In-plane loading – shear
Gross shear failure
Net shear failure(longitudinal layers)
Net shear failure(longitudinal layers)
Shear failure in crossing areas
CLT – Design and use slide 44
Design of CLT elements - ULS
Combined loading – Bending and Axial force considering buckling
Slenderness
Radius of gyration
Reduction factor for buckling
Effective stiffness (e.g. according to Gamma-method)
CLT – Design and use slide 45
Design of CLT elements - ULS
In-plane beam loading
Span-to-height ratios L/H ≤ 4 Nonlinear bending stress distributionwith higher peak values compared to the linear beam theory distribution
st
Point supported element at in-plane beam loading (wall element, H ≈ 3 m)
CLT – Design and use slide 46
Design of CLT elements - ULS
In-plane beam loading
Span-to-height ratios from about L/H > 4
Verification by beam theory possible
At holes and notches: Tension perpendicular to beam axis.
At supports:Compression perpendicular to beam axis.
Bending carried by normal stress parallel to grain in longitudinal layers
Transverse layers act as reinforcement w.r.t actions perpendicular to beam axis
CLT – Design and use slide 47
Design of CLT elements - ULS
In-plane beam loading – Tests of CLT beams with holes/notches [Lund, 2016]
Hole placed in a position of combined bending and shear – 4 individual tests
Two beams failed in parallel to grain tension/bending in longitudinal laminations around the hole
Two beams failed in parallel to grain tension/bending in longitudinal laminations at mid-span
Hole size hd = 0.5h
CLT – Design and use slide 48
Outline
Introduction• Production• Typical dimensions and layups• Out-of-plane and in-plane loading• Basic mechanical behavior
Modelling• Beam models• Plate/shell models
Design• Ultimate Limit state design• Serviceability Limit state design
Use of CLT – two examples
CLT – Design and use slide 49
Design of CLT elements - SLS
SLS - Serviceability limit state
Verification of structural behavior with respect to
• Deformation
- Ensure appearance
- Ensure utilization (avoid damage of underlying parts)
- Criteria for deformation at different load situations: Characteristic, Frequent, Quasi-permanent
• Springiness and vibrations
- Ensure acceptable floor response for user
CLT – Design and use slide 50
Design of CLT elements - SLS
Deformation – some specific considerations for CLT
Bending deformation
Shear deformation
Correct assessment of element stiffness and deformation
Long term loading and creep
CLT show larger deformation/creep (compared to e.g. GLT)
kdef SC 1 SC 2Gulam, Solid timber 0.60 0.80CLT 0.80 1.00
CLT – Design and use slide 51
Design of CLT elements - SLS
Springiness and vibrations
Eurocode 5 recommendations:
1st natural frequency (f1 ≥ 8 Hz)
Deflection from 1 kN point load (SS-EN: w ≤ 1.5 mm)
Impulse velocity response
are in many cases insufficient to assure acceptable floor performance.
Floor response governed by • Span• Stiffness• Mass• Damping• Support conditions
Frequency
w(1.0 kN)
CLT – Design and use slide 52
Design of CLT elements - SLS
Springiness and vibrations
[ProHolz, Hamm & Richter 2009]
Classification possible via acceleration response
Class I Offices, apartments in multi-family houses
Class II Single-family houses
Class III Floor with low demands
CLT – Design and use slide 53
Design of CLT elements - SLS
Springiness and vibrations – some specific considerations for CLT
Z
XY
xy
z
y
z
x
IsometricLC 1: Uniform unit load
Support conditions: CLT elements carrying loads in one or two directions?
CLT – Design and use slide 54
Design of CLT elements - SLS
Springiness and vibrations – some specific considerations for CLT
Z
XY
xy
z
y
z
x
IsometricLC 1: Uniform unit loadGlobal Deformations u
Factor of deformations: 290.00Max u: 3.29, Min u: 0.00 mm
Deformation at uniform load
CLT – Design and use slide 55
Design of CLT elements - SLS
Springiness and vibrations – some specific considerations for CLT
Z
XY
xy
z
y
z
x
IsometricRF-DYNAM CA1Normal mode No. 2 - 9.46713 HzNatural Vibration u
Factor of deformations: 0.94Max u: 1.00, Min u: 0.00 [-]
1st Natural frequency
10 Hz
8 Hz
CLT – Design and use slide 56
Outline
Introduction• Production• Typical dimensions and layups• Out-of-plane and in-plane loading• Basic mechanical behavior
Modelling• Beam models• Plate/shell models
Design• Ultimate Limit state design• Serviceability Limit state design
Use of CLT – two examples
CLT – Design and use slide 57
Concluding remarks
• Favourable mechanical properties
+ strength
+ stiffness
• Environmental friendly
• Pre-fabrication, rapid on-site erection
Cross Laminated Timber (CLT)
• Versatile element: out-of-plane loading, in-plane loading
• Complex mechanical behavior – many possible failure modes
• On-going research – not yet included in Eurocode 5
Thank you for your attention.
Henrik Danielsson
Division of Structural Mechanics, Lund University, Sweden