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

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Definitions and basic assumptions

Stiffness properties

Assumptions

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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

CLT – Design and use slide 17

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

CLT – Design and use slide 23

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)

CLT – Design and use slide 25

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

CLT – Design and use slide 34

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