optimization of wooden structures

8/2/2019 Optimization of Wooden Structures

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Optimization of Wood Structures

Jussi Jalkanen, D.Sc. (Tech)


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Contents

Introduction

Design of wood structures

Structural optimization & wood structures

Example 1: Double tapereted glulam beam optimization

Example 2: King Post roof truss optimization

Example 3: Glulam frame optimization

Conclusions


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Introduction

Modern timber structures are much more than a small log cottage.


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Wood is anisotropic material.

Design of wood structures

Wood structures are: Strong and light.

Brittle unless joints are proper designed.

Safe in the case of fire.

Made of renewable material.


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Material properties are significantlydifferent in the direction of grain

compared to other directions.

C24 solid timber Tension [MPa] Compression [MPa] Bending [MPa] Youngs module GPa

Grain direction 14,0 21,0 24,0 11,0

Perpendicular

to grain 0,5 2,5 0,37

Wood is sensitive to moisture changes: Longitudial shrinkage 0,1 0,3 %.

Radial shrinkage 2,1 7,9 %.

Tangential shrinkage 4,7 12,7 %.

Creep has to be taken into account sometimes.


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The design of wood structure should be done based on Eurocode 5 Designof timber structures:

Part 1-1: General Common rules and rules for buildings.

Part 1-2: General Structural fire design.

Part 2: Bridges.

The size and strength of timber products are standardised.

C14, C18, C24, C30, C35 and C40


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Connections can be done using:

Nails, screws and bolts.

Steel plates and other steel special parts.

Glue.


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The efficiency of load bearing building structures can be improved by:

Structural optimization & wood structures

Improving structural analysis and design.

Using mathematical optimization theory.

Optimization does not mean traditonal design based on:

Intuition.

Experience.

Experiments.

Structural optimization can be applied to wood structures basically the same

way as for steel structures.


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Basic problem types in structural optimization:

1) Sizing optimization Unknown cross section dimensions.

3) Topology optimization Unknown number of members, holes etc.

2) Shape optimization Unknown dimensions for structure.

b

a

h


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The objective function can be:

The volume of structure.

The cost of structure (material + manufacturing).

Constraints take care the feasebility of structure:

Deflection.

Strength.

Stability.

Eurocode 5

Wood structure optimization problem is usually:

Discrete or mixed-integer problem.

Nonlinear.

Constrained.


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Example 1: Double taperated glulam beam optimization

Puuinfo: Eurocode 5, Guide for industrial hall design.

The idea is to minimize the volume of glulam beam so that all Eurocode 5

demands are fulfilled.

beam with 1 ton crane


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Design variables in sizing problem: h1, hapja b.

Bending stress on the tapered edge.

Bending stress in the apex zone.

Transverse tension in the apex zone.Combined transverse tension and shear in

the apex zone.

Shear stress near support.

Lateral torsional buckling.

Final deflection.

Net final deflection.


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The type of optimization problem: Nonlinear and constrained problem with

continuous design variables.

Optimization algorithm is sequential quadratic programming, SQP.

The initial guess is taken from Puuinfoexample (1310 mm, 2200 mm ja 240

mm).

The improvement of the objective function (volume) during optimization:

0 10 20 30 40 50 60 70 80 90 1001.15

1.16

1.17

1.18

1.19

1.2

1.21

x 104

analyysien lukumr

T

ilavuus

[litraa]


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Initial guess Best found

Volume [l] 12004 11569

Cross section heigh at support h1 [mm] 1310 1231

Cross section heigh is the middle hap [mm] 2200 2382

Cross section width b [mm] 240 225Utilization rates:

- bending 93% 97%

- bending in apex zone 79% 75%

- transverse tension in apex zone 73% 92%

- tarnsverse tension and shear in apex zone 73% 90%

- shear 77% 86%- lateral torsional buckling 96% 100%

- final deflection 91% 100%

- net final deflection 84% 96%

The best found solution compared to the initial guess:

The best found solution is 435 liters (3,6%) lighter than the initial guess.

The initial guess was already rather good.


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Example 2: King Post roof truss optimization

h

Upper chord Lower chord Verticalbyp

hyp

bap

y

z

bap

hap

z

y

bver

hver

bap

z

y

22 meters long roof truss made of Kerto (laminated veneer lumber, LVL).

The volume of truss is minimized so that Eurocode 5 demands are fullfilled.

Shape and sizing optimization with design variables h, hyp, byp, hap, bap, hver, bver.


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Upper chord compression and bending.

Upper chord shear.

Upper chord buckling in plane.

Upper chord lateral torsional buckling.

Lower chord shear.

Lower chord tension and bending.

Tension in vertical.

Upper chord buckling out of plane.

Joint design, fire, deflection or pressure perpendicular to crane on supports

are not considerd.


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There are only certain Kerto

beam sizes available.height [mm]

width

[mm]200 260 300 360 400 450 500 600 900

27

33

39

45

51

57

63

75

In priciple the height of truss h is continuous design variable.

The type of optimization problem: Nonlinear, mixed integer and constrained

problem.

In practise heigh h can changed from 2 meters up to 5 meters 10 cm steps.


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Structural analysis is based on finite element method.

Tabu Search (TS) is heuristic optimization algorithm.

0 100 200 300 400 500 600 700 8003900

3950

4000

4050

4100

4150

4200

4250

FEM-analyysien lukumr

Tilavuus

[litraa]

The improvement of the objective function (volume) during optimization:


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Initial guess Best found result

Volume [l] 4199 3944

The height of truss h [mm] 3600 3100

Upper chord cross section height hyp [mm] 900 900

width byp [mm] 75 75

Upper chord cross section heighth

ap [mm] 600 500 width bap [mm] 75 75

Vertical cross section height hver [mm] 260 200

width bver [mm] 45 27

Utilization rates:

- Upper chord shear 60% 60%

- Upper chord compression and bending 63% 63%

- Upper chord buckling out of plane 59% 61%- Upper chord buckling in plane 79% 80%

- Upper chord lateral torsional buckling 98% 98%

- Lower chord shear 60% 60%

- Lower chord tension and bending 72% 99%

- Tension in vertical 5% 9%

The best found solution compared to the initial guess:

The volume of truss was reduced 255 litres (6%).

Utilization rates did not increase sigficantly.


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Example 3: Glulam frame optimization

The material cost of 28 m x 72 m industrial hall glulam frame should be minimized.

Design variables: Number of frames n

Beam h1, h2 and b

Column hp and bp

Secondary Kerto-S beam hkand bk

Constraints based on Eurocode 5.


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Optimization algorithm is heuristic particle swarm optimization (PSO).

Available glulam beam widths are 90, 115, 140, 165, 190, 215, 240 and 265mm.

Only certain sizes available for Kerto-S beams.

height [mm]

width

[mm]200 260 300 360 400 450 500 600 900

27

33

39

45

51

57

63

75


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The improvement of the objective function during optimization:

0 1000 2000 3000 4000 5000 600023

24

25

26

27

28

29

30

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Volum

e

FEM-analysis

The best found solution 23.57 (m3):

Number of frames n = 12 i.e. distance between frames 5540 mm

Beam h1= 1273 mm, h2 =2188 mm, b = 190 mm

Columns hp = 486 mm, bp = 140 mm

Secondary Kerto-S beams hk= 300 mm, bk= 39 mm

20 independent runs.


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Conclusions

Structural optimization is natural extension to the analysis of wood structures.

Optimization offers a clear way to improve the efficientcy of wood structures.

The optimization problem turns to be quite similar as in steel structure

optimization.

Timber structure design should be done based on Eurocode 5.

Wood is suitable construction material for many purposes.

optimization of wooden structures

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