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(1)

Seminar on

Sustainable Future through

Timber Design

UITM, Dec. 16.12.2014

Simon Aicher

Design Timber Structures

using

Eurocode 5

(2)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia

Contents of lecture

2

B

asics of permissible stress and

semi-probabilistic partial factor concept

Interrelationship of

- Eurocodes,

- harmonized (timber) product standards,

- classification standards, calculation standards and

- test test standards

Basics of Eurocode 5 structure and contents

Design example: straight glulam beam (EC 5 vs. permissible concept)

Design example: curved glulam beam (EC 5 vs. permissible concept)

(3)
(4)

100 years old

glulam beams,

train repair hall,

Bellinzona, Italy

(5)

Olympic Ice rink

Hammar, Norway,

1994

glulam truss beams,

span:97m

(6)

Manufacture of timber parasols for Expo 2000, Hannover

(7)
(8)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 8

HESS – Limitless –Verbindung (22)

(9)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 9

HESS – Limitless –Verbindung (23)

(10)

7-storey timber

building, Berlin, 2011

(11)

10-storey timber

building, Melbourne,

Australia 2013

(12)

Eurocodes and supporting product and test standards

Eurocodes regulate design of timber, steel, concrete structures

in conjunction with national application documents but give

no provisions on material properties

Harmonized product standards regulate material properties of

harmonized building products (e.g. not adhesives) such as

EN 14080 glulam

EN 14081-1 solid timber in conjunction with national grading rules

and classification standard EN 1912 and strength class standard

EN 338

EN 15497 finger jointed lumber

EN 16351 cross laminated timber

EN 14374 LVL

EN 13986 panel products in conjunction with product / production standards, e.g.

EN 300 for OSB

Test standards, e.g. EN 408, EN 789,…..

Calculation standards, e.g. EN 14358 on characteristic values

(13)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia

Permissible stress concept

13

σ

act

= σ

95

acting loads, hence resulting section forces E and stresses σ

represent in general 95% quantiles of the distributions

Design verification

σ

act

≤ σ

permissible

where in case of structural timber (roughly)

σ

permissible

= f

50

/3

f

50

mean value of strength

(14)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia

Semiprobabilistic design concept with partial factors

14

σ

act

= σ

95

as in permissible stress concept the loads / section forces/ stress

distributions represent 95% quantiles of the distributions

Design verification

σ

d

≤ f

d

σ

d

design stress

f

d

design strength

σ

d

= σ

act

· γ

L

γ

L

partial factor for load (1,5 for live load; 1,35 for perm. load)

f

d

= f

k

· k

mod

/ γ

M

f

k

characteristic strength property (5% quantile)

k

mod

modification factor (time, climate)

γ

M

partial factor for strength (material dependant; 1,1 to 1,3)

(15)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia

Semiprobabilistic vs. permissible stress design concept

15

σ

act

σ

d

= σ

act

· γ

L

= σ

act

· 1,5 ≤ f

d

=

γ

L

= 1,5 partial factor for load

f

05

= f

50

(1 - 1,64 · COV)

assuming COV = 0,12

f

05

= f

50

(1 – 0,2) = f

50

/ 1,25

f

05

· k

mod

f

50

· k

mod

γ

M

1,25 γ

M

with γ

M

= 1,3 and k

mod

= 0,8

f

05

· k

mod

f

50

· 0,8

γ

M

1,25 · 1,3

=

=

≈ f

50

2

f

05

· k

mod

f

50

γ

M

=

f

50

2 · 1,5 =

3 =

f

50

σ

permissible

2

Page 15 of 119

(16)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 16

Graphical illustration of semiprobabilistic design concept

Probability

density

m

s

f

s

m

s 95

m

s 95

· γ

s

k

mod

· m

R 05

/ γ

R

k

mod

· m

R 05

k

mod

· m

R

f

R

R, s

=

β · σ

z

= m

z

= k

mod

· m

R

- m

s

f

z

p

f

= 10

-6 Page 16 of 119

(17)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 17

Eurocode 5: Design of Timber Structures – Part 1-1

(18)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 18

Structural Eurocode Program comprises

(19)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 19

Scope of EN 1995

(20)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 20

Structure of Eurocode 5 ( = EN 1995)

(21)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 21

Subjects / Topics of EN 1995-1-1

(22)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 22

Normative References

(23)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 23

Normative References (continued)

(24)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 24

Normative References (continued)

(25)
(26)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 26

Section 2 of EC 5: Basis of design

(27)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 27

Section 2.2 of EC 5: Principles of limit state design

(28)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 28

2.2.2 Ultimate limit states

(29)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 29

2.2.3 Serviceability limit states

(30)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 30

2.2.3 Serviceability limit states

(31)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 31

2.3 Basic variables

(32)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 32

2.3.1.2 Load-duration classes

(33)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 33

2.3.1.2 Load-duration classes

(34)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 34

2.3.1.3 Service classes

(35)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 35

2.3.2 Materials and product properties

(36)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 36

2.3.2 Materials and product properties

(37)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 37

2.4 Verification by the partial factor method

5%- quantile value (lognormal dist.)

(38)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 38

Recommended partial factors

γ

M

for material properties

EC 5 – Table 2.3

(39)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 39

2.4.2 Design values of geometrical data

(40)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 40

2.4.2 Design value of a resistance

Example: R

k

= X

k

· relevant cross-sectional quantity

(41)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 41

EC 5 –Section 3 – Materials properties

(42)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 42

3.1.3/4 Strength and deformation modification factors

(43)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 43

EC 5 – Table 3.1 Strength modification values k

mod

(44)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 44

EC 5 – Table 3.1 Strength modification values k

mod

(continued)

(45)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 45

Accumulated duration of load [hours]

Str

eng

th

mo

dif

ica

tio

n

fa

ct

or

k

mod 0 0.2 0.4 0.6 0.8 1 1.2

0.

001

0.

01

0.

1

1

10

100

10

00

10

000

10

0000

10

0000

0

1 min 1 Woche 6 Monate 10 Jahre 50 Jahre

sehr kurz kurz mittel lang ständig

Nutzungsklasse 1/2

Nutzungsklasse 3

Madison-Kurve

Strength modification values k

mod

= f( time; moisture)

Service class 1 and2

Service class 3

short

very

short

medium

long

permanent

short

1 week

6 months

10 years

10

years

(46)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 46

EC 5 – Table 3.2 Deformation modification values k

def

(47)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 47

EC 5 – Table 3.2 Deformation modification values k

def

(continued)

(48)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 48

EC 5 – 3.2: Solid timber

EN 15497

(49)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 49

EC 5 – 3.3: Glued laminated timber

(50)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 50

EC 5 – 3.3: Glued laminated timber

EN 14080

Now large finger joints are directly regulated in the

harmonized product standard for glulam,

(51)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 51

Example of large finger joint (single joint line)

(52)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 52

Example of large finger joint (two joint lines)

(53)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 53

Example of large finger joint (two joint lines)

(54)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 54

EC 5 – 3.3: Glued laminated timber

(55)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 55

EC 5 – 3.4: Laminated veneer lumber (LVL)

(56)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 56

EC 5 – 3.4: Laminated veneer lumber (LVL)

(57)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 57

EC 5 – 3.5: Wood-based panels

(58)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 58

EC 5 – 3.6: Adhesives

Note: As permissible structural adhesive families and respective classifications have

been profoundly changed in conjunction with introduction of one-component

Polyurethane (1K-PU) and polymer isocyanate (EPI) adhesives according to EN 15425

and EN 16351 principle P (2) is no more throughout valid because of EPI definitions.

(59)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 59

EC 5 – 3.7: Metal fasteners

(60)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 60

EC 5 – Section 4: Durability

(61)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 61

EC 5 – Section 4: Durability

(62)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 62

EC 5 – Section 4: Durability

(63)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 63

EC 5 – Table 4.1 Corrosion protection of fasteners

(64)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 64

EC 5 - Section 5: Basis of structural analysis

(65)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 65

5.2 Members

(66)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 66

5.4 Assemblies

(67)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 67

5.4 Assemblies

(68)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 68

5.4.2 Frame structures

(69)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 69

5.4.4 Plane frames and arches

(70)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 70

Examples of assumed initial geometry deviations

geometry of

frames

initial geometry

deviation corresponding

to symmetrical load

initial geometry

deviation corresponding

to non-symmetrical load

Page 70 of 119

(71)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 71

EC 5 - Section 6: Ultimate limit states

(72)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 72

Tension

6.1.2 Tension parallel to the grain

6.1.2 Tension perpendicular to the grain

(73)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 73

Compression

6.1.4 Compression parallel to the grain

(74)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 74

Compression

6.1.4 Compression perpendicular to the grain

σ

c,90,d

is the design compressive stress in the effective contact area

perpendicular to the grain;

F

c,90,d

is the design compressive load perpendicular to the grain;

A

ef

is the effective contact area in compression perpendicular to

the grain;

F

c,90,d

is the design compressive strength perpendicular to the

grain;

k

c,90

is a factor taking into account the load configuration, the

possibility of splitting and the degree of compressive

deformation.

where

(75)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 75

Compression

6.1.4 Compression perpendicular to the grain

The effective contact area perpendicular to the grain, A

ef

, should be determined taking into

account an effective contact length parallel to the grain, where the actual contact length, ℓ, at

each side is increased by 30 mm, but not more than a, ℓ or ℓ

1

/2, see Figure 6.2.

2. The value of k

c,90

should be taken as 1,0 unless the conditions in the following paragraphs

apply. In these cases the higher value of k

c,90

specified may be taken, with a limiting value

of k

c,90

= 1,75.

3. For members on continuous supports, provided that ℓ

1

≥ 2h, see Figure 6.2a, the value

of k

c,90

should be taken as:

– k

c,90

= 1,25 for solid softwood timber

– k

c,90

= 1,5 for glued laminated softwood timber

where h is the depth of the member and ℓ is the contact length.

(76)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 76

Compression

6.1.4 Compression perpendicular to the grain

4. For members on discrete supports, provided that ℓ

1

≥ 2h, see Figure 6.2b, the value of k

c,90

should be taken as:

– k

c,90

= 1,5 for solid softwood timber

– k

c,90

= 1,75 for glued laminated softwood timber provided that I ℓ ≤ 400 mm

where h is the depth of the member and ℓ is the contact length.

(77)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 77

6.1.6 Bending

(78)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 78

6.1.6 Bending

(79)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 79

6.1.7 Shear

(80)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 80

6.1.7 Shear (crack factor issue)

k

cr

= 0,67

for solid timber

k

cr

= 0,67

for glued laminated timber

k

cr

= 1,0

for other wood-based products in

accordance with EN 13986 and EN

14374.

2. For the verification of shear resistance of members in bending, the influence

of cracks should be taken into account using an effective width of the member

given as:

b

ef

= k

cr

b

where b is the width of the relevant section of the member.

NOTE: The recommended value for k

cr

is given as

(81)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 81

6.1.7 Shear

(82)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 82

6.1.8 Torsion

(83)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 83

6.2.2 Compression stresses at an angle to grain

(84)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 84

6.2.3 Combined bending and axial tension

(85)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 85

6.2.3 Combined bending and axial compression

(86)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 86

6.4 Members with varying cross-section or curved shape

(87)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 87

6.4 Members with varying cross-section or curved shape

Figure 6.8 Single tapered beam

(88)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 88

6.4 Members with varying cross-section or curved shape

(89)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 89

6.4 Members with varying cross-section or curved shape

(90)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 90

6.4 Members with varying cross-section or curved shape

(91)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 91

6.4 Members with varying cross-section or curved shape

(a)

Figure 6.9 – Double tapered (a) and curved (b) beams with the fibre direction parallel

to the lower edge of the beam

Note: In curved beams

the apex zone extends

over the curved parts

of the beam

(92)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 92

Figure 6.9 – Pitched cambered beam (c) beam with the fibre direction parallel

to the lower edge of the beam

Note: In pitched cambered

beams the apex zone

extends over the curved

parts of the beam

6.4 Members with varying cross-section or curved shape

(93)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 93

6.4 Members with varying cross-section or curved shape

(94)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 94

6.4 Members with varying cross-section or curved shape

(95)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 95

6.4 Members with varying cross-section or curved shape

(96)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 96

6.4 Members with varying cross-section or curved shape

(97)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 97

6.4 Members with varying cross-section or curved shape

or

(98)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 98

6.4 Members with varying cross-section or curved shape

(99)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 99

Design of straight glulam member

- comparison of

Eurocode 5 vs. DIN 1052

Design examples

(100)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 100

GL 24 / BS 11

q = 9 kN/m, g = 6 kN/m

10 m

16x80 c

m

Geometry:

l = 10 m

b = 160 mm

h = 800 mm

S = b h²/6 = 17 ⋅ 10

-6

mm³

I = b h³/12 = 6.8 ⋅ 10

-9

mm

4

Straight beam design comparison – EC 5 vs. perm. stress concept

(101)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 101

Property

permissible concept

semi-probabilistic concept

Bending strength

σ

m,perm

= 11 N/mm²

f

m,k

= 24 N/mm²

Shear strength

τ

v,perm

= 1.2 N/mm²

f

v,k

= 3.5 N/mm²

MOE

E

m

= 11000 N/mm²

E

m,mean

= 11000 N/mm²

crack factor

-

k

cr

= 0.67

modification factor for duration

of load and moisture content

k

medium-term)

mod

= 0.6 (Service Class I/II,

Partial factor for material

properties

γ

(glulam, EC 5)

M

= 1.25

Deformation factor

k

def

= 0.8 (Service Class I)

Partial factor for permanent

actions

γ

G

= 1.35

Partial factor for variable

actions

γ

G

= 1.5

Factor for quasi-permanent

value of a variable action

ψ

2,1

= 0.3

Design comparison – EC 5 vs. perm. stress concept

(102)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 102

Result

permissible concept

semi-probabilistic concept

distributed load

F = g + q = 15 kN/m

F

d

=

γ

G

g +

γ

Q

q = 21.6 kN/m

bending moment M

M = F l² / 8 = 188 kNm

M

d

= F

d

⋅ l² / 8 = 270 kNm

bending stress

σ

m

= M/S = 11 N/mm²

σ

m

= M

d

/S = 15.8 N/mm²

utilization (bending)

11 / 11 = 1.00

f

15.8 / f

m,d

= f

m,k m,d

= 1.03

k

mod

/

γ

M

= 15.4 N/mm²

shear force V

V = F l/2 = 75 kN

V

d

= F

d

l/2 = 108 kN

shear stress

τ

v

1.5 V / (b h) = 0.88 N/mm²

1.5 V

d

/ (b h) = 1.89 N/mm²

utilization (shear)

1.2 / 0.88 = 0.73

f

1.89 / f

v,d

= f

v,k v,d

k

= 0.84

mod

/

γ

M

= 2.24 N/mm²

Design comparison – EC 5 vs. perm. stress concept

(103)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 103

deflection

𝑢 =

384𝐸𝐸 = 26𝑚𝑚

5 𝐹 𝑙

4

5𝑔𝑙

𝑢

𝑖𝑖𝑖𝑖4

= 𝑢

𝑖𝑖𝑖𝑖,𝑔

+ 𝑢

𝑖𝑖𝑖𝑖,𝑞=

384𝐸𝐸 +

5𝑞𝑙

4

384𝐸𝐸 = 10.4 + 15.6

= 26𝑚𝑚

𝑢

𝑓𝑖𝑖

= 𝑢

𝑖𝑖𝑖𝑖,𝑔

(1 + 𝑘

𝑑𝑑𝑓

) +

𝑢

𝑖𝑖𝑖𝑖,𝑞

(1 +

ψ

2,1

𝑘

𝑑𝑑𝑓

)=

16.7 + 18.4 = 35.1mm

utilitization (deflection)

𝑢

𝑙/300 = 0.78

𝑢

𝑖𝑖𝑖𝑖

𝑙/300 = 0.78

𝑢

𝑓𝑖𝑖

𝑙/150 = 0.53

Design comparison – EC 5 vs. perm. stress concept

(104)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 104

Design of curved glulam beam

- comparison of

Eurocode 5 vs. DIN 1052

Design examples

(105)
(106)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 106

HESS – Limitless –Verbindung (7)

(107)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 107

W

M

R

H

,

max ,

=

0

25

σ

R H R2 / H = 11 R1 / H = 2,5 R H H/R2 = 0,09 H/R1 = 0,4

W

M

R

H

,

R

H

,

II

+

+

=

σ

2

6

0

35

0

1

+ - H/R2 = 0,09 H/R1 = 0,4

tension stresses

perpendicular to grain

Stress distributions in curved beams with const. moment

bending stresses

parallel to grain

R

1

< R

2

R

1

< R

2

(108)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 108 h stress perp. to grain

-

+ h

-

+

Stress

σ

t,90

of curved and tapered beams with line loads

stress perp. to grain

(109)
(110)
(111)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 111

Curved beam design comparison – EC 5 vs. perm. stress concept

Geometry, dimensions and quality /strength class

of example beam

EN 14080 GL 28: f

m,k

= 28 N/mm

2

DIN 1052 BS 14: σ

m,permissible

= 14 N/mm

2

(112)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 112

Design for bending:

kr = 0,96

h

ap

/ r = 0,118

EC5

F = 23,31 kN

Curved beam design comparison – EC 5 vs. perm. stress concept

r

in

/t = 200,

k

l

= 1,05

k

1

= 1; k

2

= 0,35, k

3

= 0,6

(113)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 113

Design for bending:

kr = 0,96 kl = 1,05

EC5

fm,d = fm,k × kmod /γm GL28: fm,k = 28 N/mm2 load duration:

„medium“, kmod = 0,8 glulam: γm = 1,25

σm,d = 6,85 N/mm2 Map,d = γf × Map combined loading: γf = 1,4 fm,d = 17,92 N/mm2

ratio = 0,38

F = 23,31 kN

Curved beam design comparison – EC 5 vs. perm. stress concept

(114)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 114

Design for tension perp.:

kdis = 1,4 kVol = (V0/V)0,2 = 0,43

EC5

glulam: V0 = 0,01 m3 V = 0,691 m3

curved beam design comparison – EC 5 vs. perm. stress concept

kp = 0,0294

k

5

= 0; k

6

= 0,25, k

7

= 0

h

ap

/ r = 0,118

(115)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 115

Example: Curved Beam with pure moment loading

kp = 0,0294

EC5

ft,90,d = ft,90,k × kmodm glulam: ft,90,k = 0,5 N/mm2 load duration:

„medium“, kmod = 0,8 glulam: γm = 1,25

σt,90,d = 0,19 N/mm2 Map,d = γf × Map combined loading: γf = 1,4 ft,90,d = 0,32 N/mm2

ratio

= 1,0

F = 23,31 kN kdis = 1,4 , kVol = 0,43, 1,4 x 0,43 x 0,32 = 0,19 N/mm2

Design for tension perp.:

(116)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 116

Design for bending:

hap / r = 0,118, kl = 1,05

DIN

1052

F = 23,31 kN

σ

m

≤ σ

m,permissible

σ

m

= k

l

× 6 M

ap

/b h

2 σm,permissible = 14 N/mm2 σm = 4,66 N/mm2

ratio = 0,33

Curved beam design comparison – EC 5 vs. perm. stress concept

(117)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 117

Design für tension perp.:

DIN

1052

F = 23,31 kN

σ

t,90

≤ σ

t,90,permissible

σ

t,90

= k

p

× 6 M

ap

/b h

2 σt,90,permissible = 0,2 N/mm2 σt,90 = 0,14 N/mm2

ratio = 0,69

hap / r = 0,118, kp = 0,0294

curved beam design comparison – EC 5 vs. perm. stress concept

(118)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 118

DIN 1052

F = 23,31 kN

EC5

bending

tension perp.

1,00

0,69

0,40

0,33

no pre-stress effect

no size effect

curved beam design comparison – EC 5 vs. perm. stress concept

(119)

Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 119

Now ist time to finish!

Thank you very much for your patient listening!

References

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