Design of timber structures to EN 1995-1-1

EN 1995-1-1Design of timber structures

EC 5-1-1 Design of Timber Structures DIN 1052

EC 5-1-1 Design of Timber Structures

General conceptGeneral concept


Design situationsDesign situations

• Permanent situation Permanent situation (after erection of the (after erection of the structure)structure)


• temporary situation temporary situation (during erection)(during erection)



• Accidential situation Accidential situation (impact, fire)(impact, fire)



Limit statesLimit states

• Ultimate limit statesUltimate limit states

• Serviceability limit statesServiceability limit states

For all design situations the limit states shall For all design situations the limit states shall not be exceeded. not be exceeded.


• Characteristic Actions according Characteristic Actions according to EN 1991to EN 1991

GGkk e.g. self-weighte.g. self-weight

QQkk e.g. wind, snow, traffice.g. wind, snow, traffic

AAkk e.g. impacte.g. impact

ActionsActions


Ultimate limit stateUltimate limit state

Design values of actionsDesign values of actionsBasic combination:Basic combination:G,j G,j GGk,jk,j + + Q,1 Q,1 QQk,1k,1 + + Q,i Q,i 0,i 0,i QQk,ik,i

e.g. 1,35e.g. 1,35 GGkk + + 1,51,5 WWkk + + 1,51,5 0,5 0,5 SSkk

simplified:simplified:

Most unfavourable variable action: Most unfavourable variable action: G,j G,j GGk,jk,j + + Q1 Q1 QQk,1k,1 1,351,35 GGkk + + 1,51,5 WWkk

All unfavourable variable actions:All unfavourable variable actions:G,j G,j G Gk,jk,j + 1,35 + 1,35 Q Qk,ik,i 1,351,35 ( (GGkk + W + Wkk + S + Skk))

EC 5-1-1 Design of Timber Structures Design and calculation principles

From a statistic point of view it´s unlikely that all actions/loads act at the sametime with their fully values.

0 combination coefficient (in fundamental design situations)

1 frequent coefficient (in accidential design situations and servicability

calculations)

2 quasi-permanent coefficient (in servicability calculations)

Principle rule:

G K Q,1 K ,1 0,i Q,i K ,ii 2

G Q Q

Coefficient for represantative values of actions (for exact national data see: National Applience Documents)

Use of 0 from the second variable action/load.

Design values of actions; coefficient for representative values of actions:


Combination factorsCombination factors


Combination factors Combination factors

ActionAction 00 11 22

Domestic residential areasDomestic residential areas 0,70,7 0,50,5 0,30,3

Congregation areasCongregation areas 0,70,7 0,70,7 0,60,6

Storage areasStorage areas 1,01,0 0,90,9 0,80,8

WindWind 0,60,6 0,50,5 0,00,0

Snow (Snow ( 1000 m) 1000 m) 0,50,5 0,20,2 0,00,0


Partial safety factors for actions Partial safety factors for actions (EN 1990)(EN 1990)

ActionAction permanentpermanent variablevariable

favourablefavourable GG = 1,0 = 1,0 QQ = 0 = 0

unfavourableunfavourable GG = 1,35 = 1,35 QQ = 1,5 = 1,5

13

Ed

Effect of Actions:

Self-LoadWindSnowVariable loadsTemperatureFire....

Rd

Resistance:

StructureStructural ElementsMaterials, E-Modulus etc.cross sections, Area, Moment of Inertia

Semi-probalistic safety concept

≤

Safetyfr

eque

ncy

freq

uenc

y

Effect of actionEffect of action Load carrying Load carrying capacity Rcapacity R

95% quantile95% quantile 5% quantile5% quantile

EEkk RRkk

FF MM

EEdd RRdd

SafetySafety

15

Partial Safety Factors F ( G ,Q ) , M

Gk × G + Qk × Q kmod × Rk / M (timber: M = 1,3)

Safety factors in case of fire or other accidential situations: = 1,0

4. Sicherheitskonzepte

Safety Concept - simplified


Serviceability limit statesServiceability limit states

Calculation of Calculation of

• deformations deformations

• vibrations vibrations


III.1 Eurocode 5 in basic; loads/actions on structures

. the combination of actions under consideration

d Q kQ Q

d G kG G

Increase the actions/load by partial safety factors gamma factors)

less safety risks

Design situation G Q

Structural design calculation

favourable effect 1,0 -

unfavourable effect 1,35 1,5

Check at servicability limit state

1,0 1,0


Design values of actionsDesign values of actionscharacteristic (rare) combination: characteristic (rare) combination: GGk,jk,j + Q + Qk,1k,1 + + 0,i 0,i QQk,ik,i

GGkk + W + Wkk + + 0,50,5 SSkk

quasi-permanent combination:quasi-permanent combination:GGk,jk,j + + 2,i 2,i QQk,ik,i

GGkk + + 0,00,0 WWkk + + 0,00,0 SSkk

Serviceability limit statesServiceability limit states


Comparison of safety conceptsComparison of safety concepts

Taking into account Taking into account Semi-probalistic Semi-probalistic methodmethod

Concept of Concept of permissible permissible

stressesstresses

ActionAction

combinationscombinations Combination factor Combination factor

Safety factorSafety factor

timbertimber

Load duration - and Load duration - and service-class service-class






stressesstresses

ActionAction

combinationscombinations Combination factor Combination factor w+s/2 or s+w/2w+s/2 or s+w/2


timbertimber







stressesstresses

ActionAction


Safety factorSafety factor = 1,35 (G)= 1,35 (G) = 1,50 (Q)= 1,50 (Q)

timbertimber







stressesstresses

ActionAction



= ?= ?(permissible stress)(permissible stress)

timbertimber







stressesstresses

ActionAction




timbertimber


kkmodmod

0,6 permanent,SC 10,6 permanent,SC 10,9 short, SC 10,9 short, SC 10,5 0,5 permanent, SC 3

0,7 short, SC 30,7 short, SC 3





stressesstresses

ActionAction




timbertimber


kkmodmod



??(permissible stress) (permissible stress)

Reduction of 1/6 Reduction of 1/6 (SC 3)(SC 3)





stressesstresses

ActionAction




timbertimber


kkmodmod





Safety factorSafety factor = 1,3 (5%-Quantil)= 1,3 (5%-Quantil)




stressesstresses

ActionAction




timbertimber


kkmodmod





Safety factorSafety factor = 1,3 (5%-Quantil)= 1,3 (5%-Quantil)



kmod · fk kmod for the action/load with shortest design situation

Ultimate limit state:

Serviceability limit state:

separate for each action/load

wel · (1+ kdef)

def

E

1 k

Influence of service classes and duration of load



Ultimate limit state: 05d mod

M

XX k

Bending strength:m,k

m,d modM

ff k

t ,0 ,kt ,0,d mod

M

ff k

Servicability limit state: d mX X

Modulus of elasticity: d 0,meanE E

Design value of material properties:

Tensile strength:


d fd

loading resistance

freq

uen

cy

M

Ek

design values

5%-quantiles

fk

x G

QEd

x kmod


Structural design calculation:


Strength properties for timber (Tab. F. 5 DIN 1052)

(for exact national data see: National Annexes)


Strength properties for gluelam (Tab. F. 9 DIN 1052)

(for exact national data see: National Annexes)


++

-

-

+

-

z

z

yy+

+

-

-

+

-

z

z

yy

Vd

Maße in cm

6

5

12

18

12

24

III.2 Bending, shear, buckling

Design resistance for cross-sections


Vd = design value of the shear force S = static moment (section modulus)

= b·h2/8 (rectangle cross-section)I = second moment of area (moment of inertia)

= b·h3/12 (rectangle cross-section)b = width

fv,d = design shear strength for the actual condition

dd v,d

V1,5 f

A d

v ,d

1,5 V A1

f

dd v,d

V Sf

I b

d

v,d1

f

Shear force


dd

v ,dv ,d

A in cm²V

erf A 15 with V in kNf

f in N/mm²

proportioning:

dd v ,d

V15 f

A d

v ,d

V A15 1

f

d in [N/mm²]

Vd in [kN]

A in [cm²]fv,d in [N/mm²]

dd

A in cm²erf A 9 V with

V in kN

For sawn timber C 24, service class 2 and medium term action:


uniaxial bending

construction

Pfette

Sparren

static systems

dm,d m,d

n

Mf

W d n

m,d

M / W1

f

m,d = design value of bending stress

Md = design value of bending moment

Wn = netto moment of resistance considering the cross section weaks

fm,d = design value of bending strength

rafter

purlin


600 mm h fm,y,k

250 mm h 600 mm

h 250 mm fm,y,k · 1,1

h

0,1

m,y ,k600

fh

dm,d m,d

n

M1000 f

W d n

m,d

M / W1000 1

f

m,d in [N/mm²]

Md in [kNm]

Wn in [cm³]

fm,d in [N/mm²]

E.g. gluelam influence of height:

Ultimate limit state


nd

n dm,d

m,d

W in cm³M

erf W 1000 mit M in kNmf

f in N/mm²

proportioning:

For sawn timber C 24, service class 2 and medium term action:

nn d

d

W in cm³erf W 68 M with

M in kNm


4,3

m

w

y y

100 100 mm

yy wz

qz

yy wz

Fc

Fc

Biegung um y-Achsem,y

Knicken um y-Achsekc,y

Stability of Members


imperfections additional bending moment

c,0,dc,0,d c c,0,d

n

Fk f

A c,0,d n

c c,0,d

F A1

k f

An: local cross section weakenings might be neglected at the stress verification if they are not situated in the middle third of the buckling length.kc: local cross section weakenings might be neglected at the calculation of the buckling coefficient.

Compression members endangered by buckling

Structural design calculation using compressive stress values and reduced compressive strength:


c2 2

rel ,c

1k 1

k k

buckling coefficient / instability factor

k = 2c rel ,c rel ,c0,5 1 0,3

c = 0,2 for solid timber 0,1 for glued laminated timber and LVL

rel,c = Relative Slendernessc,0,k c,0,kef

0,05 0,05

f f

i E E

= ef

i

= Slenderness

ef = · s = effective lenght

= buckling length coefficient

i I A


buckling length coefficient


compression member with intermediate lateral support:

buckling length = distance of lateral supports

different buckling lengths ef,y and ef,z :

2

1y z

Scheibe

hho

hu3

z y

h


procedure at the design calculation:

1. determination of buckling lengths ef for buckling around the principal axis

2. calculation of the slenderness ratio y and z

3. determination of instability factors kc,y und kc,z

ef i with i = 0,289 · h resp. = 0,289 · w at rectangular cross sections

4. verification of buckling resistance

c,0,dc,0,d c c,0,d

n

F10 k f

A c,0,d n

c c,0,d

F A10 1

k f

c,0,d in [N/mm²]

Fc,0,d in [kN]

An in [cm²]

fc,0,d in [N/mm²]


a A Nd, max in kN for a buckling length of lef in m

mm mm² 2,00 2,50 3,00 3,50 4,00 4,50 5,00 5,50 6,00 6,50 7,00

100 10000 72 50,4 36,4 27,4 21,3 17 13,9 11,5 9,7 8,3 7,2

120 14400 130 97,6 72,5 55,2 43,2 34,6 28,3 23,6 20 17,1 14,8

140 19600 202 164 127 98,7 78 62,9 51,6 43,1 36,6 31,4 27,2

160 25600 284 247 202 161 129 105 86,5 72,5 61,5 52,9 45,9

180 32400 375 340 293 243 199 163 136 114 97,1 83,6 72,7

200 40000 476 444 399 343 288 240 201 170 146 126 109

220 48400 587 557 514 459 397 337 286 244 209 181 158

240 57600 709 679 639 586 522 454 391 336 290 252 221

260 67600 841 812 773 723 660 588 515 448 390 340 299

Design resistance of squared columns C 24 in Service class 2 for medium action load

for axail compression a

a


Serviceability limit state

Limiting values: Only Recommendations, disregarding is possible


Vibrations:

To reduce vibrations the fundamental frequency of the floors should be greater than 8 Hz.


Vibrations:

High stiffness of the floor reduce the vibration,

Little deflection under permanent load,

frequency greater than 8 Hz.

For single-span beams

In residential buildings vibrations of the floors often cause unacceptable discomfort to the users. To reduce vibrations the fundamental frequency of the floors should be greater than 8 Hz.

g*,instw 6 mm


Designtables for estimate calculations given in timberdesigntables.pdf

Notice:

First ask for the national standard cross-sectional dimensions, they differ in different territories!



Span tables for Timber C 24 in for floor joists permanent (dead) load gk in kN/m²Single span beams for ulitmate limit state and serviceability limit state except vibration imposed load qk in kN/m²

l gk

m kN/m² 0,60 0,70 0,80 0,90 1,00 0,60 0,70 0,80 0,90 1,001,5 60 x 160 60 x 180 60 x 180 60 x 200 60 x 200 60 x 180 60 x 200 60 x 200 60 x 240 60 x 2401,75 60 x 160 60 x 180 60 x 200 60 x 200 60 x 240 60 x 180 60 x 200 60 x 200 60 x 240 60 x 240

2 60 x 180 60 x 180 60 x 200 60 x 200 60 x 240 60 x 180 60 x 200 60 x 240 60 x 240 60 x 2402,25 60 x 180 60 x 180 60 x 200 60 x 240 60 x 240 60 x 200 60 x 200 60 x 240 60 x 240 60 x 2401,5 60 x 180 60 x 180 60 x 240 60 x 240 60 x 240 60 x 200 60 x 240 60 x 240 60 x 240 80 x 2401,75 60 x 200 60 x 200 60 x 240 60 x 240 60 x 240 60 x 240 60 x 240 60 x 240 80 x 240 80 x 240



2 80 x 240 80 x 240 120 x 200 120 x 240 120 x 240 80 x 240 120 x 240 120 x 240 120 x 240 -2,25 80 x 240 80 x 240 120 x 240 120 x 240 120 x 240 80 x 240 120 x 240 120 x 240 120 x 240 -1,5 80 x 240 80 x 240 120 x 240 120 x 240 120 x 240 120 x 200 120 x 240 120 x 240 - -1,75 80 x 240 120 x 200 120 x 240 120 x 240 120 x 240 120 x 240 120 x 240 120 x 240 - -

2 80 x 240 120 x 240 120 x 240 120 x 240 - 120 x 240 120 x 240 - - -2,25 80 x 240 120 x 240 120 x 240 120 x 240 - 120 x 240 120 x 240 - - -1,5 100 x 200 120 x 240 120 x 240 - - 120 x 240 120 x 240 - - -1,75 120 x 240 120 x 240 120 x 240 - - 120 x 240 - - - -

2 120 x 240 120 x 240 - - - 120 x 240 - - - -2,25 120 x 240 120 x 240 - - - 120 x 240 - - - -

Joist spacing e in m

imposed load qk = 2,0 kN/m² imposed load qk = 2,75 kN/m²

3,0

3,5

4,0


4,5

5,0

5,5

Span tables with german sizes, Vibrations of residential floors disregarded


Span tables for Timber C 24 in for floor joistsSingle span beams for ulitmate limit state and serviceability limit state simplified vibration analysis for residential floors included

l gk

m kN/m² 0,60 0,70 0,80 0,90 1,00 0,60 0,70 0,80 0,90 1,001,5 60 x 160 60 x 180 60 x 180 60 x 200 60 x 200 60 x 180 60 x 200 60 x 200 60 x 240 60 x 2401,75 60 x 180 60 x 180 60 x 200 60 x 200 60 x 240 60 x 180 60 x 200 60 x 200 60 x 240 60 x 240



2 80 x 240 80 x 240 120 x 240 120 x 240 120 x 240 80 x 240 120 x 240 120 x 240 120 x 240 -2,25 80 x 240 120 x 240 120 x 240 120 x 240 - 120 x 240 120 x 240 120 x 240 - -1,5 120 x 240 120 x 240 120 x 240 - - 120 x 240 120 x 240 - - -1,75 120 x 240 120 x 240 - - - 120 x 240 - - - -

2 120 x 240 - - - - 120 x 240 - - - -2,25 120 x 240 - - - - - - - - -

4,5


3,0

3,5

4,0

imposed load qk = 2,0 kN/m² imposed load qk = 2,75 kN/m²


Span tables with german sizes, with vibrations as design requirement


Thank you very much Thank you very much for your attention!for your attention!