Design of FRP-Profiles and All-FRP-Structures

Design of FRP-Profiles and All-FRP-Structures Fibre Composites FS09 A Schumacher 14102009

Design of FRP-Profiles and All-FRP-Structures

- Lecture Dr Ann Schumacher annschumacherempach

- Exercise Dr Andrin Herwig andrinherwigempach

ReferencesBank L ldquoComposites for Construction - Structural Design with FRP MaterialsrdquoJohn Wiley amp Sons Inc 2006 (Chapters 12 - 15)Fiberline ldquoFiberline Design Manualrdquo wwwfiberlinedk 2003Clarke JL (Ed) ldquoStructural Design of Polymer Composites - EUROCOMP Design Code and Handbookrdquo E amp FN Spon 1996

Design of FRP-Profiles and All-FRP-Structures


Outline

Introduction(Prorsquos and conrsquos of FRP Examples)

Materials(Manufacturing process Materials Durability)

Design Concept(Concept Basic assumptions hellip)

Bending Beam(Timoshenko theory Stresses Deformations Buckling hellip)

Axial Members(Serviceability and ultimate limit states)

Connections(Bolted joints Glued joints)


Introduction


Introduction Prorsquos and conrsquos

ProrsquosHigh specific strength

Good in-plane mechanical properties

High fatigue and environmental resistance

Adjustable mechanical properties

Lightweight

Quick assembly erection

Low maintenance

Highly cost-effective (2-10 eurokg)

maxmaxl g

σρ

=sdot

1384 km

CFRP

64 km278 km

Steel S500GFRPMaterial



ConrsquosLightweight

Brittle

High initial costs

Low to moderate application temperature (-20 up to 80 degC)

Low fire resistance (sometimes with unhealthy gases)


Introduction Common profiles

Structural profilesMost structural profiles produced in conventional profile shapes similar to metallic materials

Similarity in geom and properties however no standard geom mechanical and physical properties used by all manufacturers

Structural profiles Non-structural profiles


Introduction Examples

Footbridges

Fiberline Bridge in Kolding DK

Span 40 mCost 05 mio CHFOnly Fiberline standard profiles used

httpwwwfiberlinecomgbcasestoriescase1837asp

Pontresina bridge Switzerland

Span 2 x 125 mWeight 33 tons (installation by helicopter)




Footbridges

Composite pedestrian bridge in Lleida Spain

Span 38 mWidth 30 m



Introduction Examples (ASSET Profile)

Road bridges

West Mill Bridge England

Span 10 mWidth 68 mLoad capacity 46 tons


Klipphausen Bridge Germany





Bridgedeck (Footbridges)Wuumlrenlos Switzerland Loopersteg Switzerland



Buildings

Eyecatcher Building Basel Switzerland

Height 15 mStoreys 5


Project Maagtechnic



Laboratory bridgeEmpa Laboratory Bridge Switzerland




Noise barrier SBB

Goumlschenen Switzerland

Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic



RailingsOensingen Switzerland

Heineken brewery Switzerland


Introduction Application

Applications where GFRP structures are competitive

Significant corrosion and chemical resistance is required(Food and chemical processing plants cooling towers offshore platforms hellip)

Electromagnetic transparency or electrical insulation is required

Light-weight is cost essential(fast deployment hellip)

Prestige and demonstration objects (eg Novartis Campus Entrance Building)

Photo Prof Th Keller EPFL


Material


Only pultruded GFRP profiles will be considered in this lecture

Production of profiles with constant cross-section along the length

High quality

Continuous longitudinal fiber bundles and filament mats

Pultrusion line

Material Pultrusion process


Material Components

Pultruded profiles contain three primary componentsreinforcement

Matrix

Supplementaryconstituents

polyesterepoxyphenol

polymerisation agentsfillersadditives


Material Shapes of pultruded profiles

Available Profiles on Stock

Length up to 12 m

Special cross-sections can be designed and ordered(several kilometres are necessary rarr special tools have to be designed)


Material Durability

Various environmental and load conditions that affect durability of (G)FRPs in terms of strength stiffness fibermatrix interface integrity cracking

watersea waterchemical solutionsprolonged freezingthermal cycling (freeze-thaw)elevated temperature exposureUV radiationcreep and relaxationfatiguefirehellip


Material Durability

Environmental reduction factor for different FRP systems and exposure conditions

070Aramidepoxy

050Glassepoxy(chemical plants)

085CarbonepoxyAgressive environ

075Aramidepoxyparking garages)

065Glassepoxy(bridges piers

085CarbonepoxyExterior exposure

085Aramidepoxy

075Glassepoxy

095CarbonepoxyInterior exposure

Environ reductionFiber resin typeExposure condition


Material Durability

GFRP is more susceptible to degradation than CFRP by the following effects

alkaline effects (caution when GFRP in contact with concrete)acid effectssalt effectsfatigueUV radiation

Fire protection is a major (unsolved) issue for (G)FRP structural elements and components

Smoke generation and toxicity must be consideredStrength of GFRP is affected by fatigue loading(more than CFRP)


Material Manufacturers

GFRP profiles available on stock

In Europe two companies pultrude FRP-Profiles

Fiberline Composites Denmarkwwwfiberlinecom

Fiberline Design Manual (wwwfiberlinedk)rarr helpful tool to design structures

(material properties geometries connections hellip)

Top Glass Italywwwtopglassit




In North America

Strongwell USAwwwstrongwellcom

Creative Pultrusions USAwwwcreativepultrusionscom

Bedford Reinforced Plastics USAwwwbedfordplasticscom


Design Concept


Design Concept Basic Assumptions

Definitions and directions


Design Concept

Codes

Every manufacturer has its own profile design rarr No European Design Code is available (only EN13706 about testing and notation)

There exists European guidelines EUROCOMP 1996 Design CodeEUROCOMP 1996 Handbook

Fiberline Design Manual is based on Eurocomp 1996

Design concept (according to Eurocodes and Swisscodes)

Partial safety factors

Measured material parameters

Rules for bolted connections


Design Concept

Concept of Limit State Design (According to Euro Codes and Swiss Codes)

Ultimate limit stress

Ed le Rd

Ed hellip Calculated stress (including load factors) hellip SIA260 261

Rd hellip Rated value of the resistance capability

where

Rk hellip the calculated resistance capability

kd mγ=

RR


101020Production process

Operating temperature

111116Degree of postcuring

115115225Derivation of mat properties

FiberlineMinMaxDescriptionCoefficient

Design Concept

Reduction coefficient m m1 m2 m3 m4γ γ γ γ γ= sdot sdot sdot

m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60

Long-term loadShort-term load

Operatingtemperature degC m4γ


Design Concept

Serviceability limit states

Ed le Cd

Ed hellip the crucial action effect due to the load cases considered inthe investigated dimensioning situation Typically maximaldeflection response of the structure

Cd hellip corresponding serviceability limit SIA 261



Material Properties stength values (Fiberline Profiles)



Material Properties stiffness values (Fiberline Profiles)



Typical data sheet of a profile (Fiberline I-Profile)


Bending Beam


Bending Beam Design of hellip

Calculate bending moments Md and shear forces Qd acting on the profile using the partial coefficient (SIA 260 261)

Ultimate limit state

Bending

Shear

Ak hellip relevant shear area

d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le



Serviceability limit state

Deflection limit

hellip typically selected between 200 and 400given by SIA 261 or the building owner

hellip calculated including shear deformations

Vibrations

Light-weighted and lsquosoftrsquo structures are susceptible to vibrations (traffic wind the movement of people hellip)

max 1wL αlt

α

maxw


Bending Beam Timoshenko Theory

Pultruded profiles have a low shear modulus rarr shear deformation must be taken into account

Several bending theories have been published for beams

Euler-Bernoulli theory (1702)

Timoshenko theory (1968)

Higher order beam theory

A simply supported beam with a symmetric cross-section is discussed



Cross-sections planeand perpendicular

1 degree of freedom

w

Cross-sections plane butNOT perpendicular

2 degrees of freedom

w and ψ

Cross-sections do NOTremain plane

3+ degrees of freedom

w ψ and hellip


Bending Beam Euler vs Timoshenko Theory

Kinematic relationships

( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=

part= =minus sdotpartpartpart= + =

part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=

part= =minus sdotpartpartpart= + =minus +

part part

Hookrsquos law

0degE and G 2x x xy xyσ ε τ ε= sdot = sdot

z0deg E Iz x xxQS

M y dydz wσ= minus sdot sdot = sdot sdotintint

( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ

= minus sdot sdot = sdot

= sdot = minus sdot sdot

intint

intint



Equilibrium

Solution for the simply supported beam (distributed load)

In a first approximation the deflections are calculated by direct integration of

z0deg

( ) E IxxM xw = sdot

( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ

minus minus sdot sdot

sdot + minus sdot sdot

=minus =

= =minus

Equilibrium on an infinitesimal beam element

Coupled second order differential equation

21 1( ) (0) 0 and ( ) 02 2

M x qLx qx w w L= minus = =

( )3 2 3

0deg z

( ) 224 E Iqxw x L Lx x= sdot minus +sdot sdot

2

0deg z

1 1 1E I 2 2xxw qLx qx⎛ ⎞= minus⎜ ⎟sdot ⎝ ⎠

(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ

= == rarr = = rarr =

Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )

w x A x A x A x A x A

x B x B x B x Bψ

= + + + +

= + + +


Put in and solve for the coefficients rarr


Use the boundary conditions and the second differential eq to calculate A1 ndash A5

( )0deg z E I 0xx xw GAψ ψ κsdot + minus sdot sdot =

1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg

sdot= minus = minus minus

sdotsdot

= minus = minus minussdot

( ) ( )( )2 2

0

( )2 GA 24 E Iz

qx L x L Lx xqx L xw x

κ deg

minus + minusminus= +

sdot sdot sdot

Deflection at midspan

4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg

sdot sdot= sdot sdot sdot


General expression for the total beam deflection as a sum of the deflection due to bending and shear

GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported

Concentrated load (P)

Uniformly distr load (q)



Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L




Example influence of the shear deformation

Profile 300 x 150 mm I-beam

Load uniformly distributed

General rule of thumbfor GFRP beams withspandepth gt 25 sheardeformation can beignored


Bending Beam Example

Choose an appropriate Profile for the following specifications

1 Deflections and loading

=

=

==

1300 rarr wmax=001 mwmaxL

10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I

d ulsq L hσ sdot= sdot

maxky

12 Ad ulsq L

τ sdot=



2 Find a profile with sufficient bending stiffness

Shear deformations are neglected in a first step

rarr from specification table choose I 240x120x12 rarr

3 Check the bending and shear stresses

6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge

6 20 1369 10 NmE Izdeg = sdot

2

maxz

358 MPa8 2 Id ulsq L hσ sdot= =sdot

max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =

0 185 MPab df degle =

20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ

4 Check deflection (including shear deformation)

5 Remarks

The design of GFRP-profiles is mostly driven by serviceability criteria

Start the design iteration procedure using the maximal deflection criterion

max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)


Bending Beam Stability problems

Lateral-torsional bucklingFlange (compressive) displace laterally to the transverse load direction

Torsional stiffness is too low (especially for open section profiles)

Theoretical calculations or design measuresrarr see eg LP Kollaacuter 2003

Mechanics of composite structuresExample

Compressive flanges are kept in place by connection to the bridge deck



Flange (compressive) displaces in the direction of the transverse load

Low bending stiffness perpendicular to the pultrusion direction

Weak fiber mats

Local buckling of walls due to in-plane compression

Local buckling of walls due to in-plane shear

Web crushing and web buckling in transverse direction


Axial Members


Axial Members Tension

Ultimate limit state under axial tension Nd


Remark The critical aspect of axial members in tension are neither the serviceability nor the ultimate limit state Critical is the load transfer to the GFRP profile

0NdA

tm

fγ

degle

0deg

N LE Axδ sdot= sdot


Axial Members Compression

Ultimate limit state under axial compression Nd

hellip maximal compressive load

hellip Euler load

hellip Buckling length for columns

hellip coefficient for Youngrsquos modulus = 13

cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ



The influence of shear deformation should be considered but in the most cases the influence will be small (less than 5)

Local buckling should be considered for short columns

For more information on the various buckling modes and effects rarr see LP Kollaacuter 2003 Mechanics of composite structures

Global buckling Local buckling


Connections


Connections Introduction



(from Eurocomp Design Code 1996)


Connections Bolted joints

Bolts = Stress concentration in the profile and the bolt

It is necessary to ensure that the bolts and the profilecan withstand this concentrated local stress compression

It is necessary to ensure that the region surroundinga group of bolts will not be torn out of the profile

Basic failure modesin bolted shearconnections

bolt shear failure



The design procedure is comparable to the one for steel connections but since there exist no standard GFRP material rarr each manufacturer has its own design rules for bolted joints

IMPORTANT REMARKS

The direction of pultrusion and the direction of the force is RELEVANT(anisotropic material)

Use stainless or galvanised steel

Do not cut threads in the composite material

Use screws with shafts


Calculation of load bearing capacity of bolts

Shear in longitudinal direction (0deg)

Shear in transverse direction (90deg)

Tensile force

Minimum distances

Connections Bolted joints (Fiberline recommendations)


Joint capacity tables available for shear and tension

m

150 MPa( 13)B d

d tP γsdot sdot=

=

Shear in longitudinal direction 0deg

m

70 MPa( 13)B d

d tP γsdot sdot=

=

Shear in transverse direction 90deg



Bolted connection in shear eg shear in longitudinal direction


γmPBolt le dt720 MPaγmPBolt le dt240 MPa

γmPBolt le dt240 MPa γmPBolt le dt240 MPaγmPBolt le dt150 MPa


Bolted connections in tension

Static conditions

Bolt Tearing of bolt in threaded cross-section

Laminate Shear fracture at rim of washer

Geometry and strength

Diameter of washer2d

Tensile strength of bolt hellipfyk

Shear strength of laminatehellipfτ

Thickness of laminatet

Stress area of the boltAs

Diameter of the boltd

s ykd m

A fP γ

sdotle

2d m

d t fP τπγ

sdot sdot sdot sdotle



Connections Bonded joints

Using an adhesive agent for joining profiles can have advantages

Easy to use easy to make aesthetic joints

Typically more rigid than bolted joints

Glued joints subjected to dynamic loads are good

But be careful hellipAdhesive agents have properties that depend on time temperature humidity hellip

Failure in glued joints takes place suddenly (brittle behaviour)

The load-bearing capacity is not proportional to the area which is glued

The design of bonded joints may be based onAnalytical models for plate-to-plate connections (see Eurocomp 1996 Design Code)

Design guidelines supplemented by testing

Finite element analysis



A bonded joint has the following three primary failure modes

adhesive failure

cohesive failure of adhesive

cohesive failure of adherend

The design of any bonded joint shall satisfy the following conditions

allowable shear stress in the adhesive is not exceeded

allowable tensile (peel) stress in the adhesive is not exceeded

allowable through-thickness tensile stress of the adhesive is not exceeded

allowable in-plane shear stress of the adherend should not be exceeded

The calculation of the stresses has to be done very carefully Often calculations are supplemented by testing



Different types of bonded joint configurations

Research on bonded joints for structuralapplications


Connections Other joints

Brackets for assembly (Fiberline)

Custom pultruded connections


GFRP Some final remarks

Perpendicular to the direction of pultrusion the material is WEAK and SOFTrarr avoid such loadings if possible

In order to use pultruded GFRP-profiles economically the design must be done in a clever way eg for bridges the railings should be used as part of the load-bearing structure

GFRP structures are very light rarr vibration problems may occur


Outline

Introduction(Prorsquos and conrsquos of FRP Examples)

Materials(Manufacturing process Materials Durability)

Design Concept(Concept Basic assumptions hellip)

Bending Beam(Timoshenko theory Stresses Deformations Buckling hellip)

Axial Members(Serviceability and ultimate limit states)

Connections(Bolted joints Glued joints)


Introduction







Lightweight


Low maintenance


maxmaxl g

σρ

=sdot

1384 km

CFRP

64 km278 km





Brittle

High initial costs










Footbridges









Footbridges


Span 38 mWidth 30 m




Road bridges












Buildings




Project Maagtechnic







Noise barrier SBB


Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Introduction







Lightweight


Low maintenance


maxmaxl g

σρ

=sdot

1384 km

CFRP

64 km278 km





Brittle

High initial costs










Footbridges









Footbridges


Span 38 mWidth 30 m




Road bridges












Buildings




Project Maagtechnic







Noise barrier SBB


Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure




























Lightweight


Low maintenance


maxmaxl g

σρ

=sdot

1384 km

CFRP

64 km278 km





Brittle

High initial costs










Footbridges









Footbridges


Span 38 mWidth 30 m




Road bridges












Buildings




Project Maagtechnic







Noise barrier SBB


Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure

























Brittle

High initial costs










Footbridges









Footbridges


Span 38 mWidth 30 m




Road bridges












Buildings




Project Maagtechnic







Noise barrier SBB


Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure





























Footbridges









Footbridges


Span 38 mWidth 30 m




Road bridges












Buildings




Project Maagtechnic







Noise barrier SBB


Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
























Footbridges









Footbridges


Span 38 mWidth 30 m




Road bridges












Buildings




Project Maagtechnic







Noise barrier SBB


Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
























Footbridges


Span 38 mWidth 30 m




Road bridges












Buildings




Project Maagtechnic







Noise barrier SBB


Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
























Road bridges












Buildings




Project Maagtechnic







Noise barrier SBB


Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure



























Buildings




Project Maagtechnic







Noise barrier SBB


Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
























Buildings




Project Maagtechnic







Noise barrier SBB


Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure




























Noise barrier SBB


Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
























Noise barrier SBB


Project Maagtechnic



Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
























Balconies

Switzerland

Project Maagtechnic














Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure



































Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure































Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Material




High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure

























High quality


Pultrusion line



Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Material Components


Matrix







Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure

























Length up to 12 m



Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Material Durability




Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Material Durability


070Aramidepoxy






085Aramidepoxy

075Glassepoxy




Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Material Durability
















In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure

































In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure

























In North America





Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Design Concept





Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure


























Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Design Concept

Codes









Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Design Concept



Ed le Rd



where


kd mγ=

RR







Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure




























Design Concept


m1γ

m2γ

m3γ

m4γ

mγ mγ

31312580

2510-20 +60




Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Design Concept


Ed le Cd













Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
































Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure





























Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure


























Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Bending Beam





Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure


























Bending

Shear


d max d max 0max

M MW Wy z b

mzy

fσ γ

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

deg= + le

d maxmax

kyAy

m

Q fττ γ= le




Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure

























Deflection limit



Vibrations


max 1wL αlt

α

maxw












1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure

































1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure

























1 degree of freedom

w



w and ψ



w ψ and hellip




( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure

























( )( )

( )

2 0

x x

y

xx xx

yxxy

u y w xu w x

u y w xxuu

y x

ε

ε

=minus sdot=


part part

( )( )

( )

2 ( ) ( )

x

y

xx x

yxxy x

u y xu w x

u y xxuu x w xy x

ψ

ε ψ

ε ψ

=minus sdot=


part part

Hookrsquos law


z0deg E Iz x xxQS


( )

z0deg E I

z x xQS

y xQS

M y dydz

Q dydz w GA

σ ψ

κ τ ψ κ



intint

intint



Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
























Equilibrium



z0deg


( )( )z0deg

( ) E I 0x

x

xx x

xx x

q x w GAw GA

QM Q

ψ κψ ψ κ



=minus =

= =minus



21 1( ) (0) 0 and ( ) 02 2


( )3 2 3

0deg z


2

0deg z


(0) 0 and ( ) 0(0) 0 (0) 0 and ( ) 0 ( ) 0 x x

w w LM M L Lψ ψ


Functions4 3 2

1 2 3 4 53 2

1 2 3 4

( )

( )


x B x B x B x Bψ

= + + + +

= + + +






1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure



























1 01 1 3 3

2 02 2 4 4

24 E I4 2GA

6 E I3 GA

z

z

AB A B A

AB A B A

κ

κ

deg

deg


sdotsdot


( ) ( )( )2 2

0

( )2 GA 24 E Iz


κ deg


sdot sdot sdot


4

0

52 384 E Iz

qLLw⎛ ⎞⎜ ⎟⎝ ⎠

deg

sdot= sdot4 2

0

52 384 E I 8 GAz

qL q LLw κ⎛ ⎞ +⎜ ⎟⎝ ⎠

deg




GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
























GAxf

IExfxwz sdot+=

deg κ)()()( 2

0

1

Cantilever beam

Simply supported





Beam )( max1 wf

3845 4qLsdot

48

3PL

8

4qL

3

3PL

)( max1 wf

8

2qL

4PL

2

2qL

PL

)( maxwx

2L

2L

L

L












=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
































=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure


























=

=

==


10 kNmqdser

13 kNmqduls

30 mL

max

4 2

0

5384 E I 8 GA

d ser d serz

q L q Lw κ+

deg


2

maxz8 2 I


maxky

12 Ad ulsq L

τ sdot=







6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure




























6 24

0 max

1054 10 Nm5

E I 384d ser

zq Lwdeg = sdot

sdotsdotge


2

maxz


max

ky

1 71 MPa2 Ad ulsq L

τ sdot= =


20 MPadfτle =



m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
























m10398384

5 32

0

4

maxminus

deg

sdot=sdotsdotsdot

+sdot

sdot=

GALq

IELq

w serd

z

serd

κ


5 Remarks



max 001 mwle =

m10198384

5 32

0

4

maxminus

deg

sdot=sdot

sdot+

sdotsdot

=web

serd

z

serd

GALq

IELq

w

(77 mm) (16 mm)












Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure

































Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure


























Weak fiber mats





Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Axial Members






0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure



























0NdA

tm

fγ

degle

0deg






hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure


























hellip Euler load



cc

Euler

FNd F1 N

le+

c0degC

A fF

mγsdot

=

20

Euler 2

Nm E k

E IL

πγ

degsdot sdot=

sdot

kL

m Eγ








Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure





























Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure























Connections












bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure

































bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure































bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure




























bolt shear failure




IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure

























IMPORTANT REMARKS









Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure


























Tensile force

Minimum distances




m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
























m

150 MPa( 13)B d

d tP γsdot sdot=

=


m

70 MPa( 13)B d

d tP γsdot sdot=

=










Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure





























Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure
























Static conditions










s ykd m

A fP γ

sdotle

2d m

d t fP τπγ


















adhesive failure





































adhesive failure

























adhesive failure

















































Documents

Design of FRP-Profiles and All-FRP-Structures