F – V interaction of girders with trapezoidally corrugated ... · Research aim M r d d d d o k R R R R k γ =( 1 + 2 + 3)⋅⋅ Rd1 =kw ⋅σyw ⋅twep ⋅a Rd 2 =2⋅tf ⋅kw ⋅σyw

F – V interaction of girders withtrapezoidally corrugated webs

Balázs Kövesdi

PhD Student Prof. Dr.-Ing. László Dunai Prof. Dr.-Ing. Ulrike Kuhlmann

Supervisors:

10th Official Meeting of ECCS-TWG 8.3, 30th April, 2010, Cottbus, Germany

Introduction

• Previous research activities– Investigation of the patch loading resistance

• Development of FE based design method• Development of analytical design method

• Problem statement and research aims (F-V interaction)

• Literature overview

• Numerical modelling and structural behaviour

• Development of an F-V interaction curve

• Summary of the research work and possible further subjects


Previous research activities

Literature overview

Numerical model development

Numerical parametric study(determination of the geometricparameters which have influenceon the patch loading resistance)

Analytical design method (Uni Stuttgart)

ywwplfyww

fw

ftM42kftss

RRR

⋅⋅ρ⋅⋅⋅+⋅⋅⋅⋅ρ

=+=

α

Experimental program

FE based design method (Uni Budapest)

-Proposals for possibleimperfection shapes andapplicable magnitudes.


Research aim

M

rodddd

kkRRRR

γ⋅⋅++= )( 321

atkR wepywwd ⋅⋅⋅= σ1

fwepyffywwfd btkktR ⋅⋅⋅⋅⋅⋅⋅= σσ22

fffd tbR ⋅⋅⋅−= σ07.03

1. Design method of Kähönen

ywwplfywwfw ftM42kftssRRR ⋅⋅ρ⋅⋅⋅+⋅⋅⋅⋅ρ=+= α

- Developed for building structures.

- Does not follow the steps of the EC3 stability analysis(design methods with reductionfactors).

- Possible interactions are consideredin the design method. ko; kw; kr; Rd3

2. Enhanced design method

Based on design method of Kähönen+ numerical calculations + own experiments

cr

ywp

f

σ=λ

2

2

2

)1(12

⋅⋅

υ−⋅π⋅=σ σ

i

wcr a

tE

k Pure patch loading resistancewithout interactions.

Research aim: Development of interaction equations. (F+V ; F+M)


Problem statement

1. There are no recommendations in the EN1993-1-5 for the F-V interaction(neither for flat web nor for corrugated web girders).

Aim: New (F+V) interaction curve for trapezoidally corrugated webs.

2. In the literature only a limited numer of investigations are available dealingwith this topic, especially for corrugated web girders.

In the practice during launching of a bridge structure large shear (V) and transverse force (F) can be introduced at the same cross section .

Interaction should be considered in the design.

Mainly the web plate is loaded byboth actions.


Research strategy

- Literature overview and experimental background

- Numerical model development

- Analysis of the structural behaviour

- Numerical parametric study

- Developement of the F-V interaction curve


Literature overview

1. Analysis of the combined loading subdivided into two basic load cases

Basis of the separation is that the shear stresses due to “pure transverse force” are already included in the patch loading resistance model and a reduction of the load carrying capacity is caused only by the additional shear stresses coming from “pure shear force”.

2. Analysis of Elgaaly and Seshadri

Based on experiments

20 numerical calculations

0.15.0

25.125.1

≤

+

⋅−

RR F

F

V

FV

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

F/FNum.

(V-0

,5F

) / V

Num

.

.

Elgaaly & Seshadri numerical results

Elgaaly & Seshadri (for corrugated web girders)


Numerical modelling

Test specimen Numerical model Numerical simulation

Modell verification

Investigation of combined F+V

stiffener

Numerical parametricstudy by differentgeometries and loadingconditions.


Numerical modelling

Modelling of the half girder 1. Reduced model.

2. By defining the parameter x, many shearforce distributions can be analysed.

Analysed parameter range:

hw/tw: 100-125-150-200-250

a1/tw: 15-20-25-30-35

a: 20°-30°-40°-60°ss/hw: 0.2-0.4-0.5-0.6-0.8

V1/V2: between -1 ; 1


Structural behaviourV1/V2=-1 V1/V2=0 V1/V2=0.5 V1/V2=1

0

125

250

375

500

625

750

875

1000

1125

1250

-0,8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1 1,2 1,4

e [mm]

hw [m

m]

.

V1/V2=-1

V1/V2=0

V1/V2=0.5

V1/V2=0.86

V1/V2=1

local buckling

shear buckling (tension band)

interaction

Lateral displacementsalong a parallel fold:


Analysis of the interaction

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

F/FR,num

(V-0

,5F

) / V

R,n

um

.

numerical calculations

numerical results of Elgaaly et al

Elgaaly et al

current proposal (lower limit)

0.15.0

2.12.1

≤

+

⋅−

RR F

F

V

FV

Evaluation of the numerical calculations (using the separation methodology)

1. Proposed interaction equation:


Analysis of the interactionEvaluation of the numerical calculations (without the separation methodology)

Proposed interaction equation:

0

0,2

0,4

0,6

0,8

1

1,2

1,4

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

F/FR,num.

V2

/ V

R,n

um.

.


current proposal

0.145.2

max ≤

+

RR F

F

V

V

large scatter


Analysis of the geometric parametersEffect of the web ratio: hw/tw

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

F/FR,num.

(V-0

,5F

)/VR

,num

. .

hw/tw=200

hw/tw=150

hw/tw=125

hw/tw=100

Kuhlmann & Braun

Elgaaly & Seshadri

large hw/tw small hw/tw


Analysis of the geometric parametersEffect of the corrugation angle:

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

F/FR,num.

(V-0

,5F

)/VR

,num

. .

alpha=60°

alpha=40°

alpha=30°

alpha=20°

Kuhlmann & Braun

Elgaaly & Seshadri

Influence is quite small.

larger corrugation angle stronger interaction criterion


Analysis of the geometric parameters

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

F/FR,num.

(V-0

,5F

)/VR

,num

. .

a1/tw=35

a1/tw=30

a1/tw=25

a1/tw=20

a1/tw=15

Kuhlmann & Braun

Elgaaly & Seshadri

Effect of the fold ratio: a1/tw

Influence is negligible.


Analysis of the geometric parametersEffect of the loading length: ss/hw

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

F/FR,num.

(V-0

,5F

)/VR

,num

. .

ss/hw=0,2

ss/hw=0,5

ss/hw=0,8

Kuhlmann & Braun

Elgaaly & Seshadri

larger loading length


stronger interaction criterion

Interaction of shear and transverse forces

Patch loading resistance - Resistance of the web

- Resistance of the flange

Shear resistance Mainly depending on the web plate.

Flange contribution can be dominant

If the flange is dominant web carries only a smaller part of the applied load

Shear resistance can be larger.Conclusion:

Interaction criteria can be weaker.

Interaction criterion can be expressed bythe ratio of flange and web contributions inthe patch loading resistance.


Interaction of shear and transverse forces

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1

F/FR,Ansys

(V-0

,5F

) / V

R,A

nsys

.

F R,w / F R,fl=1,00

F R,w / F R,fl=2,0

F R,w / F R,fl=2,6

F R,w / F R,fl=3,2

F R,w / F R,fl=3,75

Kövesdi et al (a=1.6)





0.15.0 ≤

+

⋅−a

R

a

R F

F

V

FV

1,0

1,1

1,2

1,3

1,4

1,5

1,6

1,7

1,8

1,9

2,0

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0

FR,w / FR,fl

inde

x of

the

inte

ract

ion

equa

tion


developed approximation

8.0,

,25.0

+=

⋅−

flR

wR

F

F

ea 2.1>abut

Proposed interactionequation:

Determination of the index:


Summary

1. Literature overview

2. Numerical model development

3. Analysis of the structural behaviour

4. Numerical parametric study

5. Parameters which have influence on the structuralbehaviour

6. Development of interaction curve

Further research subject

Interaction of bending and patch loading (F+M).


Thank you for your attention!


F – V interaction of girders with trapezoidally corrugated ... · Research aim M r d d d d o k R R R R k γ =( 1 + 2 + 3)⋅⋅ Rd1 =kw ⋅σyw ⋅twep ⋅a Rd 2 =2⋅tf ⋅kw ⋅σyw

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