Damage computation for concrete towers under multi stage and multiaxial loading
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Damage Computation for Concrete Towers Under Multi-Stage and Multiaxial Loading. Prof. Dr.-Ing. Jürgen Grünberg Dipl.-Ing. Joachim Göhlmann Institute of Concrete Construction University of Hannover, Germany www.ifma.uni-hannover.de. Table of Contents. Introduction Fatigue Verification

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Damage Computation for Concrete Towers Under Multi-Stage and Multiaxial Loading

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Damage computation for concrete towers under multi stage and multiaxial loading

Damage Computation for Concrete Towers Under Multi-Stage and Multiaxial Loading

Prof. Dr.-Ing. Jürgen Grünberg

Dipl.-Ing. Joachim Göhlmann

Institute of Concrete ConstructionUniversity of Hannover, Germany

www.ifma.uni-hannover.de


Table of contents

Table of Contents

  • Introduction

  • Fatigue Verification

  • Energetical Damage Model for Multi - Stage Fatigue Loading

  • Multiaxial Fatigue

  • Summary and Further Work


1 introduction

1. Introduction

Nearshore Foundation Emden

Hybrid Tower Bremerhaven


Fatigue design for

Fatigue Design for …

Reinforcement

Junctions

Concrete

Tendons


2 fatigue verification by dibt richtlinie

1

Scd,min = 0,8

0,8

0,6

Scd,max

0,4

0,2

Scd,min = 0

0

0

7

14

21

28

logN

2. Fatigue Verification by DIBt - Richtlinie

Linear Accumulation Lawby Palmgren and Miner:

Design Stresses for compression loading:

Scd,min = sd ∙ σc,min ∙ c / fcd,fatScd,max = sd ∙ σc,max ∙ c / fcd,fat

Ni = Number of load cycles for current load spectrumNFi = Corresponding total number of cycles to failure

log N

S – N curves by Model Code 90


Strain evolution under constant fatigue loading

Strain evolution under constant fatigue loading


3 energetical fatigue damage model for constant amplitude loading by pfanner 2002

The mechanical work, which have to be applied to obtain a certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

!

Wda(D) = Wfat (D, fat, N)

c

fat

Fatigue Process

Monotonic Loading

Elastic-Plastic Material Model for Monotonic Loading:

c = (1 - Dfat) ∙ Ec ∙ (c - cpl)

3. Energetical Fatigue Damage Model for Constant Amplitude Loading by [Pfanner 2002]

Assumption:


Damage evolution under constant fatigue loading

Damage evolution under constant fatigue loading


Extended approach for multi stage fatigue loading

Scd,max,3

Scd,max,2

Scd,max,1

Extended Approach for Multi-Stage Fatigue Loading

Life Cycle:

Lfat = Dfat ( σifat, Ni) / Dfat ( σFfat, NF)≤ 1

Number of load cycles until failure:

NF =  Ni + Nr

Scd,min,i


Three stage fatigue process in ascending order

Three-Stage Fatigue Process in Ascending Order

Fatigue Damage Dfat

Ni


Numerical fatigue damage simulation

Numerical Fatigue Damage Simulation


Computed stress and damage distribution

Computed Stress and Damage Distribution

Dfat = 0,221

Dfat = 0,12

Dfat = 0,08

Dfat (N = 109)

 (N = 109)

 (N = 1)

1st Principal Stress

Fatigue Damage


4 multiaxial fatigue loading

4. Multiaxial Fatigue Loading

Joint of Concrete Offshore Framework

Junction of Hybrid Tower

Floatable Gravity Foundation


Fracture envelope for monotonic loading

Fracture Envelope for Monotonic Loading

TensionMeridian

fcc

 / fc

 / fc

ft

ftt

fc

fcc

fc

fc = unaxial compression strengthfcc = biaxial compression strengthft = uniaxial tension strengthftt = biaxial tension strenth

Compression Meridian

Main Meridian Section


Fatigue damage parameters for main meridians

Fatigue Damage Parameters for Main Meridians

cfat; tfat


Main meridians under multiaxial fatigue loading

Main Meridians under Multiaxial Fatigue Loading

TensionMeridian

fcc

ft

ftt

fc

Compression Meridian


Failure curves for biaxial fatigue loading

Failure Curves for Biaxial Fatigue Loading

Log N = 7

Log N = 6

Log N = 3

22,max / fc

N = 1

min = 0

fc

fcc

11,max / fc

 = 1,0

 = - 0,15


Modification of uniaxial fatigue strength

Modification of Uniaxial Fatigue Strength

Scd,min = sd ∙ cc ∙ σc,min ∙ c / fcd,fat

Scd,max = sd ∙ cc ∙ σc,max ∙ c / fcd,fat


Modified fatigue verification

1

Scd,min = 0,8

0,8

0,6

Scd,max

0,4

0,2

Scd,min = 0

0

0

7

14

21

28

logN

Modified Fatigue Verification

Design Stresses:

Life Cycle:

Scd,min = sd ∙ cc ∙ σc,min ∙ c / fcd,fatScd,max = sd ∙ cc ∙σc,max ∙ c / fcd,fat

Lfat = Dfat ( σifat, Ni) / Dfat ( σFfat, NF)≤ 1

S – N curves by Model Code 90


5 summary and further work

5. Summary and Further Work

  • The linear cumulative damage law by Palmgren und Miner could lead to unsafe or uneconomical concrete constructions for Wind Turbines.

  • A new fatigue damage approach, based on a fracture energy regard, calculates realistically damage evolution in concrete subjected to multi-stage fatigue loading.

  • The influences of multiaxial loading to the fatigue verification could be considered by modificated uniaxial Wöhler-Curves.

  • Further Work:Experimental testings are necessary for validating the multiaxial fatigue approach.


Damage computation for concrete towers under multi stage and multiaxial loading

New workplace from June 2007:

ENGINEERING

EXPO PLAZA 10

Hannover, Germany

www.grbv.de

[email protected]


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