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

Prof. Dr.-Ing. Jürgen Grünberg

Dipl.-Ing. Joachim Göhlmann

Institute of Concrete ConstructionUniversity of Hannover, Germany

www.ifma.uni-hannover.de


Table of Contents

  • Introduction

  • Fatigue Verification

  • Energetical Damage Model for Multi - Stage Fatigue Loading

  • Multiaxial Fatigue

  • Summary and Further Work


1. Introduction

Nearshore Foundation Emden

Hybrid Tower Bremerhaven


Fatigue Design for …

Reinforcement

Junctions

Concrete

Tendons


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


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


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

Fatigue Damage Dfat

Ni


Numerical Fatigue Damage Simulation


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

Joint of Concrete Offshore Framework

Junction of Hybrid Tower

Floatable Gravity Foundation


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

cfat; tfat


Main Meridians under Multiaxial Fatigue Loading

TensionMeridian

fcc

ft

ftt

fc

Compression Meridian


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

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

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


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

  • 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.


New workplace from June 2007:

ENGINEERING

EXPO PLAZA 10

Hannover, Germany

www.grbv.de

[email protected]


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