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# Damage Computation for Concrete Towers Under Multi-Stage and Multiaxial Loading - PowerPoint PPT Presentation

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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Prof. Dr.-Ing. Jürgen Grünberg

Dipl.-Ing. Joachim Göhlmann

Institute of Concrete ConstructionUniversity of Hannover, Germany

www.ifma.uni-hannover.de

• Introduction

• Fatigue Verification

• Multiaxial Fatigue

• Summary and Further Work

Nearshore Foundation Emden

Hybrid Tower Bremerhaven

Reinforcement

Junctions

Concrete

Tendons

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:

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

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

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 certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

S certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.cd,max,3

Scd,max,2

Scd,max,1

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 certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

Fatigue Damage Dfat

Ni

Numerical Fatigue Damage Simulation certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

Computed Stress and Damage Distribution certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

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 certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

Joint of Concrete Offshore Framework

Junction of Hybrid Tower

Floatable Gravity Foundation

Fracture Envelope for Monotonic Loading certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

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 certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

cfat; tfat

Main Meridians under Multiaxial Fatigue Loading certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

TensionMeridian

fcc

ft

ftt

fc

Compression Meridian

Failure Curves for Biaxial Fatigue Loading certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

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 certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

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

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

1 certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

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 certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

• 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: certain damage state during the fatigue process, is equal to the mechanical work under monotonic loading to obtain the same damage state.

ENGINEERING

EXPO PLAZA 10

Hannover, Germany

www.grbv.de