Analysis of Glass Panels Subjected to Blast Load

228 Pages·2019·49.014 MB·English

by  Matthias Förch

Fassadensysteme und Gebäudehüllen
Band 1
Matthias Förch
Analysis of Glass
Panels Subjected
to Blast Load
Fassadensysteme und Gebäudehüllen
Band 1
Reihe herausgegeben von
Frank Wellershoff , Hamburg , Deutschland
Weitere Bände in der Reihe http://www.springer.com/series/16306
Matthias Förch
Analysis of Glass Panels
Subjected to Blast Load
Matthias Förch
HafenCity Universität Hamburg
Hamburg, Germany
Doctoral dissertation to obtain the academic degree
Doktor-Ingenieur (Dr.-Ing.)
at HafenCity University Hamburg
Hamburg, 2019
ISSN 2661-8931 ISSN 2661-894X (electronic)
Fassadensysteme und Gebäudehüllen
ISBN 978-3-662-59086-7 ISBN 978-3-662-59087-4 (eBook)
https://doi.org/10.1007/978-3-662-59087-4
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V
Acknowledgments
This doctoral dissertation is the result of 6 years employment as research associate at the
Professorship for Façade Systems and Building Envelopes at HafenCity University
Hamburg.
My heartfelt thanks go to Univ.-Prof. Dr.-Ing. Frank Wellershoff, my academic supervi-
sor, for providing me the chance to be part of the research team, for his unstinting sup-
port and assistance in so many different ways. My sincere thanks also go to Univ.-Prof.
Dr.-Ing. Jens Schneider as second member of the doctoral dissertation reading commit-
tee with his passionate and helpful attitude for inspirational discussions.
I would like to acknowledge the laboratory staff Dipl.-Ing. (FH) Jens Ohlendieck, Dipl.-
Ing. (FH) Marcus Illguth, M.Eng. and Jens Eidenberg, who ably assisted me in prepara-
tion and execution of all experiments reported in this dissertation.
I would like to thank the glass association “Fachverband Konstruktiver Glasbau e.V.”,
with chairman Dr.-Ing. Frank Schneider, for the permission to publish research results
with regard to the project “Glass Strength at High Strain Rates” and the willingness of
Glas Trösch for supplying the glass specimens.
Special thanks to my dear friend Matija Posavec, M.Sc. who contributed with many rec-
ommendations by proofreading the manuscript. Last, but not least, I would like to thank
Marta Karczewska and Pakdad Pourbozorgi Langroudi, M.Sc. for their support as stu-
dent assistants.

Hamburg, February 2019 Matthias Förch
VII
Abstract
The present doctoral dissertation contributes to the analysis of glass panels subjected to
blast load. It concentrates on monolithic and laminated glass prior to glass fracture.
Further to a brief introduction in Chapter 1, Chapter 2 is devoted to fundamentals of ex-
plosions. Here, the explosion process in the spherical surrounding medium air, compari-
son techniques between different explosive charges and blast wave parameters are ex-
plained.
Chapter 3 contains blast effects on buildings. In practice, hemispherical explosions must
be considered as bombs due to terrorist attacks usually explode directly or nearby ground
surface. The incident pressure of a blast wave is reflected by buildings, resulting in in-
creasing pressures for building design. For simplification reasons, idealized blast loads
are usually considered by linearizing the reflected time-pressure history.
In Chapter 4, the basic dynamic principles of single degree of freedom systems subjected
to idealized blast load are presented, resulting in maximum dynamic load factors for this
load type.
The key research topics are examined from Chapter 5 to Chapter 8:
In Chapter 5, a rigorous solution for monolithic glass plates subjected to idealized blast
load for small deformations is shown, by extending the methodology of previous chapter
to plates. On the basis of this analysis a graphical solution for simply supported mono-
lithic glass plates subjected to idealized blast load is provided. With this nondimensional
solution, it is possible to identify maximum deformation and maximum principal stress
for small and large deformations for static and idealized blast load without software.
The next Chapter 6 investigates glass strength at high strain rates. After a brief introduc-
tion to risk integral method and consideration of load duration in standards, the conduct-
ed strain rate tests at HafenCity University Hamburg are described. In accordance with
the test results, load duration factors k for impact and blast load design for annealed
mod
glass, heat strengthened glass and fully tempered glass are proposed.
Chapter 7 follows on from the previous by analyzing the blast pressure capacity for glass
plates. Here, design strength values for impact and blast design based on the European
safety concept and German standards are suggested. In particular, partial factors γ for
M
annealed glass, heat strengthened glass and fully tempered glass are proposed. As a re-
VIII Abstract
sult, blast pressure capacity charts for monolithic fully tempered glass plates subjected to
idealized blast load are presented.
Chapter 8 points out the behavior of laminated glass subjected to combined temperature
and blast load. After presenting the strongly time-temperature dependency of interlayers,
material models for blast design are summarized from literature. Moreover, design tem-
peratures of interlayer in blast design situation based on empirical data in accordance
with Eurocode are determined for vertical double glazed and triple glazed units for Ger-
many. A parametric FE study for common idealized blast loads shows that laminated
glass should be regarded with appropriate shear relaxation modulus, as the maximum
principal stresses may be up to 52 % higher in comparison with monolithic glass ap-
proach.
The final chapter 9 draws upon the entire work and includes a discussion for further re-
search on this area.
IX

Contents
Acknowledgments ....................................................................... V
Abstract ...................................................................................... VII
Contents ...................................................................................... IX
Abbreviations ............................................................................ XIII
Symbols ......................................................................................X V
1 Introduction ............................................................................. 1
2 Fundamentals of Explosions .................................................. 3
2.1 The Explosion Process ................................................................... 3
2.2 TNT-Equivalent ............................................................................. 5
2.3 Hopkinson-Cranz Blast Wave Scaling .......................................... 6
2.4 Blast Wave Parameters .................................................................. 7
3 Blast Effects on Buildings ...................................................... 9
3.1 Hemispherical Explosion ............................................................... 9
3.2 Reflected Blast Waves on Buildings ........................................... 10
3.3 Idealized Blast Load .................................................................... 11
4 Analysis of SDOF Systems Subjected to Idealized Blast
Load ............................................................................................ 13
4.1 Basic Dynamic Equations ............................................................ 13
4.2 Rigorous Solution ........................................................................ 14
4.2.1 Free Vibration .................................................................... 14
4.2.2 Forced Vibration ................................................................ 16
4.2.3 Dynamic Load Factor DLF ................................................ 18
4.2.4 Vibration Subjected to Arbitrary Load ............................... 18
X Contents
4.2.5 Rigorous Solution for Rectangular Impulse Load .............. 21
4.2.6 Rigorous Solution for Triangular Impulse Load ................ 23
4.3 Approximate Solutions ................................................................ 26
5 Analysis of Monolithic Glass Plates Subjected to Idealized
Blast Load ................................................................................... 29
5.1 Rigorous Solution for Small Deformations ................................. 30
5.1.1 Lagrange’s Equation .......................................................... 30
5.1.2 MDOF and Continuous Systems ........................................ 31
5.1.3 Modal Analysis .................................................................. 32
5.1.4 Simply Supported Plates for Small Deformations ............. 32
5.1.4.1 Deformation ..................................................................... 35
5.1.4.2 Internal Forces and Stresses ............................................. 36
5.1.4.3 Velocity ............................................................................ 39
5.1.4.4 Acceleration ..................................................................... 39
5.1.4.5 Kinetic Energy ................................................................. 40
5.1.4.6 Elastic Deformation Energy ............................................ 41
5.2 Rigorous Solution for Large Deformations ................................. 42
5.3 Proposed Approximate Solution for Small and Large
Deformations ....................................................................................... 42
5.3.1 Nondimensional Charts for Static Load ............................. 43
5.3.2 Dynamic Load Factors for Blast Load ............................... 49
6 Glass Strength for Impact and Blast Load .......................... 59
6.1 Risk Integral ................................................................................. 60
6.2 Consideration of Load Duration in Standards ............................. 60
6.2.1 USA and ASTM Referenced Organizations ...................... 60
6.2.2 Europe ................................................................................ 61
6.2.3 Germany ............................................................................. 61
6.3 Tests at HafenCity University Hamburg (HCU) ......................... 62
6.3.1 Test Specimens ................................................................... 64
6.3.2 Corundum Treatment of Specimens ................................... 66
6.3.3 Testing Machine and Load Function .................................. 69
6.3.4 Test Results ........................................................................ 72
6.4 Verification of Risk Integral Method by Tests ............................ 75
6.4.1 Determination of Load Duration Factors k by Mean Value
mod
Method for Tests .......................................................................... 76