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HSEHealth & Safety

Executive

Modelling failure of weldedconnections to corrugated panel

structures under blast loading

Prepared by theImperial College of Science,Technology and Medicine

for the Health and Safety Executive

OFFSHORE TECHNOLOGY REPORT

2 0 0 0 / 0 8 8



HSEHealth & Safety

Executive

Modelling failure of weldedconnections to corrugated panel

structures under blast loading

L ALouca and J FriisImperial College of Science, Technology and Medicine

Department of Civil and Environmental Engineering

South KensingtonLondon

SW7 2BUUnited Kingdom

HSE BOOKS



ii

© Crown copyright 2001Applications for reproduction should be made in writing to: Copyright Unit, Her Majesty’s Stationery Office,St Clements House, 2-16 Colegate, Norwich NR3 1BQ

First published 2001

ISBN 0 7176 2045 X

All rights reserved. No part of this publication may bereproduced, stored in a retrieval system, or transmittedin any form or by any means (electronic, mechanical,photocopying, recording or otherwise) without the priorwritten permission of the copyright owner.

This report is made available by the Health and SafetyExecutive as part of a series of reports of work which hasbeen supported by funds provided by the Executive.Neither the Executive, nor the contractors concernedassume any liability for the reports nor do theynecessarily reflect the views or policy of the Executive.



iii

CONTENTS

Executive Summary iii - iv

Corrugated Panel Structures Under Blast Loading

General Overview v – x

Part 1 – Mild Steel Firewalls 1 – 31

Part 2 – Stainless Steel (316) Firewalls 1 – 42





v

EXECUTIVE SUMMARY

Recent tests carried out in a full-scale module as part of a Joint Industry Project (JIP) [1] toinvestigate uncertainties relating to the characterisation and mitigation of offshore hydrocarbon

explosions and fires, has shown that significant overpressures can occur in a typical module layout.

Many previous designs of profiled barriers have only been considered as firewalls with a nominal

blast pressure rating of up to 0.5 Bar. This has necessitated strengthening to existing topsides andhas placed greater emphasis on the design of barriers to ensure their robustness at higher

overpressures.

This project has investigated the response of shallow corrugated firewalls using an explicit finite

element analysis package in order to enhance our ability to determine containment pressures and thelimits of existing barrier designs. The work has also focussed on validating numerical models

against full-scale tests carried out during the early nineties and highlighting the uncertainties in the

numerical analysis. These uncertainties are likely to increase at high overpressures which may

produce large deformations, plasticity, possible weld tearing at connections and contact withadjacent equipment and structure.

The finite element model adopted included a failure criterion based on an equivalent plastic strainwhich was used to model a panel which suffered weld failure during testing. The model was

initially run without this failure criterion switched on in order to investigate the sensitivity of the

local strain in the weld location and the dissipated energy of the panel and its components. These parameters are commonly used in a number of ductile failure models available in numerical and

simpler analytical models. It was found that strain values were particularly sensitive to mesh

density, with strains in the vicinity of the connection detail increasing with mesh density. However

the dissipated energy values did not show any significant variation with mesh density and it was feltthat this would provide a more useful limit to failure of a typical barrier. Overall, the failure pattern

of the test was adequately predicted in a qualitative manner by the numerical model using a failure

strain of 10%. Based on this a conservative estimate of the containment pressure was established.

Prediction of strain values away from connection details compared favourably with experimentally

available data and were not sensitive to mesh density. The connections at the ends of the panelsconsisted of flexible angles. These were modelled in some detail and were found to play a

significant role in the dissipation of the blast energy.

The validation of the panels was carried out using both static material data converted to true stress

strain values and adopting a Cowper-Symonds strain rate model with appropriate constants for mild

steel and stainless steel. The values adopted for stainless steel were taken from a recent publication

from the Steel Construction Institute [2]. In general, it was established that the influence of strainrate in the model gave a stiffer response overall, as expected, improving the correlation slightly in

some instances. However, the benefits of this were small and in view of the uncertainties that still

surround the modelling of strain rates it was ignored for the remaining analyses.

One of the large scale tests conducted included a diagonal brace placed 92 mm from the face of the

wall. The purpose of the brace was to model the as built condition. During loading the panel madecontact with the brace causing large permanent deformations in the brace member. The numerical

model was run both with and without the brace to establish its influence on the response. It was

found that the brace enhanced the capacity of the blastwall by more than 0.5 bar, effectively

doubling its capacity, simply by acting as an energy absorber and relieving the high strains which



vi

were occurring at critical weld locations. The brace was essentially acting as a passive impact

protection system.

The work has highlighted a number of uncertainties with regard to failure modelling which should

be addressed. In particular, further work is required to establish an energy failure criterion for

estimating containment pressure of barriers. Also, the use of a sacrificial or passive members to act

as a means of enhancing the capacity of existing blastwalls has so far shown enormous potential andshould be studied further for recommendations to be made for both retrofit and new barrier systems.

REFERENCES

1. Blast and Fire Engineering for Topside Structures – Phase 2, Final Summary Report, SteelConstruction Institute, 1998.

2. Jones, N. and Birch, R. S. Dynamic and static tensile tests on stainless steel. The Steel

Construction Institute, March 1998.



vii

CORRUGATED PANEL STRUCTURES UNDER BLAST LOADING

GENERAL OVERVIEWIntroduction

The following summarises the most important findings from a numerical investigation of various

corrugated panel structures subjected to blast loading. The research was carried out at ImperialCollege in accordance with a contract between HSE, SHELL and BG.

The investigation focused in particular on firewall designs, which have been tested at the

Spadeadam test facility for British Petroleum (BP) and British Gas (BG) respectively.

The walls designated R0888 and R0885, which measured approximately 3.5m square, consisted of a

shallow corrugated panel supported by dog-leg angles. The panels had a 45mm wide compression

flange, an amplitude of 41mm, and a pitch of 260mm. The corrugations were profiled to 45 ° . A

diagonal 203x203 UC46 brace was placed 90mm in front of the panel. During testing, this gap

closed such as to exert bending about the minor axis of the brace. The brace was fabricated from

Grade 50D steel, whereas the panel and the angles both were fabricated from Grade 40C steel. Adetailed description of the testing and analysis of these walls has been given in progress report no.

2.

The walls FFD21, FFD23 and FFD39 had a similar corrugation profile, but were fabricated from

316 stainless steel. The walls, which measured approximately 2.5m square, were supported along

each edge by a single angle-bracket. The walls in this series did not have any external obstructionsagainst the out of plane displacements.

The dynamic response of the firewalls was predicted employing the ABAQUS/Explicit Ver. 5.7

finite element program. The walls were spatially idealised as an assembly of shell elements of type

“S4R”. The analysis accounted both for geometric and material non-linearities. In the case of R0888and R0885 the contact occurring between the panel and the brace was simulated by means of the

kinematic formulation given in ABAQUS. The weld between the panel and the frame was notexplicitly modeled, but rather represented by a strain failure criteria applied to the elements adjacent

to the angle connection.

Scope of Analysis and Validation of Experiments

The scope of work agreed in the contract included:

1. Collating data from BG Technology and BP Exploration on tests of corrugated firewalls, which

has been carried out as a part of ongoing safety studies during the early nineties.2. Set up finite element models of the test cases using ABAQUS. Validate the numerical models

against the experimental results.

3. Based on the results of 2, investigate plastic strain at weld locations in order to predict failure

(vulnerability to weld tearing).

4. Use existing failure criteria based on strain and force within the FE package to assess thecapability of modeling integrity in a simple manner.

5. Carry out an organised parametric investigation to assess the influence of varying idealised

pressure time history profiles on the overall behaviour.



viii

Comparison of results

The numerical analyses were carried out using idealised triangular representations of the raw data provided by BG Technology which was sampled at 25kHz for most tests. In general the numerical

predictions were in good agreement with the experimental results. Table 1.1 compares the

maximum deflections of given points in the tests R0888 and R0885 respectively. The node

designated “panel” was located approximately 600mm to the left of the centre of the panel, and thenode designated “brace” at the midpoint of the diagonal brace. In the case of R0885 a comparison

was only possible in terms of the close resemblance between the predicted and observed propagation of weld rupture.

Table 1.2 compares the maximum strains at the middle of the panel in the tests FFD21, FFD23 and

FFD39. The strain was measured both parallel with the corrugations, ε11, and perpendicular to the

corrugations, ε22. The node designated “peak” was located on the narrower compression flange, anc

the node designated “trough” on the wider tension flange.

Table 1.1 - Comparison of deflections – BP Panels

Maximum deflection, u3, (mm)Test Node Analysis Experimental

R0888 Panel 239 252

Brace 104 103

R0885 Panel 360* N/A

Brace 200* N/A

* Determined at the onset of weld rupture.

Table 1.2 – Comparison of strain – BG Panels

Strain at centre of panelTest Node Analysis Experimental

ε11, (%) ε 22, (%) ε 11, (%) ε 22, (%)

FFD21 Peak 1.01 -1.61 1.09 -0.95

Trough -0.80 0.92 -0.74 0.59

FFD23 Peak 1.23 -1.10 1.65 -0.57

Trough -0.80 1.01 -0.78 0.73

FFD39 Peak 0.95 -1.06 0.83 -0.23

Trough -0.85 0.82 -0.74 0.65

It should be noted that central deflections on the brace and panel were only monitored on the BP panels and strains on the BG panels.

Learning Points

The results of the analyses showed that the flexible angle connections, which are transverse to the

corrugations, contribute significantly to the dissipation of strain energy in the structural system. In



ix

contrast, the angles, which are parallel to the corrugations, have little effect. It was estimated that

for the firewall FFD23 as much as 30% of the total dissipated energy was dissipated in the

transverse angles at the time of failure. The flexible frame can furthermore reduce the amount of localised straining of the weld material. For the firewalls in the R-series it was estimated that local

weld rupture would have occurred at a static pressure of about 1.1bar had the frame been rigid. This

compares to an estimated capacity of 1.5bar for the actual wall based on the experimental results

and the numerical analyses.

Placing a diagonal brace in front the panel significantly enhanced the maximum containment pressure of the firewall. The brace participates in transferring the applied load to the supports such

as to relieve the straining of the transverse weld. It was estimated that the absence of the brace

would reduce the static load capacity of the walls R0885 and R0888 by approximately 0.5bar.Similar benefits of the brace could be observed under dynamic load conditions. It was estimated

that for a triangular pressure-time history with a rise time of 30msec the capacity of the wall

increased from 0.4bar to 0.8bar when adding the brace member. It should be emphasised that in

general the gain in capacity under dynamic loads depends on the shape of the pressure-time historyand the relative strength of the fire/blastwall to the passive brae member.

Both the tests and the numerical analysis have highlighted the transverse weld (see figure 2 in Part 1of report) as being the point of failure initiation. Numerically the integrity of the weld can be

assessed using a failure criteria based on a maximum permissible value for the equivalent plastic

strain. However, this parameter is strongly dependent on the density of the finite element mesh, asthe strain field in the vicinity of the connection is characterised by large gradients. A continued

increase of the fineness of the mesh in this region will provide more information about the strain

variations, but the predicted maximum strain value will be a mathematical fiction governed by

strain singularities. The presence of strain singularities reflects simplifications in the geometricmodeling caused by the omission of the weld detail, and the assumed sharpness of the kinks in the

corrugation profile.

The analysis of R0885 showed that, when setting the limiting equivalent plastic strain to 10%, the

numerical model accurately simulated the experimentally observed weld rupture propagation.

However, due to the uncertainties with failure modelling, the model needs to be validated against aknown result for new applications and the value cannot be taken as representative of all corrugated

wall connection details.

An extensive parametric study proved that the initiation of weld rupture predicted from a strain based failure criteria alternatively could be predicted with sufficient accuracy using a criteria based

on the total amount of strain energy dissipated in the structure. A lower bound for the energy

capacity of the firewalls R0885 and R0888 was calculated to 154KJ, which was determined for

static load conditions. Importantly, studies of mesh sensitivity showed that the calculated value for

dissipated energy converge very rapidly with mesh refinements. Thus the safety of the firewall caneffectively be assessed for different blast scenarios using the dissipated energy as a failure criteria

assuming failure occurs in a ductile tensile tearing mode and no local buckling of the corrugationsoccur.

The adopted idealisation of the pressure time curve derived from experimental transducer recordswas observed to have some influence on the predicted response. Employing a bi-linear rather than a

tri-linear diagram to represent the pressure time curve increased the predicted maximum

displacements by up to 10%. The tri-linear representation included an initial phase with a slow



x

pressure build up. After reaching approximately 25% of the peak pressure the two curves were

identical. This highlights the significance of the rise time characteristics in response predictions.

The efficiency of the various components making the firewall can be assessed by their ability to

dissipate strain energy. In the case of the firewalls R0888 and R0885 it was found that

approximately 26% of the total amount of dissipated energy had been dissipated in the cross brace.

The energy dissipated in all of the various structural components was found to be similar under static and dynamic load conditions.

Guidelines for FE modelling

Based on the results of the experimental validations and the parametric studies carried out to date,the following guidelines can be proposed:

• In regions having high strain gradients such as in the vicinity of joints it is important to be aware

of the fact that the predicted strain will be sensitive to mesh density. One way of ensuring anadequate mesh density is to compare the strain values at Gauss points with those obtained using

the standard contouring algorithm. The contouring algorithm is based on the average strain atnodal points which is extrapolated from the strain at the Gauss points in all elements sharing the

node. Thus, the difference between the strain at the Gauss points in individual elements and theaverage strain at nodal points will indicate the adequacy of the mesh refinement. The larger the

difference the more inadequate the mesh becomes.

• Where mesh density is graded, there should be no great discrepancy between the sizes of

adjacent elements. As a general rule, the equivalent dimensions in adjacent elements should not

vary by more than a factor of 2.

• The aspect ratio of the elements adopted should be no greater than 2 as an element performs best

if its shape is not too distorted. Elements generally become stiffer and lose accuracy as theaspect ratio is increased which will be more apparent at high ductility levels.

• At extreme values of loading it is important to be aware of the fact that the ductility values will

become sensitive to the loading. Coupled with the sensitivity of the mesh to element density it is

essential to carry out some form of sensitivity study to establish safe limits on any likely failure pressure. This can take the form of investigating three pressure time history profiles for a

varying peak pressure. This study overall has in fact shown the benefits of sensitivity studies

where trends or patterns can emerge which with prudent engineering judgment can provide auseful guide to the limits of the structure.

ENHANCED DELIVERABLES

This project has identified a number of key parameters which require further investigation in order

to provide a more definitive set of guidelines for the structural capacity of shallow corrugatedfirewall panels subjected to blast loading. These are listed below:

• The numerical study has demonstrated that the ability of firewalls to sustain blast loading can beassessed from the dissipated energy. It is important to provide structured guidelines on how to



xi

evaluate a lower bound value for the energy capacity of general firewall geometries. The

concluded research indicates that a static analysis based on a peak pressure may suffice, but a

further investigation is required before definitive conclusions can be reached. The further investigation will also be used to develop semi empirical expressions to estimate the energy

capacity of different wall configurations.

• It is preferable to use solid elements to determine the plastic strain developing in the weld of typical connection details when subjected to dynamic loads. The direct modeling of the weld

will require a very high resolution, and the available computer resources does in general not

permit such sophistication in the global analysis of a complete firewall. However, a local modelof the connection can be used to drive the solution of a global model. Ultimately, this will

enhance the safety assessment of a given firewall as it will enable the designer to directly apply

a limiting strain criteria to the weld material.

• Establish the pros and cons when employing either a force based concept, a fracture mechanicalconcept, or a strain based concept to assess the integrity of a typical firewall. The object of this

is to establish whether a complex fracture model will provide additional useful data and an

upper bound on more practical energy/strain models.

• The reactions forces are of crucial importance in the design of firewalls. Simplified dataregarding the reaction forces, which must be supported by the primary steel work, can beexpressed in terms of equivalent forces at a few control points. Such data may also have a

significant bearing on future experimental work.

• Further investigation of the efficiency of different support systems is needed for robust designsto result. Various support types such as short angles, long angles, and dog-leg angles should be

classified in terms of their ability to dissipate energy and limit strain concentrations. Also, the

influence of dimensions should be further investigated. Previous research has demonstrated that

the size of the angles can have significant influence on the strain concentrations.

• The benefits from a passive impact protective system, such as the diagonal brace employed inthe tests R0885 and R0888, should be fully understood and the potential for increasing thecapacity of existing and future designs exploited. Immediately, this raises questions as to the

influence of the spacing between the brace and the panel, the cross-sectional properties of the

brace, and the general configuration and type of the bracing system. Simple expressions can beestablished with further finite element validation to estimate the energy absorption

characteristics of different impact systems, which could prove useful for initial designs and

more importantly for retrofit upgrades as a result of increased blast design requirements.

• The importance of including strain rate effects in the material modeling, and evaluating their influence on the predicted structural response. The rate effects can have an adverse effect on the

load transferred to the primary steel structure.

• It is necessary to compare the structural response predicted using the actual pressure timehistory to that predicted using various idealised pressure time histories. This is necessary in

order to ensure a conservative response is produced, particularly in light of recent tests showinghigh peak pressure short duration spikes.



xii

• The final deliverable should be a set of guidelines for the analysis of firewalls using a non-linear finite element package. These guidelines will build on the initial guidelines given in this

summary.

References

1. Burgan, B. A. Concise Guide to the Design of Stainless Steel. 2

nd

Edition, The Steel ConstructionIndustry, 1999.



PART 1 - MILD STEEL FIREWALLS

CONTENTS

1. INTRODUCTION

2. EXPERIMENTAL INVESTIGATION

2.1. DESIGN OF FIREWALLS

2.2. TEST OBSERVATIONS

3. NUMERICAL ANALYSIS

3.1. FINITE ELEMENT MODEL

3.2. RESULTS AND COMPARISONS

3.3. STRAIN BASED FAILURE CRITERIA

4. EFFECT OF MODEL SIMPLIFICATIONS

4.1. TRIANGULAR PRESSURE-TIME CURVE

4.2. FLEXIBLE FRAME

4.3. DIAGONAL BRACE

5. BLAST SCENARIOS - A PARAMETRIC STUDY

6. CONCLUSIONS

7. REFERENCES

APPENDIX A



Printed and published by the Health and Safety ExecutiveC30 1/98



1

1. INTRODUCTION

This section of the report describes part of a finite element study undertaken at Imperial College

to investigate the structural behaviour of firewalls when subjected to blast loading. The study

presented has focussed on a particular firewall design that was tested for British Petroleum. The

design incorporated a UC member in front of the panel such as to represent the as built

condition.

The results presented in this report represent a more focussed study than in the first report [6] in

order to investigate more closely some of the FE parameters highlighted as playing a significant

role in structural integrity assessment such as the failure criteria available in ABAQUS/Explicit.

A short parametric study has been conducted highlighting the sensitivity of the structural response

to load idealisation, the influence of flexible angle supports, and the influence of the structural

brace member placed in the front of the wall. The results have been characterised using global

displacements, dissipated energy and plastic strains to define the local response.



2


This chapter gives a summary of two recent full scale tests, which were carried out at the

Spadeadam test facility during 1995. The tests, designated R0885 and R0888 respectively, have

been described in detail in the reports “GRC R 0885" [1] and “GRC R 0888" [2] both published

by British Gas plc for internal use only.

2.1. DESIGN OF FIREWALLS

The wall, which measured approximately 3.5m square, consisted of a 2.5mm thick corrugated

steel panel supported by a frame of 100×75×8mm angle brackets. The panel and the frame were

joined by a continuous 3mm single-sided fillet weld. The angle brackets were fixed to the primary

steel structure (test rig) by two lines of 5mm fillet welds. The panel was orientated with the

corrugations running vertically, and the wider of the corrugation flanges away from the explosion

chamber. A diagonal 203×203 UC46 brace was attached to the primary steel structure such as

to have a clearance of 92mm to the surface of the panel. During testing, this gap closed and the

brace bent about its minor axis. All structural members were manufactured from ordinary carbon

steel. The cross brace was fabricated from steel classified as Grade 50D steel, whereas the panel

and the angle brackets both were fabricated from Grade 40C steel.

100x75x8 RSA

203x203 UC46

100x75x8 RSA

t=2.5

All measures in mm

41

5mm fillet

95

90

3mm fillet

Primary steel

structure

structure

Primary steel

5mm fillet

5mm fillet

5mm fillet

3mm fillet

17431743

SECTON A

SECTION B

CORRUGATION DETAIL

VIEW ON FIREWALL

(from outside)

A

B

Figure 1

Structural configuration of firewall



3


The over-pressures generated during the tests by the burning natural gas/air mixture were

recorded at varying locations within the explosion chamber. The pressure transducers closest to

the surface of the panel recorded a 387mbar peak over-pressure in the test R0888, and a

1600mbar peak in the test R0885. The recordings from these transducers, positioned 500mm

in front of the panel, are believed to directly describe the blast load received by the panels.

The structural response was monitored in each of the tests by means of three displacement

transducers. The out of plane deflection at the midspan of the diagonal cross member was

recorded in both of the tests, but the location of the remaining transducers was changed from one

test to the other. In the test R0888, the deflections were measured at points located symmetrically

with respect to the midpoint of the panel. The deflections recorded indicated that the pressures

could have been uniformly distributed over the surface of the panel.

Post test inspection revealed that the integrity of the firewall R0888 was preserved, though

significant plastic deformation was observed. The permanent deflection, at the midpoint of the

cross-brace, was approximately 30mm in the outwards direction.

In contrast, the blast loading in test R0885 caused rupture of the majority of the welding at the

top and the bottom of the panel. Also, the lower connection between the cross brace and the

primary steel work was severed. However, as only a few short failure lines developed in the

vertical direction the panel was not completely dislodged from the frame.

Figure 2

R0885 - Damage caused by 1600mbar blast load



the centre of the panel to a final length of approximately 600mm. A small amount of plate tearing

and/or rupture of vertical welds developed at two of the corners of the test panel.

As can be seen from figure 2 and 3, the angle brackets transverse to the corrugation experienced

significant plastic deformations. The angles rotated by approximately 45° at the centre of the

panel. In comparison, the less severe load in test R0888 produced a maximum permanent rotation

of the transverse angles by about 5° [3]. In both tests the permanent deformations of the angles

parallel with the corrugation were much less pronounced.

The figures also illustrates how the negative phase of the blast load in test R0885 sucked the

partly detached panel back into the explosion chamber. However, failure was, in accordance with

the deformed shape of the angle sections, reported to have occurred in the positive phase of the

blast [3].

Figure 3

R0885 - Plastic deformation of frame

The majority of the vertical failure lines occurred along a welded splice in the panel. Two almost

identical failure lines initiated at the top and bottom edge of the plate, and propagated towards

4



5


This chapter describes the finite element analysis of the two test cases R0888 and R0885.

Special attention has been given to the validation of the numerical model, and the

establishment of a strain based failure criteria.


The numerical analysis was performed using the ABAQUS/Explicit finite element program

[5], in which the transient dynamic response is followed using an explicit time integration

scheme. The firewall was, as shown in figure 4, spatially idealised as an assembly of shell

elements of type “S4R”. These reduced integration elements are intended for both thick and

thin shell applications. The frame was included in the model, as it experienced significant

torsional rotation in the test R0885. No part of the primary steel work was included in the

model. The brackets were assumed to be rigidly connected along the first line of the 5mm

fillet welds (see figure 1). The numerical simulation of the contact between the cross brace

and the panel utilised a simplified algorithm, in which the relative sliding between the

contacting bodies is assumed to be small. Both geometric and material non-linearities were

included in the analysis.

1

2

3

1

2

3

Figure 4

Adopted meshing in the FE model

3.1.1. Material properties

The plastic material behaviour was governed by the Von-Mises yield criteria combined

with an isotropic hardening rule and an associated flow rule. The hardening rule being

described by a piecewise linear diagram approximating typical uniaxial stress-strain

relationships found in the literature. Material failure was assumed to occur immediately

after the ultimate strain had been achieved. Table 1 lists the nominal material properties

defining the tri-linear



6

diagrams for the grade 43C and 50D steel respectively. Figure 5 shows the adopted stress-

strain curves when converted into true stress-strain curves. The numerical calculations in

ABAQUS employs the concept of true stress and strain, which accounts for strain induced

changes in the area of an element’s cross section [5].

Table 1

Nominal material properties

Grade 43C 50D

Yield stress, , (MPa) 275 355f y

Range of yield plateau, , (%) 0.4 0.3, st

Ultimate strength, , (MPa) 430 500f t

Ultimate strain, , (%) 30 25, u

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Strain, ε 3 , ( m/m )

0

100

200

300

400

500

600

700

S t r e s s , σ 3 ,

( M P a )

Grade 43CGrade 50D

Elastic rangeE=0.205E6 MPa

Plasticrange

S t r a i n h

a r d e n i n g

Failure strain

Figure 5

True stress-strain relationship

3.1.2. Pressure-time curves

Figure 6 illustrates the pressure-time curves recorded during the two tests. The traces have

been reproduced by digitising the graphs given in the references [1] and [2]. Since, the

recorded curves were very complex, involving oscillations of varying frequencies, they

have been much simplified for the purpose of the numerical analysis. Two types of

idealised pressure-time curves have been adopted in the present investigation. Type 1,

represented by the curves ABCD in figure 6, incorporated an initial phase, AB, in which

the pressure increases at a relatively slowly. This is followed by a phase, BC, characterised

by a much higher rate of pressure increase. In both tests the pressure at the end of the initial





8

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300Time, t , ( msec )

-350

-300

-250

-200

-150

-100

-50

0

D e f l e c t i o n , u 3 , ( m

m )

ABAQUSN_13225N_310023

TESTN_13225N_310023

Figure 7

R0888 - Displacement-time diagrams

The numerical model, albeit overestimating the residual displacements, reproduced the

experimental observations very well. A quantified comparison between the maximum

deflections are given in table 2.

Table 2R0888 - Comparison of deflections

VARIABLEMax defln, , (mm)u 3

Residual defln, ,u3

(mm)

N_13225 N_310023 N_13225 N_310023

ABAQUS 239 104 200 65

TEST 252 103 135 30

RATIO, ABAQUS /TEST 0.95 1.01 1.48 2.17

The discrepancy between the observed and the predicted residual displacements may be

caused by inaccuracies in the material formulation. The actual yield and strength of

particular steels are often higher than the minimum specified for their grade. In addition

visco-plastic effects may have influenced the experimental results. An analysis, in which

the yield stress and the strength of the steel were raised by 25%, resulted in residual

deformations about 16% above those observed in the test. The calculated maximum

deflection at N_13225 and N_310023 became respectively 15% and 25% lower than the

test results.



When comparing the loading function shown in figure 6 with the above displacement-

time diagrams, it follows that the contact between the brace and the panel occurred within

the79msec duration of the initial loading phase. It can furthermore be seen that the

maximum deflections occurred approximately 16msec after the external load had peaked

at time t=99msec.

Figure 8 shows the predicted development of plastic strain energy in the various structuralcomponents of the firewall R0888. It is interesting that both the transverse angles (Y-

angles) and the cross brace contributes significantly in dissipating strain energy. Actually,

the combined energy dissipated in these two components is in excess of the energy

dissipated in the panel itself. The figure also shows that only a small amount of plasticity

had developed prior to time t=90msec, hence the systems response was predominantly

elastic during the initial loading phase. The elastic behaviour explains the "hump"

displayed by the graphs in figure 7.

0 20 40 60 80 100 120 140 160 180 200

Time, t , ( msec )

-5

0

5

10

15

20

25

D i s s i p a t e d e n e r g y ,

E p l ,

( K J )

Test: R0888Panel

Y-anglesX-anglesCross brace

Figure 8

R0888 - Energy dissipated in structural components

The displacement transducers in test R0885 were positioned at node N_13233 located in

the lower left quadrant of the panel, at node N_29211 located in the upper right quadrantof the panel, and at node N_310023 located at the midpoint of the diagonal brace.

Unfortunately, all the transducers were damaged upon reaching their maximum stroke

length of about 240mm, but until then the agreement between the experimental and

numerical results was satisfactory. As seen from figure 9 the numerical model

underestimated the deflections of the panel in the early stages of loading. This discrepancy

can be explained by the pressure-time function, which only resembles the recorded diagram

for pressures in excess of approximately 130mbar. The recorded trace indicates that the

pressure built up to about 130mbar over a time period of about 50msec.

9



10

0 10 20 30 40 50 60 70 80

Time, t , ( msec )

-500

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

D e f l e c t i o n , u 3 ,

( m m )

ABAQUSN_13233N_29211N_310023

TESTN_13233N_29211

N_310023

Figure 9

R0885 - Displacement-time diagrams

It follows from the loading function shown in figure 6 and the above displacement-time

diagram, that the contact between the panel and the cross brace occurred prior to the arrival

of the main pulse at time t=31msec. The extreme deflection of the panel developed

approximately 6msec after the pressure load had peaked at time t=45msec.

Figure 10 shows the predicted development of plastic strain energy in the various

structural components of the firewall when subjected to the blast load generated in test

R0885. It follows from this figure and figure 6 that much of the material has been strained

plastically during the initial loading phase. Similar to the case R0888, the transverse angles

will finally have dissipated approximately 50% less energy than the panel. The effect of

the cross brace has increased, dissipating more energy than the panel, and together with

the transverse angles accounts for 79% of the total energy dissipated in the firewall.

Figure 11 shows the plastic energy dissipated in the various structural components under

static loading conditions. Thus the dynamic loading generated in R0888 and R0885

increased the total amount of dissipated energy by 98% and 69% respectively. Thedistribution of the total plastic energy on the various components is seen to be quite similar

under dynamic and static loading conditions. The major difference being that the brace had

a higher effect, and the panel a lower effect under the dynamic loading conditions.Values

to this effect has been listed in table 3. It may be noticed from the table that the

longitudinal angles (X-angles) have little effect in dissipating strain energy.



11

0 20 40 60 80 100 120

Time, t , ( msec )

0

25

50

75

100

125

150


E p l , (

K J )

Test: R0885PanelY-anglesX-anglesCross brace

Figure 10

R0885 - Energy dissipated in structural components

0 200 400 600 800 1000 1200 1400 1600

Pressure, p 3 , ( mbar )

-10

0

10

20

30

40

50

60

70


E p l ,

( K J )

PanelY-anglesX-angles

Cross brace

Figure 11

Static loading - Energy dissipated in structural components



12

Table 3

Relative distribution of total plastic energy

Loading Component

Panel Y-angles X-angles Brace

R8-1 50% 28% 0% 23%

S8 57% 26% 0% 18%

R5-1 37% 18% 3% 42%

S5 39% 22% 2% 36%

R8-1: 387mbar blast load, type 1.

S8: 387mbar static load.


S5: 1600mbar static load..

3.2.2. Strain localisation and failure mode

The numerical model described so far did not capture the weld failure observed in the testR0885. As previously described, the test R0885 was associated with failure of nearly all

of the transverse welds between the panel and the angles. In order to explain this

phenomenon, it is helpful to track the development of equivalent plastic strain in the panel.

Figure 12a-e shows the calculated distribution of equivalent plastic strain at different times

for R0885. The plastic strain is, as throughout this report, the plastic strain determined

from the average strain over the thickness of an element.

At time t=19msec the contact between the middle of the panel and the cross member has

just occurred, and the developed plastic strains are largely confined to the centre of the

panel. The plastic straining at this stage, caused by the compressive stress in the narrower

flange of the corrugations, is of a very small magnitude, i.e. less than 0.1%.

At time t=22msec the extent and size of plastic straining just started to increase rapidly in

the interior of the panel, and has reached a maximum of about 0.3%. About half of the

corrugation strips are in contact with the cross brace at this time.

At time t=31msec the plastic strains in the interior of the panel reached a maximum of

approximately 1.5%. The maximum plastic strain developed at the midspan of the central

corrugation, but an almost equal amount of straining occurred at the quarter points of this

corrugation. Also, zones in the lower left and upper right corner of the panel was subjected

to significant plastic straining, such as to facilitate the flattening of the two extreme

corrugations. The development of a fold line in the extreme corrugations near thesupporting angles was present in R0885 (see figure 2), and has also been reported from

a comparable test [4].

At time t=41msec, the elements with relatively high plastic strain localised to a small

region adjacent to the transverse angles. The maximum plastic strain in any element

adjacent to the angles was 7.3%, which compares to the maximum 1.8% found in the

interior of the panel. At this time the flattening of the corrugations was very pronounced.



13

At time t=78msec, the plastic strain reached a maximum value of 14% in elements adjacent

to the transverse angles. In comparison, the maximum plastic strain in the interior of the

panel increased to a modest 2.1%.

SECTION POINT 3

PEEQ VALUE

+0.00E+00

+2.27E-05

+4.55E-05

+6.82E-05

+9.09E-05

+1.14E-04

+1.36E-04

+1.59E-04

+1.82E-04

+2.05E-04

+2.27E-04

+2.50E-04

+2.73E-04

+2.96E-04

Figure 12a

R0885 - Equivalent plastic strain at time t=19msec

SECTION POINT 3

PEEQ VALUE

+0.00E+00

+4.00E-04

+8.00E-04

+1.20E-03

+1.60E-03

+2.00E-03

+2.40E-03

+2.80E-03

+3.20E-03

+3.60E-03

+4.00E-03

+4.40E-03

+4.80E-03

+5.20E-03

Figure 12bR0885 - Equivalent plastic strain at time t=22msec



14

SECTION POINT 3

PEEQ VALUE

+0.00E+00

+1.78E-03

+3.56E-03

+5.35E-03

+7.13E-03

+8.91E-03

+1.07E-02

+1.25E-02

+1.43E-02

+1.60E-02

+1.78E-02

+1.96E-02

+2.14E-02

+2.32E-02

Figure 12c


SECTION POINT 3

PEEQ VALUE

+0.00E+00

+5.63E-03

+1.13E-02

+1.69E-02

+2.25E-02

+2.81E-02

+3.38E-02

+3.94E-02

+4.50E-02

+5.07E-02

+5.63E-02

+6.19E-02

+6.76E-02

+7.32E-02

Figure 12dR0885 - Equivalent plastic strain at time t=41msec



15

SECTION POINT 3

PEEQ VALUE

+0.00E+00

+1.57E-02

+3.15E-02

+4.72E-02

+6.29E-02

+7.87E-02

+9.44E-02

+1.10E-01

+1.26E-01

+1.42E-01

+1.57E-01

+1.73E-01

+1.89E-01

+2.05E-01

Figure 12e


Figures 13 and 14 show the plastic strain histories at critical points in the interior of the

panel. It is interesting that the peak pressure of the applied blast load had almost no effect

on the maximum strain. For R0888 the maximum strain was 2.3% compared to 2.1% in

R0885. However, with figure 8 and 10 in mind, it follows that the amount of plastically

strained material was much increased in R0885.

0 20 40 60 80 100 120 140 160 180 200

Time, t , ( msec )

0

5

10

15

20

25

E q u i v a l e n t p l a s t i c s t r a i n , ε p q ,

( m

m / m )

Test: R0888E_2041E_20837E_21225

Figure 13

R0888 - Plastic strain history in the interior of the panel



0 10 20 30 40 50 60 70 80Time, t , ( msec )

0

5

10

15

20

25

30

E q u i v a l e n t p l a s t i c s t r a i n , ε

p q ,

( m m / m )

Test: R0885E_2041E_20837E_21225

Figure 14

R0885 - Plastic strain history in the interior of the panel

0 20 40 60 80 100 120 140 160 180 200

Time, t , ( msec )

0

2

4

6

8

10

12

14

16

E q u i v a l e n t p l a s t i c s t r a i n , ε p q , ( m m / m )

Test: R0888E_47E_2848E_15648

E_20048

Figure 15

R0888 - Plastic strain history at the angle supports

16



17

0 10 20 30 40 50 60 70 80

Time, t , ( msec )

0

20

40

60

80

100

120

140

160


( m m / m )

Test: R0885E_47E_2848E_16048E_19648

Figure 16

R0885 - Plastic strain history at the angle supports

Figure 15 and 16 shows the plastic strain histories at critical points adjacent to the angle

supports. At these locations a major difference can be noticed between the two load cases.

For R0888 the maximum plastic strain was 1.4%, which compares to the 14% in R0885.

Also, the location of the maximum strain differed between the two load cases. For R0888

the maximum strain occurred in an element near the lower left corner of the panel, whereas

in R0885 it occurred close to the middle of the transverse angle. Thus, the numerical model

rightly predicts that the transverse welds in R0885 are subjected to a very high level of straining.

3.3. STRAIN BASED FAILURE CRITERIA

Plastic strain are often used as a guide to estimate the integrity of welded steel structures

with a maximum value taken as 5% (currently given in the IGN). However, in the context

of a finite element analysis care must be exercised as the calculated strains can be very

sensitive to the density of the mesh.

3.3.1. Sensitivity to mesh density

The effect of mesh density on the predicted structural response was primarily investigated

by means of a much simplified model consisting of a single corrugation strip supported at

the ends by flexible angle brackets. The boundary-conditions along the free edges of the

panel and angle sections were prescribed such as to simulate a true one-way span. The strip

was subjected to a uniform pressure, which varied according to a triangular pressure-time

curve. The peak over-pressure was set to 400mbar, the rise time to 20msec, and the

duration to 40msec. The employed pressure history is quite similar to the one obtained

when simplifying the over-pressure trace recorded in the test R0888. The previously

described material model, illustrated in figure 5, was employed in the analysis.



18

Four different mesh densities were tested. The finest mesh represented the corrugation

strip by 40 elements in the transverse direction and 192 elements in the longitudinal. Table

1 lists the influence of the mesh density on selected variables.

Table 4

Sensitivity to mesh density

Mesh

size

Max defln.

, (mm)u3

Max dissipated

energy

Max equiv. plast. strain

, (%), pq

, (KJ) End MidEpl

24×5 458 3.8 4.1 0.4

48×10 476 4.1 9.4 0.7

96×20 484 4.2 13 0.5

192×40 485 4.2 19.1 0.5

An eight fold refinement from the 24×5 mesh results in an increase in the maximumdeflection and the dissipated energy by 6% and 11% respectively. For the 48×10 mesh the

value of these variables are within 2% of those determined from the finest mesh.

The maximum equivalent plastic strain in elements connected to the supporting angle

exhibited a much more sensitive behaviour to the density of the mesh. An eight fold

increase in the mesh density from the crude 24×5 mesh caused an increase in the maximum

equivalent plastic strain of 366%. The dramatic increase can be ascribed to the presence

of a numerical strain singularity at the points where the corrugations fold lines intersect the

supporting angle. The singularity is clearly seen from figure 17, showing the maximum

equivalent plastic strain in the first row of elements. Furthermore, the figure shows that,

except for the crude mesh, the strain predicted at given points are comparable.

Figure 18 shows the equivalent plastic strain at the midspan of the corrugation strip. No

strain singularities are present at this position, and mesh refinements do not, in general,

cause an increase in the predicted strain.

Figure 19 illustrates the rate by which the maximum strain decreases when moving away

from the supporting angle. Again, it can be seen that the predicted strain at a given distance

from the angle is not sensitive to the mesh density. At a distance of 100mm the maximum

strain has reduced to about 5%, which equals the maximum strain predicted between the

singularity points in figure 17. Thus, it is reasonable to assume that the singularity has no

or little influence on the strain calculated beyond this distance from the angle. In the caseof the 48×10 mesh this equals one element width.

The real behaviour of the corrugation is likely to exhibit some strain magnification at the

connections, though not strain singularities as in the finite element model. Thus a strain

based failure criteria should, providing the numerical modelling concept is not changed,

be adjusted such as to reflect the difference between real and numerical behaviour. Such

an adjustment has been attempted in an ad-hoc fashion in the following.



-130 -110 -90 -70 -50 -30 -10 10 30 50 70 90 110 130

Transverse distance from centre of strip, (mm)

-10

10

30

50

70

90

110

130

150

170

190

210


( m m / m )

24x548x1096x20192x40

Trough Web Peak Web Trough

Figure 17

Distribution of equivalent plastic strain near end of corrugation

-130 -110 -90 -70 -50 -30 -10 10 30 50 70 90 110 130

Transverse distance from centre of strip, (mm)

-1

1

3

5

7

9

E

q u i v a l e n t p l a s t i c s t r a i n , ε p q ,

( m m

/ m )

24x548x1096x20

192x40


Figure 18

Distribution of equivalent plastic strain across corrugation near centre

19



0 25 50 75 100 125 150 175 200 225 250 275 300 325

Longitudinal distance from end, (mm)

-10

10

30

50

70

90

110

130

150

170

190

210


( m m / m )

24x548x1096x20

192x40

Figure 19

Distribution of equivalent plastic strain along the corrugation

3.3.2. Employing strain based failure criteria

The progressive failure of the transverse welds, observed in the test R0885, was

numerically simulated by letting the panels outer elements represent the behaviour of the

welding material. Without altering the shape of the stress-strain curve the rupture strain of

the boundary elements was reduced to either 8%, 10% or 12%. Figure 20a-c shows the

resulting contour plots of the predicted equivalent plastic strain in the firewall after the

blast load. As seen from the figures, the panel has partially detached from the frame. The

detachment has graphically been emphasised by removing all failed elements. The adoption

of a 10% rupture strain criteria caused the numerical model to mimic the experimentally

observed weld failure very accurately.

It is interesting that the time at which weld failure was initiated was insensitive to the

employed rupture strain. Thus, as seen from table 5, the dissipated energy and the

maximum deflections at the time of first weld failure are largely independent of the

prescribed rupture strain.

20



21

33

SECTION POINT 3

PEEQ VALUE

+0.00E+00

+1.99E-02

+3.99E-02

+5.98E-02

+7.97E-02

+9.97E-02

+1.20E-01

+1.40E-01

+1.59E-01

+1.79E-01

+1.99E-01

+2.19E-01

+2.39E-01

+2.59E-01

Figure 20a

R0885 - Detachment of panel using 8% rupture strain

33

SECTION POINT 3

PEEQ VALUE

+0.00E+00

+1.66E-02

+3.33E-02

+4.99E-02

+6.65E-02

+8.31E-02

+9.98E-02

+1.16E-01

+1.33E-01

+1.50E-01

+1.66E-01

+1.83E-01

+2.00E-01

+2.16E-01

Figure 20b




22

33

SECTION POINT 3

PEEQ VALUE

+0.00E+00

+1.56E-02

+3.13E-02

+4.69E-02

+6.25E-02

+7.81E-02

+9.38E-02

+1.09E-01

+1.25E-01

+1.41E-01

+1.56E-01

+1.72E-01

+1.88E-01

+2.03E-01

Figure 20c


Table 5

State at first weld rupture

Rupture strain Time Dissip. energy Max. defln.

, (%), pq t , (msec) , (KJ) , (mm)E pl u 3

8 42.7 131.4 413.6

10 42.7 133.1 411.6

12 42.7 133.7 411.2



23

4. EFFECT OF MODEL SIMPLIFICATIONS

This chapter discusses the influence of three model modifications on the predicted structural

response of R0888 and R0885. In the first model, the pressure history has been represented by

a triangular diagram. In the second, the flexible frame has been ignored, i.e. the boundaries of the

panel has been assumed to be fixed. In the third, the cross brace has been omitted.

4.1. A TRIANGULAR PRESSURE-TIME CURVE

Table 6 illustrates the effect of ignoring the initial phase of the pressure-time curve on the ultimate

behaviour of the firewalls R0888 and R0885. The load function labeled R8-2 was of a triangular

shape characterised by a 387mbar peak pressure, a 26msec rise time, and a 66msec duration.

For R5-2 the same variables were: 1600mbar, 19msec, and 38msec. The results obtained when

including the initial loading phase have been labeled R8-1 and R5-1. The table also contains the

results under static loading conditions, which has been labeled S8 and S5 respectively. Although,

the initial loading phase only applied up to approximately 25% of the peak pressure, it can be

seen to have a significant effect on the structural response of the firewalls. Overall, the triangular

pressure curves had an adverse effect on the response.

Table 6

Effect of pressure-time idealisation

Loading Max defln.

, (mm)u3

Max energy

, (KJ)E


, (%)e pq

Panel Brace Ekin Eel E pl Edge Interior

R8-1 289 104 8.6 10.5 41.6 1.4 b

2.3e

R8-2 322 146 16.9 12.1 62.2 2.3 b 1.8f

S8 242 67 N/A 9.5 21 0.7a 1.9e

R5-1 460 358 38.4 18.5 276.8 14.1d 2.1f

R5-2 518 380 153.5 26.4 483.8 23.7c 3.1f

S5 426 266 N/A 18.1 163.6 10.9c 1.9e



R8-1, S8, R5-1, S5: As in table 3

a: E_47, b: E_2848, c: E_15648, d: E_16048,

e: E_20837, f: E_21225

The dynamic magnification factor on the maximum deflections of the panel increased from 1.19

to 1.33, and from 1.08 to 1.22 in the case of R0888 and R0885 respectively. Likewise, the

magnification factor on the maximum deflection of the brace increased from 1.55 to 2.18, and

from 1.35 to 1.43.

For R0888 the maximum kinetic energy increased by 97%. For R0885 the increase was 300%.

As a consequence of the increase in motion energy a large increase in the plastic strain energy

could be observed. The maximum plastic strain at the connection to the transverse angles

increased by approximately 66%.



24

4.2. THE FLEXIBLE FRAME

Table 7 compares the structural response of a firewall having flexible to a wall having rigid angle

supports. The triangular pressure-time curves shown in figure 6 represented the dynamic loading.

As seen from the table, the rigid boundaries significantly reduced the maximum deformation of the

firewall. This was both the case for dynamic and static loading conditions, but the effect of the

rigid boundaries was somewhat more pronounced under static loading conditions.

Also, the dissipated energy was much reduced by the rigid boundaries. The relative reduction was

observed to be larger under dynamic than under static loading conditions. Although, the total

amount of plastic energy is reduced, the maximum plastic strain in the vicinity of the supports often

increased. This may have an adverse effect on the integrity of the firewall.

Table 7

Influence of flexible frame

Model Max defln.

, (mm)u3

Max energy

, (KJ)E


, (%)e pq

Panel Brace Ekin Eel E pl Edge Interior

R8-2 322 146 16.9 12.1 62.2 2.3 b 1.8h

R8-2-a 126 27 4.9 6 20.6 5.0c 0.3f

S8 242 67 N/A 9.5 21 0.7a 1.9g

S8-a 94 4 N/A 4.4 9 3.0c 0.1f

R5-2 518 380 153.5 26.4 483.8 23.7d 3.1h

R5-2-a 367 261 53.7 12.9 308.7 19.6c 3.2i

S5 426 266 N/A 18.1 163.6 10.9d 1.9g

S5-a 273 143 N/A 12.1 142.1 14.4d 1

R8-2-a: No angles, 387mbar blast load, type 2.

S8-a: No angles, 387mbar static load.

R5-2-a: No angles, 1600mbar blast load, type 2.

S5-a: No angles, 1600mbar static load.

R8-2, S8, R5-2, S5: As in table 5

a: E_47, b: E_2848, c: E_14848, d: E_15648,

e: E_3241, f: E_19637, g: E_20837 ,h:

E_21225,

i: E_22425

4.3. THE DIAGONAL BRACE

Table 8 shows the influence of the diagonal brace under dynamic as well as static loading

conditions. Again, the triangular pressure-time curves given in figure 6 represented the dynamic

load on the panel.

The diagonal brace reduced the maximum deflection of the panel by 29% to 48%. The largest

reduction occurred for the wall subjected to the blast load having a 1600mbar peak pressure. The

panel subjected to a 1600mbar static load exhibited the least reduction.



25

For the dynamic loading conditions the presence of the diagonal brace had a very significant effect

in limiting the maximum plastic strain developing in the transverse welds. In view of the 10%

rupture strain criteria, it is unlikely that the firewall without the diagonal brace can sustain the

modest blast load generated in the test R0888.

Table 8

Influence of diagonal brace

Model Max defln.

, (mm)u3

Max energy

, (KJ)E


, (%)e pq

quart mid Ekin Eel E pl Edge Interior

R8-2 322 231 16.9 12.1 62.2 2.3 b 1.8g

R8-2-

b425 532 42 10.5 107.9 12.9d 1.7

S8 242 158 N/A 9.5 21 0.7a 1.9f

S8-b 319 401 N/A 9.1 37.3 1.4 b 1.4

R5-2 518 479 153.5 26.4 483.8 23.7c 3.1g

R5-2-

b798 997 294.8 19.3 835.9 270.9d 5.8h

S5 426 360 N/A 18.1 163.6 10.9c 1.9f

S5-b 473 603 N/A 11.5 170.9 18.8d 1.7

R8-2-b: No brace, 387mbar blast load, type 2.

S8-b: No brace, 387mbar static load.

R5-2-b: No brace, 1600mbar blast load, type 2.

S5-b: No brace, 1600mbar static load.

R8-2, S8, R5-2, S5: As in table 5

a: E_47, b: E_2848, c: E_15648, d: E_20048,

e: E_2041, f: E_20837, g: E_21225, h:

E_21625



26

5. BLAST SCENARIOS - A PARAMETRIC STUDY

A parametric study was carried out in order to study the effect on the structural response to

varying pressure-time histories. All the utilised pressure-time curves were triangular, and had a

rise time equal to half the duration of the blast. The results from the parametric study are listed in

table 9. The dynamic load having a peak of 400mbar and a duration of 120msec has been

designated D4-12, the load with a peak of 1600mbar and a duration of 80msec has been

designated D16-8, and so forth. Furthermore, the results for corresponding static loading

conditions are listed in the table.

Figure 21 shows the predicted maximum equivalent plastic strain in the weld, which connects

the panel to the angles, as a function of the peak pressure. The horizontal line at 10% strain

represents the predicted rupture strain of the welding material. It follows from the figure that a

decrease in the duration of the blast load is associated with a reduced peak pressure capacity.

Figure 22 shows the dissipated energy as a function of the peak pressure. The horizontal line at

an energy level of 133KJ represents the initiation of weld failure determined for the load case

R0885 described in section 3.3.2. In the parametric study the dissipated energy for the critical

load combinations resulting in a maximum plastic strain of approximately 10% fell within a narrow

band of 154KJ to 188KJ. The lower limit of this band has been shown in the figure. The region

between the two lines in the figure shows the influence of the load representation on the predicted

energy capacity of the firewall.

Figure 23 shows the maximum deflection of the panel as a function of the peak pressure.

According to load case R0885 described in section 3.3.2 weld failure was initiated when themaximum deflection reached 412mm. In the parametric study, based on several load

combinations, the maximum deflection at the time of weld rupture was found to lie between

412mm and 429mm.



27

Table 9

Influence of varying pressure-time histories

Model Max defln.

, (mm)u3

Max energy

, (KJ)E


, (%)e pq

panel brace Ekin Eel E pl Edge Interior

D4-4 309 127 20.2 11.3 57.9 2.1 b 2.0g

D4-6 323 146 15.2 12.1 62.9 2.3 b 1.8g

D4-8 311 139 8.8 11.8 54.2 2.1 b 1.5f

D4-12 260 91 5 9.6 31.3 1.5 b 1.5g

S4 245 70 N/A 9.6 21.9 0.7a 1.9f

D6-4 383 197 42 13.2 120.2 5.8c 2.7g

D6-6 390 218 29.5 14.1 122.4 5.9c

2.4g

D6-8 370 208 18.9 14 102.2 3.5c 1.8g

D6-12 330 159 8.8 12.4 63.9 2.2 b 1.5f

S6 310 127 N/A 12.9 46 1.0a 1.9f

D8-4 430 257 65.3 15.1 192.1 12.8c 2.9g

D8-6 428 274 43.8 15.7 184.7 10.9c 2.9g

D8-8 405 257 29.5 15 150 7.0d 2.4g

D8-12 362 188 15.4 14.5 94.6 3.6

c

1.8

g

S8 350 166 N/A 14.9 69.3 2.4c 1.9f

D12-4 500 351 116.6 16.9 353.5 22.8c 3.3g

D12-6 481 356 74 16.8 310.9 18.9c 3.0g

D12-8 456 323 51.3 16.1 244.1 14.3d 3.1g

D12-12 416 265 29.5 15.6 161.4 8.5d 2.5g

S12 395 223 N/A 17 114.7 6.5c 1.9f

D16-8 499 74 19.6 342.3 17.9 3.1g

D16-12 454 311 43.8 17.7 229.1 14.0c 3.0g

S16 426 266 N/A 18.1 163.6 10.9c 1.9f

D7.1-4 412 231 54.8 14.4 158.9 9.5c 2.6g

D7.6-6 422 264 40.9 15.4 172.1 9.9d 2.9g

D9.6-8 427 287 38 16.1 187.8 10.1d 3.0g

D13.2-12 429 281 33.8 15.9 181.7 10.1d 2.8g

S15.3 421 259 N/A 17.9 154.4 10.0c 1.9f

a: E_47, b: E_2848, c: E_15648, d: E_16048,

e: E_20048, f: E_20837, g: E_21225



28

0 200 400 600 800 1000 1200 1400 1600

Peak pressure, p 3 , ( mbar )

0

5

10

15

20

25

M a x e q u i v . p l a s t i c s t r a i n , ε

p q ,

( % )

Duration40msec60msec80msec

120msecinfinity

Safe region

Failure region

Figure 21

Max. equivalent plastic strain as a function of the peak pressure

0 200 400 600 800 1000 1200 1400 1600


0

50

100

150

200

250

300

350


E p l ,

( K J )

Duration

40msec60msec80msec

120msecinfinity

Failure region

Safe region

Figure 22

Dissipated energy as a function of the peak pressure



29

0 200 400 600 800 1000 1200 1400 1600


150

200

250

300

350

400

450

500

550

600

M a x d e f l e c t i o n , u 3 , ( m m )

Duration40msec60msec80msec

120msecinfinity

Failure region

Safe region

Figure 23

Maximum deflection as a function of the peak pressure



6. CONCLUSION

The triangular representation of the pressure-time history had a significant, butconservative, influence on the predicted ultimate response of the firewalls. The initialrange of the experimentally observed pressure-time diagrams, which is valid up to about

25% of the peak pressure, cannot be ignored when validating test results.

Exclusion of the flexible frame in the finite element modeling grossly exaggerates thestiffness of the firewall. Furthermore, the rigid boundaries will aggravate thedevelopment of large strains at the ends of the corrugation strips.

The diagonal brace was found to be a very important structural part of the firewall design,without which their ability to sustain blast loading practically disappears.

For all the analysed variations of blast loads, the structural integrity of the firewall could be determined quite accurately from the value of a single parameter. The parameter giving the capacity of the wall based on the study presented here, could be the overall

dissipated energy. This parameter was found to be insensitive to the mesh density of thefinite element model. However, further work is being suggested in order to apply theenergy concept to other structural configurations.

7. REFERENCES

1. GILLAN, I.W. AND GREENER, A.S. British Petroleum panel test programme - Mech-Tool test 9th February 1995British Gas Research & Technology, Report GRC R 0885, 26 June 1995

2. GILLAN, I.W. AND GREENER, A.S. British Petroleum panel test programme - Mech-Tool test 26th April 1995British Gas Research & Technology, Report GRC R 0888, 25 July 1995

3. PLANE, C.A., BEDROSSIAN, A.N. AND GORF, P.K. FE analysis and full scale blast tests of an offshore firewall panel Int. Conf. On Offshore Structural Design Against Extreme Loads, ERA,London 1994.

4. BROWN, M. AND PAPAGEORGE, N.Theoretical analyses of experimental test of A0 firewalls: Static test, Dynamic test FFd39British Gas Research & Technology, Report R4533, February 1991

5. HIBBITT, KARLSSON AND SOERENSEN, INC. ABAQUS/Explicit Users manual, Version 5.5

6. LOUCA, L.A. Modelling failure of welded connections to corrugated panel structures under blast loading Progress Report No. 1, Imperial College of Science Technology and Medicine

30



APPENDIX A

Guide to nodes and elements

17431743

E_2048

E_2848

E_2041

E_3241

E_2441

E_14848

E_16048

E_15648

E_19648

E_20848

E_20048

E_19637

E_20837

E_20437

E_21225

E_22425

E_21625

E_47

N_13233

N_13225

N_29211

N_21225

E_3248

31






PART 2 - STAINLESS STEEL (316) FIREWALLS

CONTENTS

1. INTRODUCTION

2. EXPERIMENTAL INVSETIGATION

2.1 DESIGN OF BLASTWALLS

2.2 TEST OBSERVATIONS

2.3 MATERIAL PROPERTIES


3.1 FINITE ELEMENT MODEL

3.2 STATIC TEST - ST3

3.3 BLAST TEST - FFD39



4. FAILURE MODELLING

4.1 DISSIPATED ENERGY

4.2 STRAIN CONCENTRATIONS

4.3 WELD RUPTURE

5. CONCLUSIONS

6. REFERENCES






1

1. INTRODUCTION

This section of the report describes the second part of a finite element study undertaken at

Imperial College to investigate the blast resistance of stainless steel (316) corrugated firewalls.

The study was funded by the HSE, SHELL, BG Technology and BP.

A number of full scale tests, conducted at the Spadeadam testing facility on A0 firewalls during

the 90's provided the necessary data for validation of the numerical models. The strains recorded

during the blast tests, and the displacements recorded during a static control test was available

for this purpose.

The sensitivity of the structural response to variations in the applied pressure history and

employed mesh density was investigated. Also the modelling consequences of a strain rate

dependent material behaviour were investigated.

Assuming full strength welds, the capacity of the firewalls was classified in terms of their ability

to dissipate energy without loss of integrity. The importance of the transverse angles in helping to

dissipate energy was highlighted.

This investigation also addressed the development of the critically high strains in the immediate

vicinity of the welding material.



2


This chapter outlines an experimental investigation of the resistance of A0 firewalls subjected to blast

loading. The three tests, named FFD39, FFD21 and FFD23, were all carried out at the Spadeadam test

facility during 1990. Together with the findings from a static control test ST3.

2.1. DESIGN OF BLASTWALLS

Figure 2.1.1 illustrates the design of the shallow profiled A0 blastwalls, which measured approximately 2.5m

square. The design consisted of a 2.5mm thick corrugated panel, which was supported along all four edges

by 75×75×6mm angle brackets. Both the panel and the framing angles were manufactured from stainless

steel. The panel was connected to the angles by a continuous 3mm single-sided fillet weld, and the brackets

were secured to the primary steel structure (test rig) by two lines of 5mm fillet welds. The panel was

orientated with the more compact flange acting as the compression flange.

75x75x6 RSA

75x75x6 RSA

t=2.5

45

5mm fillet

38

22.5

3mm fillet

Primary steel

structure

structure

Primary steel

5mm fillet

5mm fillet

5mm fillet

3mm fillet

1175

SECTION A

SECTION BCORRUGATION DETAIL

VIEW ON FIREWALL

inside

A

B

1175

outside

Figure 2.1.1

Structural configuration of the A0 blastwall



3


The over-pressures generated during the tests by the burning natural gas/air mixture were monitored by

several transducers mounted directly on the surface of the panel. The position and labelling of the pressure

transducers are shown in figure 2.2.1, and the recorded pressure time histories are shown in the figures

2.2.2 - 2.2.4. The gas mixture was ignited 1m in front of the midpoint of the panel, hence the resulting

pressure loading was expected to be symmetric about the centre of the panel. A visual inspection of therecorded pressure traces indicates that, for the purpose of a numerical analysis, the pressure distribution

can be assumed to be uniformly distributed over the surface of the panel. The difference between pressure

time traces recorded at points located far apart are in general not greater than the difference between

pressure time traces recorded at points located closely together. Thus the variations are believed to be of

a local, and probably statistical, rather than of a global nature. The very large variations in the later part of

the pressure time histories recorded in the test FFD23 can be attributed to the fact that this panel was

almost completely torn apart from the frame during the test.

P5

P1 P2

P3 P4

P6

P7

Figure 2.2.1

Position of pressure transducers

During the blast tests both longitudinal and transverse surface strains were continuously monitored at various

points. The strain gauges, see figure 2.2.5, were mainly located at the midpoint and near the horizontal edge

of the central corrugation strip. The set of strain gauges near the midpoint of the vertical edge of the panel,

designated S2 in the figure, were not employed in the test FFD39. The test recordings from the gauges will

be described in conjunction with the numerical analysis in chapter 3.



4

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-1500

-1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

O v e r p r e s s u r e , p 3 ,

( m b a r )

Test: FFD39P1

P2P3P4P5P7

Figure 2.2.2

FFD39 - Recorded pressure time history

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-1500

-1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500


( m b a r )

Test: FFD21

P2P4P5P6P7

Figure 2.2.3


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-1500

-1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

O v e r p r e s s u r

e , p 3 ,

( m b a r )

Test: FFD23P1P2P3

P4P5P6P7

Figure 2.2.4




5

Post test inspections showed that, despite the significant plastic deformations illustrated in figure 2.2.6, the

integrity of the specimens FFD39 and FFD21 were maintained during testing. The permanent central

deflection was measured to140mm for FFD39 and 104mm for FFD21. However, the testing of FFD21

was associated with some problems as the framing angles to rig connection was not entirely stationary.

Panel FFD23 was subjected to a significantly higher overpressures and failed during the test. High speedcine recordings showed that rupture was initiated at the midpoint of the bottom weld, and shortly

afterwards began to develop at the midpoint of the top weld. Hereafter, the rupture progressed steadily

along the transverse welds, and then along the longitudinal welds. Finally, displaying a hugely distorted

configuration, the panel had almost completely separated from the frame.

The wall configurations were also tested under static load conditions to gauge the degree of dynamic

amplification and general. A special rig was constructed for this purpose, and the structural response of the

wall was monitored by a centrally positioned LVDT. The LVDT has been labeled L1 in figure 2.2.5. During

the static test it became evident that the weld between the panel and the angles started to fail at a uniform

pressure of about 1.1bar. This is also the approximate load range for the recorded pressure deflection tracegiven in reference [1]. However, it was possible to increase the pressure up to a final 4bar without any

significant worsening in the amount of weld rupturing. The permanent deflection after the test was measured

to be approximately 300mm, but this result may be somewhat flawed as the test rig was found to deform

significantly for pressures above about 2bar.

S1B S1AS2

S3B S3A

L1

Figure 2.2.5

Position of strain gauges and displacement transducer



6

Figure 2.2.6

FFD39 - Permanent deformations caused by blast load

2.3 MATERIAL PROPERTIES

A few coupons were cut from the stainless steel panels and tested in quasi static uniaxial tension according

to BS18. Figure 2.3.1 shows the average nominal stress strain relationship obtained from these tests. Also

shown in the figure is the corresponding true stress strain relationship, which has been calculated byassuming that the steel behaves as an incompressible material.

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60

Strain, ε , ( m/m )

0

100

200

300

400

500

600

700

800

900

1000

S t r e s s , σ

,

( M P a )

Stainless steelNominalTrue

E=0.205E6 MPa

Figure 2.3.1



7



8


This chapter describes in detail the finite element analysis of the A0 blastwalls. Special attention

are given to the influence of the load description and mesh density on the predicted structural

response. Whenever possible the numerically results are compared with test data.


The numerical analysis was performed employing the ABAQUS/Explicit finite element program[5], which is suitable for analysing the brief transient dynamic events caused by blast loading.

Besides being very efficient in terms of the required computing resources, the employment of

the explicit time integration scheme has the added benefit of automatically accounting for the

effects of possible local buckling of the corrugation profile.

The corrugated panel and the connected angle brackets were geometrically modeled as an

assembly of flat quadrilateral shell elements of type "S4R". These reduced integration elements,

which are intended for both thick and thin shell applications, are designed for the analysis of

structural problems involving large displacements as well as finite membrane strains.

It follows from the inherent symmetry in the structural configuration combined with the loadingconditions that only a quarter of the wall need to be specifically defined in the numerical model.

The interaction with the omitted quadrants was included in the model by superimposing simple

boundary conditions to the nodal displacements such as to express the symmetry. The angle

brackets were assumed to be encastre along the edge beyond which the legs are directly

supported by the very stiff structural components of the test rig. Figure 3.1.1 illustrates one of

the models employed in the present investigation, and figure 3.1.2 shows a "close up" of the

different mesh densities used.

Encastre Encastre

X-Symmetry Y-Symmetry1 2

3

1 2

3

Figure 3.1.1

FE model of 1/4 blastwall



9

Rough Coarse Fine

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

1 2

3

Figure 3.1.2Adopted meshing in FE models

The rough, coarse and fine meshes have a total of 774, 4258 and 16386 elements respectively.

Mechanical constitutive model

In the elasto plastic range the biaxial material behaviour is governed by the Von-Mises’s yield

function for isotropic materials combined with an isotropic hardening rule and associated flow

rule.

The Von Mises’s yield function is the standard for metals for which the hydrostatic pressure has

no appreciable effect on the yielding. Thus yielding begins when the octahedral shearing stress,, reaches a critical value, . Work hardening is incorporated in the model by letting be aoct k k

function of the strain history as described by the equivalent plastic strain, .,

eqp

J

oct'

2

3k

For a biaxial stress state the octahedral shear stress can be written in terms of the principal stress

as:

J

oct'

2

9F

12

% F

22

& F

1F

2

The effective stress, used to monitor the multiaxial stress state during the analysis, is evaluated

from:

F

eff ' F

12

% F

22

& F

1F

2

For the special case of uniaxial conditions the effective stress simplifies to the uniaxial stress.

Likewise, the hardening parameter relates the uniaxial stress strain curve to the multiaxial stress

state through the equivalent plastic strain defined by the incremental plastic work.

F

eff d

,

eqp

' F

ijd

,

ijp

The total equivalent plastic strain is evaluated by:

,

eqp

'

m

d,

eqp

It can be shown that a consequence of adopting the associated flow rule is that the plastic

material behaviour is incompressible.



10

3.2. STATIC TEST - ST3

Figure 3.2.1 and 3.2.2 shows the calculated and measured midpoint deflections as a function of

the applied static pressure. Whereas, the relationship shown in figure 3.2.1 only includes values

of pressure for which experimental displacement data is available, the relationship shown in

figure 3.2.2 includes the maximum pressure applied during the test. It can be seen from the

figures that further refinements of the coarse mesh has a negligible influence on the predicted

displacements.

In view of figure 3.2.1 it can be concluded that the numerical models predicted a somewhat

stiffer response than that experienced in the test. The predicted displacements obtained using the

coarse mesh always lied within approximately 15% of the test results.

It is interesting, see figure 3.2.2, that the numerical model predicts the gradual development of

a stiffening response of the blastwall for pressures in excess of approximately 500mbar. This

behaviour can be attributed to the effect of membrane forces, which are caused by the large

deflections of the panel. However, the shape of the experimental curve indicates that the

predicted results are much less, or not at all, conservative when the pressure exceeds the 1.1bar

data limit.

Figure 3.2.3 - 3.2.12 shows the numerically calculated surface strains at the gauge locations used

in the dynamic tests. For each direction and each mesh density the calculated strain pressure

diagram was calculated for opposite surfaces on the panel. The curves drawn with the solid line

style refer to the gauged surface, and the dashed curves refer to the opposite surface.

The strains at the midpoint of the panel, station S1A and S1B, are almost unchanged when

employing the fine mesh density rather than the coarse mesh density in the numerical analysis.

Thus, the influence of mesh refinements can be assumed to have been eliminated for the coarse

mesh. In contrast, the strains predicted in the vicinity of the welded connections, station S1A,

S3B and S2, does not appear to converge with continued mesh refinement. The lack of convergence is caused by a combination of significant local strain variations and numerical strain

singularities. The strain singularities arise due to the geometric simplifications performed in the

modelling of the connection details.

It is interesting that the compressive longitudinal strain at the midpoint of the panel, S1AY, got

an absolute maximum corresponding to a pressure loading of about 500mbar. When loaded

beyond 500mbar the incremental strain becomes tensile, but the total strain remains compressive

at the maximum pressure of 4bar. Likewise, the tangent of the pressure strain diagram in the

tension flange, S1BY, becomes significantly less steep for pressures in excess of about 500mbar.

The level of pressure at which the rate of straining of the centre of the panel is significantly

reduced coincides fairly well with a significant growth in the rate of straining along theboundaries of the panel.

The longitudinal strains at the stations S3A and S3B indicates the development of a plastic hinge,

which is subjected to a severe and increased amount of stretching. However, the straining of the

compression flange appears in comparison with the straining of the tension flange to be much

less critical. The development of transverse strains at opposite surfaces in the vicinity of the

vertical angle, station S2, indicates the occurrence of a rather sudden and fixed amount of rotation.



11

Although the predicted strain at the edges is mesh sensitive this is, as can be seen from figure

3.2.13, not the case for the dissipated energy. The energy dissipated in the structure is practically

unchanged when further refining the coarse mesh. Opposite the strains at the middle of the panel

the increase in dissipated energy does not slow down with increased pressure. This behaviour is

partly due to the very large strains developing in the vicinity of the connections and partly due

to the spreading of the plastic zones in the interior of the panel.

0 100 200 300 400 500 600 700 800 900 1000 1100 1200

Pressure, p3 , ( mbar )

-300

-250

-200

-150

-100

-50

0


( m m )

Test: ST3Node: L1

roughcoarsefine

Figure 3.2.1

Predicted midpoint deflection

0 500 1000 1500 2000 2500 3000 3500 4000 4500


-450

-400

-350

-300

-250

-200

-150

-100

-50

0

D e f l e c t i o n , u

3 ,

( m m )

Test: ST3Node: L1

roughcoarsefine

Figure 3.2.2




12

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Pressure, p 3 , ( msec )

-12

-10

-8

-6

-4

-2

0

2

4

6

8

N o m i n a l s t r a i n ,

ε 1 1 ,

( m m / m )

Test: ST3: S1AYouter surface

roughcoarsefine

Figure 3.2.3

Longitudinal strain near midpoint of panel

0 500 1000 1500 2000 2500 3000 3500 4000 4500


-6

-4

-2

0

2

4

6

8

10

12

14


ε 2 2 ,

( m m / m )

Test: ST3: S1AXouter surface

rough

coarsefine

Figure 3.2.4Transverse strain near midpoint of panel

0 500 1000 1500 2000 2500 3000 3500 4000 4500


0

2

4

6

8

10

12

14

16

18

20


ε 1 1 ,

( m m / m )

Test: ST3: S1BYouter surface

roughcoarsefine

Figure 3.2.5




13

0 500 1000 1500 2000 2500 3000 3500 4000 4500


-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8


ε 2 2 ,

( m m / m )

Test: ST3: S1BXouter surface

roughcoarsefine

Figure 3.2.6

Transverse strain near midpoint of panel

0 500 1000 1500 2000 2500 3000 3500 4000 4500


-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

60


ε 1 1 ,

( m m / m )

Test: ST3: S3AYinner surface

rough

coarsefine

Figure 3.2.7Longitudinal strain near horizontal angle connection

0 500 1000 1500 2000 2500 3000 3500 4000 4500


-2

0

2

4

6

8

10

12

14

16

18

20

22

24

N o m

i n a l s t r a i n ,

ε 2 2 ,

( m m / m )

Test: ST3: S3AXinner surface

roughcoarsefine

Figure 3.2.8

Transverse strain near horizontal angle connection



14

0 500 1000 1500 2000 2500 3000 3500 4000 4500


-80

-40

0

40

80

120

160

200

240

280

320


ε 1 1 ,

( m m / m )

Test: ST3: S3BYinner surface

roughcoarsefine

Figure 3.2.9

Longitudinal strain near horizontal angle connection

0 500 1000 1500 2000 2500 3000 3500 4000 4500


-50

-40

-30

-20

-10

0

10

20

30

40


ε 2 2 ,

( m m / m )

Test: ST3: S3BXinner surface

roughcoarsefine

Figure 3.2.10


0 500 1000 1500 2000 2500 3000 3500 4000 4500


-10

-8

-6

-4

-2

0

2

4

6

8

10


ε 1 1 ,

( m m / m )

Test: ST3: S2Yinner surface

roughcoarsefine

Figure 3.2.11




15

0 500 1000 1500 2000 2500 3000 3500 4000 4500


-200

-160

-120

-80

-40

0

40

80

120

160

200


ε 2 2 ,

( m m / m )

Test: ST3: S2Xinner surface

rough finecoarse

Figure 3.2.12

Transverse strain near vertical angle connection

0 500 1000 1500 2000 2500 3000 3500 4000 4500


0

20

40

60

80

100

120

140

160


E p l ,

( K J )

Test: ST3roughcoarsefine

Figure 3.2.13

Dissipated energy



3.3. BLAST TEST - FFD39

The influence of the shape of the idealised pressure time curve on the structural response was

investigated by means of three different idealisations. The piecewise linear curves, shown in

figure 3.3.1, were all derived from "free hand" curve fitting to the available experimental results.

The criteria governing the shape of the idealised curves was that they should as far as possiblerepresent what seemed to be the most likely pressure at a given time. All the estimated loading

curves has a peak pressure of 969mbar. The type d curve includes an initial phase with the

pressure increasing by a relatively slow rate. After having reached approximately 20% of the

final peak pressure this phase is followed by a second phase in which the pressure increases

rapidly, approximately by 75bar/sec, until reaching its peak value. The presence of the initial

phase is a typical feature of experimentally produced pressure time histories. The type n curve

is similar to the type d curve but extended such as to include the negative phase of the blast

loading. The type t curve is a standard triangular representation of the pressure time history. As

the required computing time is proportional with the duration of the event the triangular

representation is in terms of computing time the most efficient.

Results from the analysis of FFD39 based on the coarse mesh density are illustrated in the

figures 3.3.2 - 3.3.6. It follows from the figures that the adopted type of pressure time curve in

general has a negligible influence on the results. The exception is the transverse strains at S3B,

which are somewhat enhanced when employing the type t loading description.

At the sampling points located in the interior of the panel the numerical models are in general

capable of reproducing, though somewhat conservative, the experimentally obtained strain

diagram. However, the reversal in straining observed in the test after approximately 90msec was

not predicted by the numerical models. The lack of rebound after the passage of the blast also

explains why the residual displacement at the centre of the panel, measured in the test to 140mm,

was inaccurately predicted in the numerical calculations.

The strain at the edges of the panel are as expected not predicted very well by the numerical

model. The minimum strain in the longitudinal direction at location S3B is calculated to

approximately -28.2mm/m, which compares to the -0.9mm/m measured in the test. In contrast

the maximum strain was calculated to 1.9mm/m, which compares to the 1.8mm/m measured in

the test. Altogether, the calculated strains are only in close agreement with the test results in the

initial phase of the strain diagram. Furthermore, it was found that convergence with increasing

refinements of the mesh density only was present in this phase of the strain diagram.

Table 3.3.1 shows the extremum values of the key variables obtained using the different load

representations. These have whenever possible been compared the test results.

16



17

Table 3.3.1

FFD39 - Comparison of results

Loading description

Variable type d type n type t static test

Defln. L1, (mm) -310.2 -310.2 -323.9 -237.0 -

Strain S1BY, (mm/m) 9.1 9.1 9.2 6.5 6.7

Strain S1BX, (mm/m) -8.1 -8.1 -8.4 -6.1 -7.4

Strain S3BY, (mm/m) -28.2*

-28.1*

-28.1*

-16.0 -0.9*

Strain S3BX, (mm/m) 1.3**

1.3**

1.3**

0.8 -

* ) Maximum respectively: 1.9, 1.9, 1.9 and 1.8**) Minimum respectively: -1.1, -1.2 and -2.5

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-800

-600

-400

-200

0

200

400

600

800

1000

1200

1400

1600

1800


( m b a r )

Test: FFD39P1P2P3

P4P5P7

A B

C

D

E

F

G

ACDE type d

ACDFG type nBDE type t

Figure 3.3.1

Pressure time history idealisations

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-450

-400

-350

-300

-250

-200

-150

-100

-50

0


( m m )

Test: FFD39Node: L1

load type dload type nload type t

static

Figure 3.3.2




18

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12


ε 1 1 ,

( m m / m )

Test: FFD39: S1BYload type dload type nload type t static

Figure 3.3.3


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12


ε 2 2 ,

( m m / m

)

Test: FFD39: S1BXload type dload type n

load type t

static

Figure 3.3.4

Transverse strain near midpoint of panel

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30

N o m i n

a l s t r a i n ,

ε 1 1 ,

( m m / m )

Test: FFD39: S3BYload type dload type nload type t

static

Figure 3.3.5




19

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12


ε 2 2 ,

( m m / m )

Test: FFD39: S3BXload type dload type nload type t

static

Figure 3.3.6


Influence of rate dependent material behaviour

From studying the developments in equivalent plastic strain the maximum strain rates occurringin the above described analyses could be estimated. The maximum strain rate near the centre of

the panel was estimated to 1.3s-1, and the maximum strain rate near the angle connections was

estimated to 14.9s-1. Considering the significant magnitude of the strain rates it was decided to

perform another analysis, which incorporated the effects of high strain rates on the material

properties. The new analysis was based on the type d loading curve and the coarse mesh density.

The influence on the calculated results of a rate dependent material model is illustrated in the

figures 3.3.7 - 3.3.11, and summarised in terms of critical values in table 3.3.2. Although, the

inclusion of the rate dependent material behaviour improved the numerical results somewhat, its

influence was ignored in the remainder of this investigation. Especially, as the structural

influence of the material rate dependent behaviour to a large extent was a consequence of theartificially high strain rates occurring in the vicinity of the angle connections.

Table 3.3.2


Material description

Variable rate

independent

rate

dependent

test

Defln. L1, (mm) -310.2 -280.7 -

Strain S1BY, (mm/m) 9.1 8.6 6.7

Strain S1BX, (mm/m) -8.1 -7.7 -7.4

Strain S3BY, (mm/m) -28.2*

-23.9*

-0.9*


1.5**

-

* ) Maximum respectively: 1.9, 2.0 and 1.8**) Minimum respectively: -1.1 and -0.1



20

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

D e f l e

c t i o n , u 3 ,

( m m )

Test: FFD39Node: L1

rate dependentrate independent

static

Figure 3.3.7


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12


ε 1 1 ,

( m m / m )

Test: FFD39: S1BYrate dependent

rate independentstatic

Figure 3.3.8


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

N o m i n a l

s t r a i n ,

ε 2 2 ,

( m m / m )

Test: FFD39: S1BXrate dependentrate independent

static





22


The pressure time curves recorded during the test FFD21 were quite unusual as so far as

indicating that the pressure remained almost constant for approximately 10msec after having

reached its peak value. The influence of a maintained peak pressure was explored through the

applied pressure curves designated type h and type p in figure 3.4.1. The only difference between

these curves is that the built up in pressure described by the type h curve initially develops at

lower rate. The low rate was estimated to apply until the pressure had reached approximately21% of the peak pressure. Hereafter, the pressure increases at a much higher rate, about

67bar/sec, until finally reaching its maximum of 1150mbar. Also, an analysis based on the

traditional triangular representation of the pressure time history, designated type t , was carried

out.

The effect of including the initial phase in the load description is, as can be seen from figure

3.4.2, to reduce the calculated maximum deflection somewhat. The relative reduction in peak

deflection was calculated to 6%, which compares to the 4% determined in the case of FFD39.

Although, the peak pressure was increased by 19% compared to FFD39 the predicted maximum

deflection increased by a modest 8%. Thus the stiffening behaviour observed under the dynamic

loading conditions is much alike the one observed under static loading conditions. It can also benoticed from figure 3.4.2 that the presence of a 10msec waiting period before the pressure is

released has a negligible influence on the predicted deflections.

The recordings from the strain gauges mounted near the centre of the panel are very similar to

those in test FFD39, and once again the numerically calculated strains S1BY and S1BX are in

reasonable good agreement with the test results. However, whereas the measured strains actually

are of a slightly smaller magnitude in FFD21 compared to FFD39, the numerically calculated

strains are as expected somewhat larger. Furthermore, it can be seen from the figures 3.4.3 and

3.4.4 that the utilised load representation has a negligible influence on the predicted strains at the

centre of the panel.

The predicted strain diagrams at the location near the transverse angle connection, i.e. S3BY and

S3BX, are characterised by much more pronounced strain reversals than those predicted in

FFD39. Whereas, the strain diagrams for S3BY got an almost identical minimum in the two

loading cases, the predicted residual strains are vastly different. Likewise, the strain diagrams for

S3BX got an almost identical maximum, but the absolute value of the minimum is in the case

of FFD21 approximately increased by a factor 4. It should be reminded that the strains predicted

in this region is of qualitative rather than of quantitative importance. Not only is the strain history

in this region strongly dependent on the mesh density, it is also very sensitive to the assumed load

representation.

As seen from figure 3.4.7 and 3.4.8 the strain diagrams determined in the vicinity of thelongitudinal angle connection are both in terms of extremum values and shape vastly different

from the test results.

Table 3.4.1 shows a numeric comparison of results determined form the analysis and the test

respectively.



23

Table 3.4.1


Loading description

Variable type h type p type t static test

Defln. L1, (mm) -332.5 -353.7 -350.5 -254.0 -

Strain S1BY, (mm/m) 9.4 9.7 9.6 6.8 5.9

Strain S1BX, (mm/m) -8.3 -8.8 -8.7 -6.4 -7.4

Strain S3BY, (mm/m) -27.9 * -27.9 * -27.8 * -19.9 -


1.3**

1.3**

0.9 -

Strain S2Y, (mm/m) -0.1 -0.1 -0.1 -0.1 -1.3

Strain S2X, (mm/m) 67.4 66.7 67.4 62.5 3.2

* ) Maximum respectively: 1.6, 1.9 and 1.9** ) Minimum respectively: -4.3, -8.2 and -7.3

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-800

-600

-400

-200

0

200

400

600

800

1000

1200

1400

16001800

2000


( m b a r )

Test: FFD21

P2P4P5P6P7

A B

C

D E

F

ACDEF type hBDEF type pBDF type t

Figure 3.4.1


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

D e f l e c

t i o n , u 3 ,

( m m )

Test: FFD21Node: L1

load type hload type pload type t

static

Figure 3.4.2




24

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12


ε 1 1 ,

( m m / m )

Test: FFD21: S1BYload type hload type pload type t static

Figure 3.4.3


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12


ε 2 2 ,

( m m / m

)

Test: FFD21: S1BXload type hload type p

load type t

static


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30


ε 1 1 ,

( m m / m )

Test: FFD21: S3BYload type hload type pload type t

static

Figure 3.4.5




25

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12


ε 2 2 ,

( m m / m )

Test: FFD21: S3BXload type hload type pload type t

static

Figure 3.4.6


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6


ε 1 1 ,

( m m / m )

Test: FFD21: S2Yload type hload type p

load type t

static

Figure 3.4.7Longitudinal strain near vertical angle connection

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-70

-60

-50

-40-30

-20

-10

0

10

20

30

40

50

60

70

N o m i

n a l s t r a i n ,

ε 2 2 ,

( m m / m )

Test: FFD21: S2Xload type hload type pload type t

static

Figure 3.4.8





As previously described the pressure generated during the test FFD23 caused the firewall to

almost entirely separate from the frame. The failure of the wall was reflected in the measured

strain diagrams as follows:

The peak strains recorded at the centre of the panel did not, as was the case in the tests FFD39

and FFD21, remain almost constant for a relatively long time period. As seen from figure 3.5.3

and 3.5.4, the peak of the strain diagrams recorded in the test FFD23 were quite distinct.

Compared to the test FFD39 the maximum strain in the longitudinal direction was increased by

a modest 0.6mm/m, and the maximum compressive strain in the transverse direction by

0.4mm/m. Thus, an increase in the applied peak pressure by about 150% caused the midpoint

strains to increase by a very modest 5 to 9%.

The progressive rupture of the weld between the panel and the frame was initiated near mid-

length of the transverse weld. The maximum longitudinal strain measured in this region increased

from approximately 2mm/m in the test FFD39 to 17mm/m in the test FFD23. The shape of thestrain diagram for S3BY indicates that failure of the weld was initiated after about 60msec.

The transverse strains at S2 are only significant well after 60msec, and does as such reflect the

behaviour of the wall after the transverse weld has begun to rupture. Considering figure 3,5,8

it can be deducted that the weld local to S2 failed after approximately 75msec.

Two types of pressure time curves, namely the earlier described type d and type t , were employed

for the analysis of FFD23. The peak pressure was estimated from the experimental data to

2445mbar, and the rate by which the pressure was applied to 116bar/sec. The initial phase of the

type d load description terminates at the point where the pressure has reached approximately 25%

of its peak value.

From the figures 3.5.2 - 3.5.6 it can be concluded that, opposite the two previous investigated

load cases, the utilised pressure time curve has a very significant bearing on the predicted results.

Overall the type t load description leads to the prediction of a more severe structural response.

The rate of straining at the centre of the panel is predicted much better by the type d curve than

by the type t curve. Thus, the type d idealisation is believed to be more representative for the blast

load received by the panel in test FFD23.

Irrespective of the load description the numerical models are not capable of predicting the

observed collapse of the firewall. The reason being that, the numerically determined equivalent

plastic strain does not at any location exceed the ultimate value of 42% defined in the material

model.

Table 3.5.1 lists some of the key results from this part of the investigation.

26



27

Table 3.5.1


Loading description

Variable type d type t static test

Defln. L1, (mm) -334.3 -444.5 -320.0 -

Strain S1BY, (mm/m) 10.5 18.9 8.9 7.3

Strain S1BX, (mm/m) -7.9 -15.4 -7.5 -7.8

Strain S3BY, (mm/m) -28.4 * -27.2 * -23.6 -0.3 *

Strain S3BX, (mm/m) -5.5**

-17.3**

-1.5 -

Strain S2Y, (mm/m) -0.2 -0.3 -0.1 -

Strain S2X, (mm/m) 68.8 64.7 63.9 3.1***

* ) Maximum respectively: 1.6, 33.9 and 17.4** ) Maximum respectively: 1.2 and 1.5 ***) Minimum: -18.9

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-1500

-1000

-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500


( m b a r )

Test: FFD23

P1P2P3P4P5P6P7P8

A B

C

D

E

ACDE type dBDE type t

Figure 3.5.1


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-450

-400

-350

-300

-250

-200

-150

-100

-50

0

D e f l e c

t i o n , u 3 ,

( m m )

Test: FFD23Node: L1

load type dload type t

static

Figure 3.5.2




28

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-24

-20

-16

-12

-8

-4

0

4

8

12

16

20

24


ε 1 1 ,

( m m / m )

Test: FFD23: S1BYload type dload type t

static

Figure 3.5.3


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-24

-20

-16

-12

-8

-4

0

4

8

12

16

20

24


ε 2 2 ,

( m m / m

)

Test: FFD23: S1BXload type dload type t

static


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-35

-30

-25

-20-15

-10

-5

0

5

10

15

20

25

30

35


ε 1 1 ,

( m m / m )

Test: FFD23: S3BYload type dload type t

static

Figure 3.5.5




29

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-24

-20

-16

-12

-8

-4

0

4

8

12

16

20

24


ε 2 2 ,

( m m / m )

Test: FFD23: S3BXload type dload type t

static

Figure 3.5.6


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6


ε 1 1 ,

( m m / m )

Test: FFD23: S2Yload type dload type t

static

Figure 3.5.7Longitudinal strain near vertical angle connection

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-70

-60

-50

-40-30

-20

-10

0

10

20

30

40

50

60

70


ε 2 2 ,

( m m / m )

Test: FFD23: S2Xload type dload type t

static

Figure 3.5.8




30

4. FAILURE MODELLING

In this chapter the performance of the firewall has been assessed in terms of an ultimate value

for its ability to dissipate energy, and in terms of an ultimate value for the equivalent plastic

strain in the welds. Also, the influence of the progressive weld rupture observed in the test

FFD23 is discussed.

4.1 DISSIPATED ENERGY

An earlier investigation carried out by the author [6] had shown that the structural integrity of

a firewall can be assessed from the amount of dissipated energy.

Figure 4.1.1 - 4.1.3 illustrates the numerically calculated developments in dissipated energy for

the investigated pressure histories. A comparison of the final amount of dissipated energy can

be read from table 4.1.1.

Considering that the wall survived the blast generated in the test FFD21 without loss of integrity,

and that each of the three numerical analyses carried out produced a good fit to the experimental

strain results, it is reasonable to assume that the wall in this test safely dissipated between 89 and

103KJ of energy. It can be seen from figure 3.2.13 that an energy level of 89KJ corresponds to

a static pressure of 2.8bar, which the wall indeed was capable of sustaining without the weld

rupturing.

In the case of FFD23 the calculated amount of dissipated energy is, as can be seen from figure

4.1.3, very sensitive to the adopted load description. The estimated upper bound value for the

energy capacity was 103KJ for load type d , and 203KJ for load type t . However, the analysis

based on the type t load idealisation significantly overestimated the rate of straining at the centre

of the panel, and is as such not a good representation of the actual loading conditions.

Statically the wall was tested for a maximum pressure of 4bar, at which point 150KJ of energy

has been dissipated in the structure. Assuming, as observed in the investigation reported in [6],

that the static load conditions gives a lower bound value for the walls capability to dissipate

energy, it follows that the idealised load best representing the test blast is more severe than the

type d used in the analysis. However, in this context it should be emphasised that the problems

encountered during the static testing may have delayed the failure initiation. Thus the static test

results may not be reliable when assessing the walls capacity to dissipate energy.

Table 4.1.1

Comparison of dissipated energy, (KJ)

Test case

Loading conditions FFD39 FFD21 FFD23

load type d 62.5 - 102.9

load type n 63.1 - -

load type t 70.5 97.7 202.6

load type h - 89.4 -

load type p - 103.3 -

static 27.1 33.5 78.9



31

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

0

10

20

30

40

50

60

70

80


E p l ,

( K J )

Test: FFD39load type dload type nload type t

static

Figure 4.1.1

FFD39 - Dissipated energy history

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

0

10

20

30

40

50

60

70

80

90

100

110


E p l ,

( K J )

Test: FFD21load type hload type p

load type t

static

Figure 4.1.2FFD21 - Dissipated energy history

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

0

20

40

60

80

100

120

140

160

180

200

220


E p l ,

( K J )

Test: FFD23load type dload type t

static

Figure 4.1.3

FFD23 - Dissipated energy history



Dissipated energy and structural components

Figure 4.1.4 illustrates the plastic energy dissipated in the different structural components under

static and dynamic loading conditions. Under dynamic loading conditions the dissipated energy

was calculated using load type d for FFD39 and FFD23, and load type h for FFD21.

The diagrams show that the transverse angles plays a significant role in dissipating energy,whereas the influence of the longitudinal angles is negligible. As much as between 32% and 40%

of the total amount of plastic energy was dissipated in the transverse angles. Compared to the

static loading conditions a somewhat higher percentage of the total energy was dissipated in the

panel under dynamic loading conditions. Also, the percentage of energy dissipated in the panel

increased somewhat with increasing peak pressure.

FFD23-d FFD21-h FFD39-d

0

10

20

30

40

50

60

70

80

90

100

110


E p l ,

( K J )

FFD Seriesdynamicstatic

Panel Y-Angles X-Angles

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70


E p l ,

( K J )

FFD39, 969mbardynamicstatic


0

5

10

15

20

25

30

35

40

45

50

55

60

65

70


E p l ,

( K J )



0

5

10

15

20

25

30

35

40

45

50

55

60

65

70


E p l ,

( K J )


Figure 4.1.4

Dissipated energy distribution

32



4.2. STRAIN CONCENTRATIONS

The influence of mesh density on the calculated equivalent plastic strains was initially studied

by means of a simplified model consisting of a single corrugation strip supported at the ends by

flexible angle brackets. The boundary conditions were specified such as to represent a true one-

way span system. The applied pressure history was the type d used in the analysis of FFD23.

Figure 4.2.1 shows the equivalent plastic strains at the centre of the elements connected to the

angle supports. In general, the smaller the size of the elements become, the closer the sampling

points gets to the face of the angle, and the larger the calculated equivalent plastic strains

become. Thus, a strain based failure criteria can only be applied to these boundary elements if

it can take proper account for these numerical deficiencies.

Strain determined at the midspan of the corrugation strip will converge rapidly with refinements

of the mesh density. Thus, the ultimate strain applicable in the central region can be directly

obtained from the materials stress-strain curve.

Figure 4.2.3 illustrates the variation in the maximum equivalent plastic strain when moving away

from the angle connection towards the midspan of the corrugation strip. Clearly, at a set distance

from the angle all the mesh densities, except the most crude, results in approximately equal

values of equivalent plastic strain. In other words, it is the proximity of the sampling points to

the angle connection rather than the mesh density itself which are responsible for the

discrepancies in the calculated strains.

Figure 4.2.4 - 4.2.6 shows the final distribution of equivalent plastic strain near the supports of

the central corrugation strip for the quarter panel model. The analysis of FFD39 and FFD23 was

based on load type d , and the analysis of FFD21 was based on load type h. Likewise, figure 4.2.7

and 4.2.8 shows the distribution of equivalent plastic strain under static loading conditions fora few selected pressures.

It is noticeable that the maximum value of equivalent plastic strain obtained for FFD21 is of a

comparable magnitude to the strain obtained for FFD23. The maximum strain of 141.9mm/m

obtained for FFD21, when employing a coarse mesh, can be seen to correspond to a static load

of approximately 2.8bar. For the fine mesh the same variables were determined to 205.8mm/m

and 2.9bar respectively. Thus from these results the wall can be estimated to have a static load

capacity of at least 2.8bar. However, from the analysis of FFD23 it follows that the weld can

expected to rupture for a static load of as little as 2.9bar.

Compared to the strip model the quarter model predicts a less stiff response, as it permits thecorrugations to open up during loading. The midpoint displacement is increased by 3.5%, and

the maximum equivalent plastic strain is increased by a massive 26%.

33



34

-130 -110 -90 -70 -50 -30 -10 10 30 50 70 90 110 130

Transverse distance from centre, (mm)

0

20

4060

80

100

120

140

160

180

200

220

240

260

280

300

E q u i v a l e n t p l a s t i c s t r a i n ,

ε p q ,

( m m / m )

Beam modelmesh:5x2614x5228x9856x198


Figure 4.2.1

Equivalent plastic strain in vicinity of the supports

-130 -110 -90 -70 -50 -30 -10 10 30 50 70 90 110 130


0

2

4

6

8

10

12

14

16

18


( m m / m )

Beam modelmesh:5x2614x5228x98

56x198


Figure 4.2.2

Equivalent plastic strain at midspan

0 25 50 75 100 125 150 175 200 225 250 275 300 325

Longitudinal distance from end, (mm)

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300


ε p q ,

( m m / m )

Beam modelmesh:5x2614x5228x9856x198

Figure 4.2.3

Maximum equivalent plastic strain in vicinity of the supports



35

-130 -110 -90 -70 -50 -30 -10 10 30 50 70 90 110 130


0

20

40

60

80

100

120

140

160

180

200

220

E q u i v a l e n

t p l a s t i c s t r a i n ,

ε p q ,

( m m / m ) Test: FFD39

roughcoarsefine


Figure 4.2.4

FFD39 - Equivalent plastic strain in vicinity of the supports

-130 -110 -90 -70 -50 -30 -10 10 30 50 70 90 110 130


0

20

40

60

80

100

120

140

160

180

200

220


ε p q , (

m m / m ) Test: FFD21

roughcoarse

fine


Figure 4.2.5FFD21 - Equivalent plastic strain in vicinity of the supports

-130 -110 -90 -70 -50 -30 -10 10 30 50 70 90 110 130


0

2040

60

80

100

120

140

160

180

200

220

E q u i v a l e

n t p l a s t i c s t r a i n ,

ε p q ,

( m m / m ) Test: FFD23

roughcoarsefine


Figure 4.2.6

FFD23 - Equivalent plastic strain in vicinity of the supports



36

-130 -110 -90 -70 -50 -30 -10 10 30 50 70 90 110 130


0

20

40

60

80

100

120

140

160180

200

220

240

260

280

300

E q u i v a l e n t p l a s t i c s t r a i n , ε

e q , p

l ,

( m m / m ) Test: ST3

Coarse mesh512mbar1072mbar2068mbar

2968mbar4080mbar


Figure 4.2.7

ST3 - Equivalent plastic strain in vicinity of the supports

-130 -110 -90 -70 -50 -30 -10 10 30 50 70 90 110 130


020

40

60

80

100

120

140

160

180

200

220

240

260

280

300

E q u

i v a l e n t p l a s t i c s t r a i n ,

ε e q , p

l ,

( m m / m ) Test: ST3

Fine mesh496mbar992mbar1996mbar3072mbar4000mbar


Figure 4.2.8

ST3 - Equivalent plastic strain in vicinity of the supports

Table 4.2.1

Comparison of max equiv plastic strain, (mm/m)

Coarse mesh Fine mesh

Loading conditions dynamic static dynamic static

FFD39 - load type d 100.3 36.0 154.8 66.9

FFD21 - load type h 141.9 46.4 205.8 80.7

FFD23 - load type d 151.6 120.8 207.2 173.7



4.3 WELD RUPTURE

The numerical calculations described so far were based on the uniaxial stress strain relationship

shown in figure 2.3.1, and did as such not explicitly capture the progressive weld rupture

observed in the test FFD23. The weld rupture observed in this test can at least qualitatively be

modelled by reducing the ultimate strain used in the material description of stainless steel.

Figure 4.3.1 - 4.3.5 illustrate the predicted structural response when using the type t load

description, and assuming the ultimate strain equals 6%, 10%, 14% and 42% respectively.

Except for the 42% ultimate strain all the values leads to the complete detachment of the panel

from the angle frame.

Evidently, the strain relaxation measured by the strain gauges positioned in the central region of

the panel could, at least qualitatively, be reproduced by the numerical models. However,

significant strain relaxation was also observed during the testing of FFD39 and FFD21, both of

which did not suffer a loss of structural integrity. Thus, the unzipping of the weld can only

provide a partial explanation for the observed strain relaxation.

Figure 4.3.6 illustrates the distribution of strain in the firewall just prior to initiation of weld

rupture. Although, the predicted magnitude of the strains in the vicinity of the angle connections

is strongly influenced by the numerical model simplifications, the strain localisation in this

region is a real feature of corrugated panels. It is the very sudden developments of large strains

in this region which is responsible for the failure of the firewall.

Figure 4.3.7 shows the panel at a particular instant during the rapidly propagating failure process.

Shortly afterwards, approximately 3.5msec, the panel had completely detached from the angle

frame.

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-1400

-1200

-1000

-800

-600

-400

-200

0


( m m )

Test: FFD23Node: L1

6% fail. strain10% fail. strain14% fail. strain42% fail. strain

Figure 4.3.1


37



38

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-24

-20

-16

-12

-8

-4

0

4

8

12

16

20

24


ε 1 1 ,

( m m / m )

Test: FFD23: S1BY6% fail. strain

10% fail. strain14% fail. strain42% fail. strain

Figure 4.3.2


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

30


ε 2 2 ,

( m m / m )

Test: FFD23: S1BX6% fail. strain

10% fail. strain

14% fail. strain42% fail. strain


0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-40

-20

0

20

40

60

80

100

120

N o

m i n a l s t r a i n ,

ε 1 1 ,

( m m / m )

Test: FFD23: S3BY6% fail. strain


Figure 4.3.4




39

0 10 20 30 40 50 60 70 80 90 100 110 120

Time, t , ( msec )

-24

-20

-16

-12

-8

-4

0

4

8

12

16

20

24

N o

m i n a l s t r a i n ,

ε 2 2 ,

( m m / m )

Test: FFD23: S3BX6% fail. strain


Figure 4.3.5


1 2

3

1 2

3

SECTION POINT 3

PEEQ VALUE

+0.00E+00

+5.71E-03

+1.14E-02

+1.71E-02

+2.29E-02

+2.86E-02

+3.43E-02

+4.00E-02

+4.57E-02

+5.14E-02

+5.71E-02

+6.28E-02

+6.86E-02

+7.43E-02

DISPLACEMENT MAGNIFICATION FACTOR = 1.00

RESTART FILE = dpa_cx2 STEP 1 INCREMENT 6441

TIME COMPLETED IN THIS STEP 1.500E-02 TOTAL ACCUMULATED TIME 1.500E-02

ABAQUS VERSION: 5.8-1 DATE: 17-MAY-1999 TIME: 15:49:51

Figure 4.3.6

Strain concentrations at transverse weld, t=62.0msec



40

1 2

3

1 2

3

SECTION POINT 3

PEEQ VALUE

+0.00E+00

+8.36E-03

+1.67E-02

+2.51E-02

+3.34E-02

+4.18E-02

+5.02E-02

+5.85E-02

+6.69E-02

+7.52E-02

+8.36E-02

+9.20E-02

+1.00E-01

+1.09E-01

DISPLACEMENT MAGNIFICATION FACTOR = 1.00

RESTART FILE = dpa_cx2 STEP 1 INCREMENT 8440

TIME COMPLETED IN THIS STEP 1.950E-02 TOTAL ACCUMULATED TIME 1.950E-02

ABAQUS VERSION: 5.8-1 DATE: 17-MAY-1999 TIME: 15:49:51

Figure 4.3.7

Progressive rupture of transverse weld, t=66.5msec



41

5. CONCLUSION

The numerical models are capable of accurately predicting the strains in the interior of the panel,

but not in the immediate vicinity of the connected angles. The strains fail to converge with

continued mesh refinements because the sampling points used for calculating the strains gets

increasingly closer to the edge of the panel. However, the strains predicted at a set distance from

the face of the angle rapidly converges with mesh refinements.

The capacity of the structural system to dissipate energy can be used to assess the structural

integrity of firewalls when subjected to blast loading. This parameter converges rapidly with

continued mesh refinements, and is as such unaffected by the strain singularities existing at the

interface between the panel and the framing angles.

The transverse angles played a very significant role in the dissipation of energy in the firewalls.

Between 32% and 40% of the blast energy was dissipated in the transverse angles, and the

remaining almost entirely in the corrugated panel.

Including rate dependent material properties improved the numerical results somewhat, but does

not provide the designer with additional information about the magnitude of the strains in the

critical boundary region of the panel.

The triangular representation of the loading function was in found to have a very limited but

conservative effect on the predicted structural response in the case of FFD39 and FFD21, but

in the case of FFD23 this representation produced excessively conservative results.



6. REFERENCES

1. BROWN, M. AND PAPAGEORGE, N.

Theoretical analyses of experimental tests of A0 firewalls: static test, dynamic test

FFD39

British Gas Research & Technology, Report R4533, February 1991

2. PAPAGEORGE, N.

Theoretical analyses of experimental tests of A0 firewalls: dynamic test FFD21

British Gas Research & Technology, Report R4535, April 1991

3. BROWN, M. AND FLETCHER, R.

Theoretical analyses of experimental tests of A0 firewalls: dynamic test FFD23

British Gas Research & Technology, Report R4537, December 1991

4. JONES, N. AND BIRCH, R.S.

Dynamic and static tensile tests on stainless steel

The Steel Construction Institute, March 1998

5. HIBBITT, KARLSSON AND SOERENSEN, INC.

ABAQUS/Explicit, Users manual Vol. I

Users manual, Version 5.8

6. FRIIS, J. AND LOUCA, L.A.

Modelling failure of welded connections to corrugated panel structures under blast

loading

Progress Report No. 2, Imperial College of Science Technology and Medicine

Printed and published by the Health and Safety ExecutiveC0.35 11 /01



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