rr124 - pulse pressure testing of 1/4 scale blast wall panels with

HSE Health & Safety

Executive

Pulse pressure testing of 1/4 scale blast wall panels with connections

Prepared by Liverpool University for the Health and Safety Executive 2003

RESEARCH REPORT 124

HSE Health & Safety

Executive

Pulse pressure testing of 1/4 scale blast wall panels with connections

G K Schleyer, G S Langdon Department of Engineering

Impact Research Centre Liverpool University

A study was carried out at the University of Liverpool on the response of a panel/connection of a 1/4 scale stainless steel blast wall under pulse pressure loading. The aim of the work was to investigate the influence of the connection detail on the overall performance of the panel/connection system under pulse pressure loading and to develop appropriate analytical and numerical model of the blast wall/connection system for correlation with the test results. This is the first time that a detailed experimental study of the behaviour of blast walls made from profiled stainless steel sheet has considered the modes of failure and end effects of the support construction.

This report and the work it describes were funded by the Health and Safety Executive (HSE). Its contents, including any opinions and/or conclusions expressed, are those of the authors alone and do not necessarily reflect HSE policy.

HSE BOOKS

© Crown copyright 2003

First published 2003

ISBN 0 7176 2706 3

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

Applications for reproduction should be made in writing to: Licensing Division, Her Majesty's Stationery Office, St Clements House, 2-16 Colegate, Norwich NR3 1BQ or by e-mail to [email protected]

ii

EXECUTIVE SUMMARY

An extensive programme of experimental work has been carried out on ¼ scale stainless steel blast wall panels with connections subjected to pulse pressure loading to determine their various modes of failure and blast resistance beyond the design limit. The panel design was based on the deep trough trapezoidal profile with welded angle connections top and bottom and free sides. A series of laboratory tests were carried out at the University of Liverpool Impact Research Centre on a panel of a ¼ scale stainless steel blast wall and on various panel/connection systems. The loading applied to the test panel was a triangular pulse pressure representative of a gas explosion overpressure. This project was sponsored by EPSRC, Mobil North Sea Ltd and HSE (Offshore Division) with technical support from Mech-Tool Engineering Ltd who designed and manufactured the test panels. The aim of this work was to investigate the influence of the connection detail on the overall performance of the panel/connection system under pulse pressure loading and to develop appropriate analytical and numerical models of the panel/connection system for correlation with the test results.

The work has shown that the connection detail can significantly influence the response of the panel to extreme pressure loading. Large permanent plastic deformations were produced in the panel/connection system without rupture. Independent connection tests were used to characterise the support conditions for analytical modelling. Different methods were used to estimate the response and hence the capacity of the test panel and the panel/connection system.

Laboratory Tests The performance of several test panels was investigated using a pulse pressure test facility. Three types of panel/connection system were studied, namely a short, medium and long welded angle connection to compare the influence of the angle length. In general, the flexibility of the angle connection and thus the test panel/connection system increases as the angle length increases and larger displacements are produced in the panel for a given test pressure. It is important to optimise the design of the blast wall to absorb as much energy in bending and stretching and at the same time limit displacements that could affect other equipment and processes.

Numerical Modelling The data generated in the laboratory tests were used to develop finite element numerical models of the test panel/connection system. Once satisfactory correlation between the tests and the model is achieved (the ability to predict failure modes and permanent displacements), the numerical model can be used to predict the response of full size blast walls.

Analytical Modelling A simplified analytical model of the panel/connection system was developed to enable the model to be used as a versatile design tool. Design of in-place blast walls should consider a more appropriate assessment of the wall’s resistance taking into account connection flexibility and stretching modes of deformation as well as bending modes.

Note: The intention is to make available further technical details and comparisons of the experimental and numerical/analytical data. The means of access will be announced in HSE’s Offshore Research Focus.

iii

GLOSSARY

Analytical model A simplified mathematical representation of a structure

Angle connection An integral part of the blast wall panel used to attach the profiled section of the blast wall panel to the primary framework

Blast wall A continuous structure used on offshore topside installations spanning decks to offer resistance to an explosion overpressure

Blast wall test panel A scaled down section of a full size blast wall with connections for laboratory testing

Connection The structure joining the blast wall to the primary framework

Connection test A laboratory test in which the connection structure is tested independently of the test panel

Design (rated) capacity This is the manufacturer’s rating applied to the blast wall (panel) in terms of a dynamic pressure and load duration to give a certain permanent plastic deformation and relates to the particular design method used

Failure mode One of several ways in which a structure (in this case the panel/connection system) can fail e.g. permanent deformation, buckling, etc.

Flexible angle The angle section of the connection which is designed to be the first member to yield

Laboratory test A test carried out under controlled laboratory conditions usually at a reduced scale

Load direction The direction in which the load is applied. In the case of the blast wall panel, this is the direction in which the net pressure load is applied to the panel

Material characterisation The test procedure used to determine the static and dynamic material properties of the test structure

Numerical model A finite element representation of a structure

Panel/connection system The combination of profiled sheet and end connection structure

Primary framework The primary load bearing structure of an offshore topside installation

Pulse pressure loading Dynamic pressure loading usually idealised as a triangular pulse

Pulse pressure test A laboratory test in which a dynamic pressure pulse is applied to a structural member

Tensile/compression test A laboratory test in which the specimen is subjected to a uniaxial tension or compression load

Test specimen A general term used for structural components tested in the laboratory e.g. tensile test specimens

iv

NOTATION

Ci Generalised displacement

Ci & Generalised velocity

D, Dy Cowper-Symonds constant and at yield

max Maximum displacement

perm Maximum permanent displacement

Et Tangent modulus in the plastic range

e Strain

e& Strain rate

emin& Strain rate at which the minimum UTS is observed

nome& Strain rate = 0.422 s-1

ue& , ye& Strain rate at rupture and at yield

r True strain at rupture

xK Translation spring stiffness in x direction

yK Translation spring stiffness in y direction

qK Rotational spring stiffness

Lflex Leg length of ‘flexible’ angle

Mp q

Fully plastic moment capacity of rotational spring

P Pressure

q Cowper-Symonds constant

qy Cowper-Symonds constant at yield

Rmx Maximum spring resistance in x direction

Rmy Maximum spring resistance in y direction

Su Ultimate tensile strength (UTS)

Sy Yield strength

r True stress at rupture

tdur Load duration

tm Time at maximum pressure

w Transverse displacement

w& Transverse velocity

w(x,t) Transverse displacement function

v

CONTENTS

EXECUTIVE SUMMARY iii

GLOSSARY iv

NOTATION v

CONTENTS vi

1 INTRODUCTION 1

2 BLAST WALL DESIGN 3

2.1 CORRUGATED PANELS AND CONNECTIONS USED OFFSHORE 3

2.2 TEST PANEL DESIGN 3

3 EXPERIMENTAL INVESTIGATION 8

3.1 MATERIAL CHARACTERISATION 8

3.2 CONNECTION TESTS 21

3.3 PANEL TESTS 26

4 ANALYTICAL MODELLING 58

4.1 BEAM MODEL 58

4.2 CONNECTION MODEL 63

5 NUMERICAL MODELLING 65

5.1 FINITE ELEMENT MODEL 65

5.2 MODELLING PREDICTIONS – 195 MM DEEP BLAST WALL PANEL 65

6 CONCLUDING COMMENTS 69

ACKNOWLEDGEMENTS 71

REFERENCES 72

vi

1 INTRODUCTION

A study was carried out at the University of Liverpool on the response of a panel/connection of a ¼ scale stainless steel blast wall under pulse pressure loading. The study commenced on 1st

October 1999 and finished on 30th September 2002. The project was funded by EPSRC, Mobil North Sea Ltd and HSE (Offshore Division) with technical support from Mech-Tool Engineering Ltd who designed and manufactured the test specimens. The work was carried out by a PhD student, Mrs Genevieve Langdon and supervised by Dr Graham Schleyer. The aim of the work was to investigate the influence of the connection detail on the overall performance of the panel/connection system under pulse pressure loading and to develop appropriate analytical and numerical model of the blast wall/connection system for correlation with the test results. This is the first time that a detailed experimental study of the behaviour of blast walls made from profiled stainless steel sheet has considered the modes of failure and end effects of the support construction. The scope of the work was:

%� to produce static and dynamic material characterisation data for numerical simulations,

%� to perform pulse pressure tests in the dynamic range 0.5-3 bar peak overpressure on scaled blast wall panels complete with connections in order to evaluate the influence of the connection detail on the performance of the panel,

%� to determine the modes of failure of the blast wall/connection system,

%� to develop simplified analytical and numerical models of the blast wall/connection system,

%� to perform separate static tests on the connection detail in order to determine the characteristics of the connection for input to the analytical model,

%� to correlate the analytical and numerical models using the experimental data, and

%� to disseminate the results of the above activities.

Blast loading of various flat, stiffened and corrugated panels has been studied by previous researchers [3, 4] and by the blast wall manufacturers themselves, with the aim of enhancing their blast resistance capacities. However, due to the design of the experimental facilities available to the blast wall manufacturers, the connection details used on offshore platforms have not been examined as part of the test programme. Experimental testing of the connection details would have required major structural modifications to the test rig and this was not commercially viable. The test facilities available at the University of Liverpool were able to incorporate the connection details and, as a result, do not suffer from these limitations.

The experimental and modelling work at Liverpool has enabled a more accurate assessment of the ultimate capacity of the blast wall based on the influence of the connection detail. A reliable method of including the connection detail in the assessment of the blast response of the wall will undoubtedly lead to savings and increased safety through better understanding of the blast wall behaviour in an accidental explosion.

The work at Liverpool has established that modelling the support correctly is fundamental to the response of the blast wall. Current design practice is to assume a single plastic hinge formation at the ends of the blast wall (treated as a one-way member) and to ignore end effects. The capacity of the wall is therefore based on a simple bending resistance model and generally leads

1

to conservative designs. The actual capacity of the wall to resist a dynamic event is considerably larger than the simple design estimate when considering the support construction and attachment to the primary framework.

This report gives an overview of the work carried out in this project. A brief description of the construction of blast walls is given in section 2 along with the summary design details of the test panels. Section 3 contains a summary of the experimental work, namely static and dynamic material characterisation, panel tests and tension/compression tests on connection specimens. A large number of tests were performed on 3 types of panels with their connections, which represents a unique body of data that can be used for model validation and design evaluation as well as studying the modes of failure. Typical results of these tests are included in the report. In section 4, the development of a simplified analytical approach used to estimate the elasticplastic response of the panel/connection system is briefly described. Section 5 presents some finite element modelling results of the blast wall profile. Concluding comments are given in section 6.

2

2 BLAST WALL DESIGN

2.1 CORRUGATED PANELS AND CONNECTIONS USED OFFSHORE

Typical blast walls consist of stainless steel walls, about 12 m wide and 4 m high with corrugations running top to bottom; a schematic drawing is shown in Fig. 1. A blast wall on a modern topside installation is shown in Fig. 2. Blast walls are connected top and bottom to the primary steelwork by angles, and are normally free at the sides. The connections usually consist of two angles welded together and to the structural steelwork of the platform. A schematic of the connection detail (¼ scale) is shown in Fig. 3. This appears to be the most common form of blast wall system, although others exist such as the “post and panel” design shown in Fig. 4.

Blast walls are ‘rated’ to a certain pressure, that is they are designed by the manufacturer to resist a certain dynamic pressure (usually in the range of 1 to 4 bar) with some permanent deformation. There is no agreed, common basis for determining this rating or an acceptable deformation. In general, industry standard guidance notes [1] as issued by FABIG and the Steel Construction Institute (SCI) are used to design blast walls for fire and blast loading. Technical Note 5 [2] provides further detailed guidance on the design of stainless steel blast walls to resist explosion loading.

Figure 1: Typical blast wall construction made from corrugated stainless steel sheet with end connections top and bottom

2.2 TEST PANEL DESIGN

The test panels for this project were designed and manufactured by Mech-Tool Engineering Ltd. The same batch of 316 stainless steel material was used to make all the blast wall panels, the connection test specimens and the material test specimens. The blast wall design was based on a non-symmetric trapezoidal deep trough profile, angle connections top and bottom and free

3

sides. The profile dimensions are shown in Fig. 5 and given in Table 1. The dimensions of the end connections are shown in Fig. 6 and given in Table 1.

The blast wall was rated using the time-domain equivalent SDOF method and assumed to behave as a one-way span beam with cross-sectional properties of the deep trough profile. The properties are given in Table 2. End fixity was assumed to be pinned at both ends. The resistance of the beam to dynamic loading was due to inertia, elastic bending stiffness and plastic hinge formation at the mid-span of the beam. A strain-rate enhancement factor of 1.175 was used to specify the dynamic yield stress of the material. A pulse load of 950 mbar overpressure and load duration of 50 msec as shown in Fig. 7 was applied to the SDOF model and produced a maximum permanent displacement of 14 mm, considered acceptable. The blast panel was therefore ‘rated’ at 950 mbar for a triangular pulse load duration of 50 msec.

Figure 2: Rear (left photo) and front (right photo) views of a blast wall on a modern topside installation

Figure 3: Cross-section of the ¼ scale blast wall connection detail (side elevation view)

4

Figure 4: “Post and panel” blast wall design (courtesy of Mech-Tool Engineering Ltd)

220 220 220 220

880

15

40.52.0 thk

35 13585

Pressure Pressure

Figure 5: Deep trough profile dimensions (all bend radii 10 mm) of test panel

5

20 35

65

3 3

2 4 thk

3 thk

10 25

100 x 75 x 12 RSA

195, 255, 315

85, 145, 205

Figure 6: Connection details of test panel (side elevation view)

950

Pressure (mbar)

Time (msec)

25 50

Figure 7: ‘Design’ pulse pressure load

6

Table 1: Description of non-symmetric trapezoidal deep trough profile of test panel

Profile width 220.0 mm Profile depth from top surface to inside bottom surface 40.5 mm Corner internal bend radius 10.0 mm Base thickness of profile 2.0 mm Cross-section area of profile 512.0 mm2

Profile material density 7970.0 kg/m3

Profile weight per unit plan area 19.3 kg/m2

Table 2: Deep trough test panel properties

Mass of beam section / unit length 4.2 kg/m Second moment of area 13.5 cm4

Young’s modulus 200.0 MN/mm2

Moment of resistance 2.3 kNm Base yield stress 265.0 N/mm2

Design dynamic yield stress 311.4 N/mm2

Elastic stiffness 2.1 kN/mm Elastic-plastic stiffness 2.1 kN/mm Plastic resistance 18.6 kN Displacement to first yield 6.61 mm Displacement to full plasticity 8.81 mm Plastic displacement 14.07 mm Maximum displacement (occurs after 32 msec) 22.88 mm Ductility ratio 2.6 Natural elastic period 7.5 msec

7

3 EXPERIMENTAL INVESTIGATION

3.1 MATERIAL CHARACTERISATION

This section of the report describes the quasi-static and dynamic tensile tests performed on the materials used to manufacture the test panels and connections and presents the test results. All the panels were manufactured from the same batch of material, namely 2, 3 and 4 mm thick AISI 316L austenitic stainless steel sheet and with the same orientation. The corrugated plate was made from the 2 mm thick sheet material and the angle connections were made from the 3 and 4 mm thick sheet material. Tensile test specimens were taken from this same batch of material, half of the specimens with their major axis in the rolling (longitudinal) direction and half with their major axis perpendicular to the rolling (transverse) direction. These material tests were part of the wider experimental research programme to investigate the response of ¼ scale blast wall panels to pulse pressure loading.

3.1.1 Experimental Procedures

Static tests

All of the test specimens used for material characterisation had a rectangular cross-section and the geometry of the specimens is shown in Fig. 8. The nominal material properties, as supplied by the manufacturer, are given in Table 3. Non-uniform deformation after necking leads to an engineering strain that depends on the gauge length. A nominal gauge length of 60 mm was used for both the quasi-static and dynamic tensile tests.

Figure 8: Geometry of the tensile test specimens

The aim of the quasi-static tensile tests was to determine the static material properties of 316L stainless steel, namely

%� static yield stress, Sy, %� static ultimate tensile strength (UTS), Su and %� ductility in the form of percentage elongation.

A typical engineering stress-strain curve, obtained from these tests on stainless steel, is shown in Fig. 9. The static yield stress, UTS and ductility were measured during each test. Standard tensile test procedures were adhered to throughout and the tests were conducted using an INSTRON 4204 tensile test machine. A longitudinal extensometer was used to measure the strain during the elastic phase, and was subsequently removed to prevent damage to the instrument.

8

The head speed was set to 1 mm/min during the initial yield phase and 2 mm/min after the onset RI� SODVWLFLW\�� 7KHVH� WHVW� VSHHGV� JDYH� DQ� DYHUDJH� \LHOG� VWUDLQ� UDWH�� y, of 2.78 = 10-4 s-1 and an

-1DYHUDJH�SODVWLF�VWUDLQ�UDWH�� u, of 5.56 = 10-4 s . It should be noted that, in this work, the term ‘static’ relates to tests performed at the above rates of strain.

Table 3: Nominal material properties of 316L stainless steel, as supplied by the blast wall manufacturer (Mech-Tool Engineering Ltd)

1Young’s Modulus Static Yield Stress Dynamic Yield Stress Density

200 GPa 265 MPa 311.4 MPa 7970 kg m-3

1 At a strain rate of 0.422 sec-1

stre

ss (

MP

a)

Ultimate Tensile Stress 700

600

500

400

300

200

100

0

Yield Stress

0 0.1 0.2 0.3 0.4 0.5

strain

Figure 9: Typical engineering stress-strain curve for stainless steel (obtained from 2 mm thick tensile tests)

Dynamic tests

Dynamic tensile tests were performed to characterise the behaviour of the material at different strain rates and reveal any strain rate effects. Dynamic tests were conducted using an electroservo hydraulic (ESH) tension/compression test machine. The ESH test facility comprises three basic units: the main frame, the control panel and the power control unit. The load, displacement and strain were measured using a high frequency response piezoelectric load cell, in-built displacement transducers, an optical extensometer (Zimmer) and a pair of strain gauges. The experimental arrangement is shown in Fig. 10. A TRA 800 transient recorder, capable of a 25 MHz sampling frequency, captured the output signals from the sensors. The number of samples recorded per test was kept constant (15,000 data points per channel per test) and the

9

0.6

sampling frequency varied according to the speed of the test to ensure that a sensible quantity of data was recorded. The signals were processed using WinWave software and converted to EXCEL format for further analysis. Grooves were machined into the dynamic test specimens, and special clamps with mating grooves were used to grip the specimens during the tests, to prevent slippage.

The strain gauges were attached to the test specimens in pairs, one on each side of the specimen, one pair at the head and one pair within the gauge length of each specimen. Bending effects were eliminated by the paired configuration and an average strain reading from the two strain gauges was measured. During a dynamic test, the upper grip is rapidly accelerated to a pre-set ramp velocity before engaging the specimen. The head gauges were adhered to the bottom of the specimen to avoid registering an untrue large strain at the head due to the sudden movement of the upper grip. The location of the strain gauges is shown schematically in Fig. 11.

The specimen response was idealised as an initial acceleration period, during which the specimen yields, followed by a virtually constant velocity during the plastic phase until rupture occurs. The strain rate during yielding is lower than the strain rate at the ultimate tensile strength (UTS) and at rupture. The mean average strain rates associated with these two regions DUH�UHIHUUHG�WR�DV�WKH�\LHOG�VWUDLQ�UDWH�� y��DQG�WKH�RYHUDOO�VWUDLQ�UDWH�� u, respectively.

For low speed tensile tests, force is relatively straightforward to measure using a built-in load cell. In the dynamic case, however, this can prove difficult. At higher test speeds, the load cell signal contains strong fluctuations due to stress wave propagation effects and cannot be used. The scale for the head gauge is determined by keeping the amplifier gain constant throughout the tests. At low speeds, the load cell and head gauge signals can be compared and a load cell/gauge signal ratio was calculated. This factor was used to convert the head gauge signal for load determination in the higher speed tests.

As stainless steel tends to exhibit gradual yielding, the flow stresses at various plastic strains were calculated. Flow stresses were found at the following values of strain: e = 0.1%, 0.2%, 1%, 2%, 5%, 10% and 20%. The maximum value of tensile stress was also found from the test results referred to as the ultimate tensile strength or UTS.

Figure 10: Schematic of dynamic tensile test set-up using the ESH

10

Figure 11: Strain gauge positions on the dynamic tensile test specimens

3.1.2 Quasi-Static Test Results

The static tensile test results for each thickness, in the transverse and longitudinal directions, are summarised in Tables 4 and 5. Fig. 12 shows the engineering stress-strain curves for each quasi-static tensile test. The stainless steel yields gradually, with no clearly defined yield point. The main feature of the quasi-static tensile tests was the pronounced strain hardening effect, evident from the engineering stress-strain curves in Fig. 12. The plots show that, in all cases, the curves have a positive slope until necking occurs just before the point of fracture where the slope falls to zero. The 0.2 % proof stress is taken to be a measure of ‘yield stress’ to allow for consistent comparison between test results for different directions, thickness and strain rate.

11

Table 4: Material properties obtained from static tensile tests

Thickness (mm) [Direction1]

Yield Stress2

(MPa) UTS (MPa) Ductility3 (%)

Mean SD4 Mean SD4 Mean SD4

2 [L] 293.7 3.62 644.7 3.68 51.49 1.79

2 [T] 298.2 7.33 639.8 7.97 57.31 1.84

3 [L] 276.2 615.4 61.21

3 [T] 286.8 619.0 64.83

4 [L] 283.3 616.6 63.68

4 [T] 312.4 628.0 63.34

1 L = Longitudinal (direction of roll), T = transverse to direction of roll 2 Yield Stress defined as the 0.2% proof stress 3 Ductility measured as percentage elongation 4 SD stands for standard deviation from the mean

Table 5: True stress-strain results from selected static tensile tests for 2, 3 and 4 mm thick 316L stainless steel

Thickness (mm) Direction1 mr

(MPa) ¡r Et

(GPa)

2 L 1672 0.956 1.254

T 1695 0.987 1.250

3 L 1874 1.117 1.355

T 1866 1.122 1.340

4 L 2038 1.203 1.396

T 1880 1.102 1.343

1 L = Longitudinal (direction of roll), T = transverse to direction of roll

12

13

0

100

200

300

400

500

600

700

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Engineering Strain

Eng

inee

ring

Str

ess

(MPa

)

T1 T2 T3 T4T21S L21S L22S L1L2 L3 L4

(a) 2 mm thick material

0

100

200

300

400

500

600

700

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Engineering Strain

Eng

inee

ring

Str

ess

(MPa

)

L31 L32 L33 T32 T33

(b) 3 mm thick material

Figure 12: Engineering stress-strain curves obtained from quasi-static tensile tests.

(a) 2 mm (b) 3 mm (c) 4 mm thick 316L stainless steel.

14

0

100

200

300

400

500

600

700

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Engineering Strain

Eng

inee

ring

Str

ess

(MPa

)

L41S L42S L43S

T41S T42S T43S

(c) 4 mm thick material

Figure 12 (contd): Engineering stress-strain curves obtained from quasi-static tensile tests. (a) 2 mm (b) 3 mm (c) 4 mm thick 316L stainless steel.

3.1.3 Dynamic Test Results The results are summarised in Tables 6 to 8. Fig. 13 illustrates typical dynamic engineering stress-strain curves at various strain rates. Table 8 contains a summary of the results obtained by converting selected test results to true stress-strain, including a measure of the strain hardening behaviour.

Table 6: Dynamic characterisation - Cowper-Symonds coefficients at yield for 2, 3 and 4 mm thick 316L stainless steel

Nominal Thickness

(mm) Direction1

0.2 % Proof Stress (MPa) Cowper-Symonds

Coefficients

at e& nom = 0.422 s-1 2 Minimum Maximum Dy (sec-1) qy

2 L 353.2 306.0

(0.00379 s-1) 377.6

(2.86 s-1) 1522 5.13

2 T 358.7 309.1

(0.00148 s-1) 395.2

(5.89 s-1) 1887 5.27

3 L 326.8 286.4

(0.0039 s-1) 354.2

(4.57 s-1) 429 4.08

3 T 333.8 299.8

(0.00301 s-1) 356.6

(4.62 s-1) 1911 4.87

4 L 345.4 308.2

(0.0021 s-1) 370.5

(4.22 s-1) 2720 5.78

4 T 381.7 331.5

(0.0022 s-1) 407.7

(3.77 s-1) 809 5.02

1 L = Longitudinal (direction of roll), T = transverse to direction of roll 2 No test results exist at the e& = 0.422 s-1 strain rate; tabulated values are calculated from experimental results and the Cowper-Symonds equation.

18

2

Table 7: Dynamic characterisation - Cowper-Symonds coefficients at the UTS for 2 mm thick 316L stainless steel

Cowper-Symonds Nominal UTS (MPa) Coefficients

Thickness (mm)

Direction1

Max Variation from

static UTS Min

emin& 2 D (sec-1) q

2 L 689.6

(18.5 s-1) + 7.0 % -4.2 %

617.9 0.03 10.0 x 105 3 3.44 3

2 T 680.9

(19.7 s-1) + 6.4 % - 7.2 %

593.9 0.07 0.64 x 105 3 2.47 3

3 L 663.4

(55.5 s-1) +7.8 % -4.3 %

588.9 0.03 0.38 x 105 3 2.71 3

3 T 657.8

(18.6 s-1) + 6.3 % - 4.2 %

593.3 0.03 242.8 0.84 3

4 L 721.0

(18.8 s-1) + 17.76 % 670.5 0.21 894 x 106 3 9.98

4 T 728.7

(118 s-1) + 16.8 % -6.2 %

589.2 0.03 11 x 106 3 5.94 3

1 L = Longitudinal (direction of roll), T = transverse to direction of roll is the strain rate at which the minimum UTS is observed e&min

3 The calculated Du and qu, are in these cases, only valid for strain rates over 2 s-1

19

Table 8: True stress-strain results from selected dynamic tensile tests on 2, 3 and 4 mm thick 316L stainless steel

Thickness (mm) Direction1

e& (s-1)

mr

(MPa) ¡r Et

(GPa)

0.0293 1104 0.591 0.971

0.218 1085 0.553 0.971

2 L 2.02 1172 0.592 1.043

19.9 1221 0.619 1.063

49.0 1110 0.536 1.015

0.0289 1145 0.623 1.000

0.228 1233 0.681 1.050

2 T 1.99 1243 0.663 1.085

20.6 1202 0.597 1.079

49.9 1444 0.804 1.172

0.0295 1361 0.839 1.081

0.209 1401 0.833 1.121

3 L 1.96 1371 0.766 1.130

19.7 1403 0.759 1.174

55.5 1298 0.769 1.091

0.0292 1271 0.772 1.040

3 T 0.216 1377 0.834 1.108

2.02 1356 0.790 1.106

18.6 1379 0.744 1.159

0.0281 1466 0.774 1.176

4 L 0.217 1613 0.857 1.285

2.06 1483 0.770 1.220

18.5 1535 0.749 1.284

0.0274 1371 0.830 1.090

0.219 1561 0.827 1.240

4 T 1.92 1576 0.895 1.222

18.4 1620 0.795 1.325

118.34 1522 0.782 1.240

1 L = Longitudinal (direction of roll), T = transverse to direction of roll

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3.2 CONNECTION TESTS

Quasi-static tension/compression tests were performed on connection specimens with a view to characterising the connection behaviour independently of the full panel tests. The connection test specimens were manufactured from the same material used for the panels and to the same specification thus avoiding any additional material characterisation. The geometry of the connections was of the same type as the panels with a short, intermediate and long angle connection detail as shown in Fig. 14. This section describes the experimental arrangement and summarises the test data. The aim of these tests was to determine the parameters used to define the boundary conditions of the panels for use in the analytical model of the blast wall/connection system. The test data was also used to validate FE simulations of the connection tests.

Figure 14: Connection specimen types (left to right) Lflex = 60mm (short), 120mm (intermediate) and 180mm (long), respectively

3.2.1 Experimental Arrangement

A hydraulically operated tensile test machine with a maximum load capacity of 250 kN and a maximum speed of 500 mm s-1 was used to apply a load to the connection specimens in four directions as shown in Fig. 15. The test machine can apply a vertical tensile or compressive load, depending on its operation mode. To apply loads in other directions (relative to the specimen), it was necessary to orientate the specimen to achieve the required direction. A special jig for each direction was used to hold the specimens. All tests were performed at a crosshead speed of 5 mm/min.

Two pairs of gauges were attached to the specimens at the mid-point of the flexible angle on both sides of the specimen. The gauge pairs were used to record the surface strain at defined

21

points on the flexible angle that could be compared to finite element simulations. The gauge results would also give a measure of bending and axial strain at that point, giving insight into the type of deformation induced by the loading. The strain gauge outputs were individually captured, along with load and crosshead displacement, using a data logger and its dedicated software. The results were then converted to EXCEL format for post-processing. High-speed digital photography was also used to capture the motion of the connection relative to its original position.

In an operational situation, the connections used on actual blast walls continue the whole length of the wall. It was not practical to test such a wide specimen using the available facilities. The behaviour of the connection can be considered as a 2-D problem since the cross-section does not vary along the length of the blast wall. The blast wall panels tested in the pulse pressure loading rig were bolted to the rig via a so-called “rigid” angle. To simulate this fixing condition, symmetrical specimens with two 28 mm diameter boltholes were designed, 150 mm wide. These are shown schematically in Fig. 16. Thus, the connections were bolted to the mounting jig in the same way that the blast wall panels were fixed to the pulse pressure loading rig support plate.

Loads were applied along the ‘top’ edge of the plate angle, in four directions defined below and as shown in Fig. 15:

%� ‘A’ – Tensile loading ‘upwards’, stretching the connection and causing the angles to open out.

%� ‘B’ – Inward bending (relating the pulling-in of a blast wall panel due to axial shortening of the beam span).

%� ‘C’ – Outward bending, same plane of movement as ‘B’, but in the opposite direction1. %� ‘D’ – Compressive loading of the connection ‘downwards’, causing the angles to close up.

All dimensions of the connection details remained constant during the pulse pressure tests, except the “flexible” angle length, Lflex. Lflex is the length from the toe of the 125 = 75 = 12 “rigid” angle to the end of the “flexible” 3 mm thick angle and is defined in Fig. 17. Three lengths were used: Lflex = 60, 120 and 180 mm. All three “flexible” angle lengths were tested during the connection tests described in this section. The results of these tests are summarised in Table 9 and were used in conjunction with the connection model as described in section 4 to determine the spring constants used to define the end fixity in the analytical model of the blast wall/connection system.

1This type of movement would be unlikely to occur in an actual blast wall connection but the tests were performed for completeness.

22

A

CB

D

Deep trough profile section

Pressure load

Figure 15: Load directions in connection tests

23

Table 9: Summary of tests performed on the connection details

Max load b b

Bending Axial Bending Axial

C601 D 3.41 53.0

C602 D 2.93 50.9 - - - -

C603 D 2.66 49.5 41.7 3.76 0.24 - -

C604 A 107.5 50.8 39.2 - - -

C605 A 62.4 61.7 33.1 0.69 0.31 0.30 0.22

C606 B 2.17 97.8 87.2 - - - -

C607 B 8.40 49.4 45.6 - - - -

C608 B 12.45 55.1 50.4 0.63 0.40

C609 C 2.84 90.0 74.5 2.06 0.04 1.80 0.02

C610 C 3.23 80.3 73.9 - - - -

C1202 D 2.70 51.0 - - - -

C1203 D 2.45 51.6 0.62 0.03 - -

C1204 B 2.04 75.5 66.3 - - -

C1205 B 2.23 70.0 63.3 0.25 0.08

C1206 C 1.10 94.9 79.1 0.53 0.34

C1207 C 1.10 95.6 78.8 0.52 0.31

C1208 A 85.57 45.9 40.0 - - -

C1209 A 60.0 39.4 31.8 0.25 0.11 0.05 0.05

C1801 D 3.55 42.4 22.7 - - - -

C1802 D 3.52 44.8 24.2 0.68 0.00 0.43

C1803 B 0.86 95.5 77.2 - - -

C1804 B 0.95 95.4 74.0 0.21 0.01 0.05 0.00

C1805 C 0.98 151.9 128.6 0.29 0.02 0.09 0.01

C1806 C 0.61 95.0 64.2 - - - -

C1807 A 76.7 39.5 30.8 0.09 0.14 0.04

C1808 A 67.3 37.5 29.4 0.083 0.11 0.02

Max Strain (%) Perm Strain Test Ref.

Direction (kN)

max

(mm) perm

(mm)

-0.06 -0.06

Shor

t con

nect

ions

(L

flex

= 6

0 m

m)

-0.02 -0.02

-0.07 -0.07

-0.03 -0.03

Inte

rmed

iate

con

nect

ion

(Lfl

ex =

120

mm

)

-0.00

-0.01

Lon

g co

nnec

tion

(L

flex

= 1

80 m

m)

-0.01

24

Figure 16: Schematic of connection specimen design showing overall dimensions

Figure 17: Definition of the “flexible” arm length, Lflex

(side elevation view)

25

3.3 PANEL TESTS

This section describes the pulse pressure tests carried out on the three types of blast wall panels as shown in Fig. 18. The purpose of these tests was to gather data on the influence of the connection on the overall response of the panel, to identify the modes of failure of the panels and connections and to study the design parameters that affect blast wall performance. The data was also used to validate the modelling work later described in sections 4 and 5. A summary of the test results is given in Table 10.

915

255

AB915

195

915

315

Figure 18: Panel types (from left to right) short, intermediate and long angle connection (side elevation view)

3.3.1 Experimental Configuration

The panel tests were carried out on a pulse pressure test facility shown in Fig. 19 developed in the Impact Research Centre. This is a rig, which consists of a support plate and clamping frame sandwiched between two back-to-back pressure chambers. The chambers are designed to BS5500 and are suspended, along with the support plate, from a 3 tonne capacity mobile gantry. This is shown, in schematic form, in Fig. 20. Each chamber has a large flanged nozzle that is closed by either a solid end plate or a thin diaphragm. The support plate has an outside diameter of 1.760 m and is 70 mm thick. There is a 1.005 m square central aperture for mounting specimens.

Generally, test plates are clamped between the support plate and a 1.2 m square clamping frame by means of studs in the support plate. Pressure can be applied to an area of 1 m2. A reduction

26

plate can be used to reduce the aperture area from 1m2 to 0.25m2. A smaller clamp frame is used to hold the smaller test specimens in this case. Other fixing conditions can be used, allowing structures with a wide range of boundary conditions to be tested.

Figure 19: Photograph of the pulse pressure loading rig (PPLR)

1m0.5m

Lifting frame

Test plate

Support plate

Clamping frame

Pressure loading chambers

Diaphragm clamping rings

Diaphragm clamping rings

Figure 20: Schematic of the pulse pressure loading rig including the 0.5 m reduction plate

27

Static Mode

A solid end plate is bolted to the end flange of one chamber and the specimen is mounted to the support plate and held in place. The closed chamber is gradually pressurised whilst the other chamber is vented to atmosphere.

Dynamic Mode

Thin sheets of Melinex are used to seal both nozzles, making the two chambers airtight. A loop of fuse wire is attached to each of these diaphragms. When energised by an electrical current, the wire heats up and ruptures the diaphragm, accurately controlling the blow-down times of each chamber. The general test procedure is represented in Fig. 21 and is as follows:

%� The two pressure vessels are pressurised simultaneously, to a maximum of 4 bar overpressure, to ensure that no net load is applied to the specimen.

%� At t = t1, the diaphragm in one chamber is ruptured causing a differential pressure across the specimen.

%� At t = t2 (t2 – t1 is pre-defined), the second diaphragm is burst and the pressure is vented to atmosphere. The total load duration is equal to t = t3.

This procedure has been shown to generate uniform, repeatable and controllable pressure-time histories that are representative of the over-pressure loading developed in partially confined gas explosions.

Figure 21: Principle of dynamic operation of the PPLR

The dynamic pressure pulse generated by the timed blow-down of the two chambers is idealised to a triangular shape with the same impulse and peak pressure. An idealised triangular pressuretime history is shown in Fig. 22.

28

Figure 22: Idealised Triangular Pressure Pulse

3.3.2 Instrumentation

The response of the test specimens were measured using various sensors and equipment:

%� Endevco piezoresistive pressure transducers

%� RDP Linear Variation Differential Transducers (LVDT), power units and amplifiers

%� Fylde transducer amplifiers, with in-built bridge conditioning units

%� Tektronix differential amplifiers and bridge conditioning units

%� TLM YFLA-2 strain gauges

%� Multi pulse trigger-delay unit and trigger circuit box

%� Kontron TRA 800 transient recorders

Endevco 8515C-15 piezoresistive pressure transducers were used for measuring pressures up to 2 bar. For pressures above 2 bar, Endevco 8515C-50 piezoresistive pressure transducers were used. A maximum of three pressure transducers can be located on each side of the support plate.

The transducers are low mass miniature devices capable of measuring steady state and dynamic absolute pressures, with high sensitivity and a wide frequency response. To calibrate the transducers, the PPLR was incrementally pressurised and the pressure recorded by a hand held

29

pressure device. The pressure readings were compared to the voltage output from the pressure transducers. The output was checked for linearity and a calibration constant obtained in bar per volt.

The displacement of the test panel was measured using an ACT 4000C 200 mm stroke LVDT placed at the mid-span of the central corrugation. A small hole was drilled through the panel and a steel screw was used to attach the LVDT. When the deformation of the panel was likely to exceed the stroke of the LVDT, a nylon screw was used to fix the LVDT actuator to the panel.

The LVDT was supplied with its own power unit and dedicated amplifier. The amplifier gain can be adjusted to suit the deflection range being measured. To obtain accurate calibration factors for the LVDT unit, a CNC machine was used to provide a known displacement that is incremented over the stroke of the LVDT, whilst the LVDT output was measured using an oscilloscope. This process was repeated using different gain settings and zero positions.

The trigger-delay unit and firing circuit were used to control the timing of the pressure release in the pulse pressure tests. The firing mechanism was calibrated to account for any delay in the two relays. A TRA 800 transient recorder, capable of a 25 MHz sampling frequency, captured the output signals from the sensors; the signals were processed using WinWave software. Further analysis was necessary to obtain displacement, strain and pressure pulse shapes, so the raw data was converted to text format and input to Microsoft Excel software. To relate the pressure tests on the scaled blast walls to the connection characterisation tests described in section 3.2, a measurement that could be compared between both sets of tests was required.

Strain gauges were attached to most of the blast wall specimens, for comparison with the strain gauges attached to the connections tested using the Dartec tensile test machine. The three panel types had different flexible angle lengths. It was decided to position the gauges mid-way between the rigid angle weld and the corrugated angle weld. Strain gauges were attached at two positions along the mid-line of the flexible angle length, one pair along the plate centre-line and a pair 150 mm in from one edge. The gauges were attached to both sides of the panel on the bottom connection, and their positions are shown in Fig. 23. The strain values for each gauge were individually monitored.

Strain gauges were also attached at the mid-point of the central corrugation in some tests to gain insight into the deformation process, particularly in cases where use of the LVDT would may have led to damage of the transducer (because of the high displacements anticipated due to local buckling of the section). The combination of the gauge results from each pair gave a relative measure of axial strain (allowing for bending effects) and bending strain (allowing for axial effects). The strain gauges had four functions: (1) to provide a measure of the uniformity of deformation across the plate as the two connection gauge pairs should give similar values, (2) to act as an indicator of the strain rates involved during the blast wall tests, (3) to serve as a comparative measurement between connection tests and pulse pressure tests and (4) to provide insight into the local buckling failure anticipated at higher peak pressures.

30

915 1005 1105 hole 1205

Loading

= =

457.5

40 deep profile, 2.0 thk, 220 pitch, 316L st.st.

100 x 75 x 12 RSA

60 x 30 x 4, 316L st.st.

85 x 35 x 3, 316L st.st.

195, 255, 315

centres

direction

1 pair @ mid-width 1 pair @ 150mm from edge

Figure 23: Location of strain gauges on test panels (side elevation view)

31

3.3.3 Test Results on 195 mm Deep Panel

A Direction

Five tests were performed that could be described as elastic response tests resulting in no appreciable permanent deformation at pulse pressures of 0.51 to 1.04 bar. Loading and response data for the 0.91 bar test are given in Fig. 24.

Two tests were performed, at pulse pressures of 1.21 and 1.92 bar. The 1.21 bar test produced a small permanent central displacement of 4.0 mm in the panel and no connection movement or buckling of the corrugations were observed. The pressure-time history and permanent displacement profile are given in Fig. 25. A much larger permanent central displacement of 69 mm was recorded in the 1.92 bar test, and local buckling at the centre of the corrugations (the location of maximum bending moment) was observed. The pressure-time history and the permanent displacement profile are shown in Fig. 26. Photographs of the highly deformed panel, referred to as c622, are shown in Fig. 27.

B Direction

One elastic test was performed in the B direction with a pulse pressure of 0.47 bar. The recorded central displacement was only 2.5 mm. A test at 0.94 bar was performed, which resulted in a small permanent displacement measured by the displacement transducer. The pressure-time and displacement-time histories for the 0.94 bar test are given in Fig. 28, where it can be seen that a maximum transient displacement of 8.3 mm and a permanent displacement of 1 mm were recorded. This displacement is slightly greater than that recorded during the equivalent ‘A direction’ test at the same nominal pulse pressure (Fig. 25). An elastic limit of 7.3 mm in the B direction was estimated from Fig. 28.

A further three tests at higher pressure were performed, but only one of these resulted in the typical triangular pressure-time history that was representative of a gas explosion due to difficulties containing the pressure on one side of the panel once the panel deformation becomes too large. The test at a pulse pressure of 1.18 bar resulted in local buckling of the corrugations and a permanent central displacement of 283 mm. The pressure-time history and permanent displacement profile are shown in Fig. 29. The deformed panel can be seen in Fig. 30.

Discussion

The deformation of the panels in the B direction was substantially higher than that of the equivalent ‘A direction’ panel (283 mm compared with approximately 5 mm) as the ‘A direction’ panel at a pulse pressure of 1.2 bar did not buckle. The strain measurements from the gauges located on the connection were also significantly higher, with maximum bending strains of approximately 0.7% recorded during the tests in the B direction compared with strains of less than 0.1% in the A direction. This confirms the sensitivity of the blast wall panels to load direction and shows that they are more capable of resisting the load in the A direction due to the different buckling capacities of the corrugated profile in the two directions and the geometry of the connection. Additional resistance to deformation in the A direction was provided by the dishing mechanism in the tension flange, causing the profile of the blast wall panels to flatten. Buckling of the corrugated profile at the centre of the panel is initiated at a lower pressure in the B direction due to the non-symmetry of the profile about the plane of the panel. In the B direction, the connection geometry allows the flexible angle to fold back on itself thus offering less restraint and greater flexibility of the panel.

32

Pre

ssur

e (b

arg)

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

-0.1 0 10 20 30 40 50 60 70

Time (msec)

(a) pressure-time history

Cen

tral

Dis

plac

emen

t (m

m)

8

7

6

5

4

3

2

1

0

0 10 20 30 40 50 60 70 80

Time (msec) (b) displacement-time history

Figure 24: Transient test measurements for an elastic pressure test on a short angle type blast panel (A load direction)

33

80

1.4

1.2

1

0.8

0.6

0.4

0.2

0

Pre

ssur

e (b

arg)

-20 -10 0 10 20 30 40 50 60 70 -0.2 Time (msec)


0

1

2

3

4

5

6

Per

man

ent

Dis

plac

emen

t (m

m)

Central Corrugation

Corrrugation A (LHS)

Corrugation B (RHS)

Plate Centre

(Viewed From Chamber VII)

-400 -300 -200 -100 0 100 200 300 400

BOTTOM PART OF PLATE

Distance along corrugation (y-direction) TOP PART OF PLATE

(b) permanent displacement profile

Figure 25: Pressure-time history and permanent displacement profile for a short angle test panel subjected to a pressure pulse of 1.21 bar (A load direction)

34

80

2

1.8

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

Pre

ssur

e (b

arg)

-0.2 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12

Time (sec)


0

10

20

30

40

50

60

70

80

Per

man

ent

Dis

plac

emen

t (m

m) Central Corrugation


Corrugation B (RHS)

Plate Centre


-400 -300 -200 -100 0 100 200 300 400 BOTTOM PART TOP PART OF OF PLATE Distance along corrugation (y-direction) PLATE


Figure 26: Pressure-time history and permanent displacement profile for a short angle test panel subjected to a pressure pulse of 1.92 bar (A load direction)

35

(a) overall panel deformation

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(b) local buckling of the corrugations (c) connection deformation

Figure 27: Photos of deformed blast panel c622 subjected to a peak pressure pulse of 1.92 bar

36

1

0.8

0.6

0.4

0.2

0

-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06

-0.2 Time (sec)

Pre

ssur

e (b

arg)


Dis

plac

emen

t (m

m) 10

9

8

7

6

5

4

3

2

1

0

-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06

Time (sec)

(b) displacement-time history

Figure 28: Transient test measurements for a 0.94 bar pulse pressure test on a short angle type panel (B load direction)

37

0

1

0 20 40 60 80 100 120

Pre

ssur

e (b

arg)

-0.2

0.2

0.4

0.6

0.8

1.2

Time (msec)


0

50

100

150

200

250

300

Dis

plac

emen

t (m

m)

plate centre

-400 -300 -200 -100 0 100 200 300 400

BOTTOM PART Distance along Corrugation (mm)

TOP PART OF OF PLATE PLATE

(b) permanent displacement profile of the central corrugation

Figure 29: Pressure-time history and permanent displacement profile for a short angle type panel subjected to a pressure pulse of 1.18 bar (B load direction)

38

(a) overall panel deformation (side elevation)

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(b) local buckling (c) connection deformation

Figure 30: Photos of deformed test panel 60CORR1 subjected to a peak pressure of 1.18 bar (B load direction)

3.3.4 Test results on 255 mm Deep Panel

A Direction

Five elastic tests were performed in the A direction, two with a nominal pulse pressure of 0.5 bar and three with a nominal pulse pressure of 1.0 bar. Fig. 31 shows the typical pressure-time and displacement-time histories for a test with a pulse pressure of 1.06 bar and an approximate maximum displacement of 9.2 mm. The results of a test where the onset of plasticity occurred indicate that the elastic limit displacement of this panel in the A direction is 11 mm.

Higher test pressures resulted in much larger permanent deformations of the panels and local buckling of the corrugations as observed in the 195 mm deep panels. Fig. 32 shows the permanent displacement profile of a panel after a pulse pressure of 1.48 bar. The main features of the failed panel are captured in the photographs of Fig. 33. Fig. 32 shows that the maximum displacement of the panel was approximately 100 mm, with the three corrugations displaced uniformly, which can also be seen in the photograph of the deformed panel profile in Fig. 33a. The localised buckling of the corrugations at the panel centre is pictured in Fig. 33b. Fig. 33c

39

clearly displays the deformation of the connection detail, including the extending of the flexible angle and the plastic hinge formation along weld line. The plasticity of the connection appears to be more localised than in the shorter connection detail (195 mm deep panel). Dishing of the flange, and flattening of the deformed profiles in the central portion of the walls was evident during the post-test inspections, and increased in magnitude with increasing applied pressure.

B Direction

Four tests were performed in the B direction with pulse pressures of 0.52, 0.97, 1.26 and 1.30 bar. As in all the panel types, once local buckling of the panels occurred in the B direction it was very difficult to contain the pressure and hence peak pressures above 1.3 bar could not be achieved. The test at a pulse pressure of 0.52 bar resulted in an elastic response as shown in Fig. 34, which shows the pressure-time and displacement-time histories with a maximum displacement of 3.4 mm.

The test performed at 0.97 bar, referred to as c1211-7, produced a permanent displacement of approximately 2 mm at the panel centre. The transient displacement measurements are shown in Fig. 35 indicating a central displacement of 9.3 mm. An elastic limit of 7.3 mm was estimated in the B direction, which is consistent with the result for the small connection detail (shown in Fig. 28). Hence, the directionality of the elastic limit displacement (that is 11 mm in the A direction and 7.3 mm in the B direction) appears to be due to the asymmetry of the corrugated profile and is independent of connection geometry. The elastic limit pressure, however, is dependent on the connection geometry and will be lower as support restraint decreases (as is in the case with longer angles).

The tests with pulse pressures of about 1.3 bar had rise times of approximately 25 msec, but longer load durations of approximately 125 msec due to the difficulties of pressure containment. Fig. 36 shows a typical permanent displacement profile for test c1214. Test panel c1214 is pictured in Fig. 37. From the displacement profile in Fig. 36 and the photograph of the panel profile in Fig. 37a, it can be seen that the higher pulse pressures produce very large central displacements, 469 mm approximately. Localised buckling of the corrugations occurs at the panel centre, as shown in Fig. 37b. The connections fold back on themselves, rotating about the weld line and extending the flexible angle in the way shown in Fig. 37c. The connection deformation contributes about 220 mm of the total central permanent displacement of 469 mm, shown in Fig. 36. Thus the panel corrugations deformed around 249 mm, which is comparable to that of the displacement of the panel with the short angle at the same nominal pulse pressure loading allowing for the connection deformation.

40

-0.2 Time (sec)

Pre

ssur

e (b

arg)

1

0.8

0.6

0.4

0.2

0

-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08


0

1

2

3

4

5

6

7

8

9

10

Dis

plac

emen

t (m

m)

-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 Time (sec)


Figure 31: Transient test measurements for an elastic pressure test on an intermediate angle type panel (A load direction)

41

0

20

40

60

80

100

120

Per

man

ent

Dis

plac

emen

t (m

m)

Central Corrugation


Corrugation B (RHS)

Plate Centre

(Viewed From Chamber

-400 -300 -200 -100 0 100 200 300 400

BOTTOM PART TOP PART OF

OF PLATE Distance along corrugation (y-direction) PLATE

Figure 32: Permanent displacement profile for an intermediate angle type panel subjected to a pressure pulse of 1.48 bar (A load direction)

42

(a) overall panel deformation (side elevation view)

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Figure 33: Deformed blast panel c1212 (peak pressure = 1.48 bar)

43

0

0

-0.1

0.1

0.2

0.3

0.4

0.5

0.6

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Time (sec)

Pre

ssur

e (b

arg)

D

ispl

acem

ent

(mm

)


4

3.5

3

2.5

2

1.5

1

0.5

0

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

time (sec)


Figure 34: Transient measurements for an elastic pressure test on an intermediate angle type panel (B load direction)

44

0

1

2

3

4

5

6

7

8

9

10

Dis

plac

emen

t (m

m)

-0.04 -0.02 0 0.02 0.04 0.06 0.08 Time (sec)

Figure 35: Displacement-time history for a 0.97 bar pressure test on an intermediate angle type panel (B load direction)

0

100

200

300

400

500

Per

man

ent

Dis

plac

emen

t (m

m)

Central Corrugation


Corrugation B (RHS)

Plate Centre


-400 -300 -200 -100 0 100 200 300



Figure 36: Permanent displacement profile for an intermediate angle type panel subjected to a pressure pulse of 1.3 bar (B load direction)

45

400


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Figure 37: Deformation of blast panel c1213 subjected to a pressure pulse of 1.3 bar (B load direction)

46

3.3.5 Test Results on 315 mm Deep Panel

A Direction

Six tests were performed in the pulse pressure range 0.54 to 2.93 bar, two of which resulted in no permanent deformation of the panels. Fig. 38 shows the pressure-time and displacementtime histories for one of the elastic response tests, loaded to a pulse pressure of 0.99 bar and resulting in a maximum displacement of 9.4 mm. The strain gauges attached to the connection and the mid-point of the central corrugation recorded small strains of less than 0.1% in all cases.

Large permanent displacements were produced during the tests with higher pulse pressures. Fig. 39 shows the pressure-time history and permanent displacement profile of test c1803 with a pulse pressure of 1.37 bar and a maximum permanent displacement of 131 mm. The deformed panel is pictured in Fig. 40. Fig. 40a is a photograph of the blast wall profile showing equal deformation of the three corrugations, which is confirmed by the post-test measurements illustrated in Fig. 39. The post-buckling strengthening was again provided by the dishing of the tension flange and the flattening of the panel profile, as shown in Fig. 40.

B Direction

Three tests were performed in the B direction, one of which resulted in an elastic response of the panel at a pulse pressure of 0.47 bar. The displacement-time and pressure-time histories are given in Fig. 41 and show that the panel deformed to a maximum of 3.85 mm. The tests performed at higher pulse pressures resulted in large permanent deformation of the panels. Fig. 42 shows the pressure-time history and the permanently deformed profile for a test with a 1.0 bar pulse pressure. The test produced a maximum permanent central displacement of 144 mm, as illustrated in Fig. 42b. The post-test inspection revealed that the panel buckled in the centre as in previous B-direction tests.

Increasing the pulse pressure to 1.22 bar resulted in the complete folding back of the connections and a maximum permanent displacement of 602 mm at the panel centre. The permanent profiles of the corrugations are given in Fig. 43. The deformed panel is pictured in Fig. 44. From Figs. 43b and 44c, the connection was shown to rotate by 180° about the weld line and a second plastic hinge zone forms as the flexible angle extends due to the span of the corrugations getting smaller and the axial force pulling inwards.

47

-0.2 Time (sec)

Pre

ssur

e (b

arg)

1.2

1

0.8

0.6

0.4

0.2

0

-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08


0

1

2

3

4

5

6

7

8

9

10

Dis

plac

emen

t (m

m)

-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Time (sec)


Figure 38: Elastic response of a 0.99 bar pressure test on a long angle type panel (A load direction)

48

1.4

1.2

1

0.8

0.6

0.4

0.2

0

0.1

Pre

ssur

e (b

arg)

-0.04 -0.02 0 0.02 0.04 0.06 0.08 -0.2 Time (sec)


0

20

40

60

80

100

120

140

Per

man

ent

Dis

plac

emen

t (m

m)

Central Corrugation


Corrugation B (RHS)

Plate Centre


-400 -300 -200 -100 0 100 200 300 400 BOTTOM PART OF PLATE

Distance along corrugation (y-direction) TOP PART OF

PLATE


Figure 39: Pulse shape and deformed profile for a 1.37 bar test (C1803) on a long angle type panel (A load direction)

49

0.12


J JH�'LVKLQ �RI�WHQVLRQ�IODQ


Figure 40: Deformed blast panel C1803 subjected to a pressure pulse of 1.37 bar (A load direction)

50

0.6

0.5

0.4

0.3 D

ispl

acem

ent

(mm

)

0.2

0.1

0

-0.02 -0.01 0 0.01 0.03 0.04

-0.1 Time (sec)

0.02

Pre

ssur

e (b

arg)


5

4

3

2

1

0

-0.02 -0.01 0 0.01 0.02 0.03 0.04

-1 Time (sec)


Figure 41: Elastic response of a 0.47 bar test on a long angle type panel (B load direction)

51

1.2

1

0.8

0.6

0.4

0.2

0

( )

Pre

ssur

e (b

arg)

-0.2 Time sec

-0.04 -0.02 0 0.02 0.04 0.06 0.08


0

20

40

60

80

100

120

140

160

Per

man

ent

Dis

plac

emen

t (m

m)

Central Corrugation


Corrugation B (RHS)

Plate Centre

(Viewed From Chamber

-400 -300 -200 -100 0 100 200 300 400




Figure 42: Pulse shape and deformed profile for a 1.0 bar test (C1801-4) on a long angle type panel (B load direction)

52

0

100

200

300

400

500

600

700

Per

man

ent

Dis

plac

emen

t (m

m)

Central Corrugation


Corrugation B (RHS)

Plate Centre


movement of the connection

-400 -300 -200 -100 0 100 200 300 400 BOTTOM PART TOP PART

OF PLATE Distance along corrugation (y-direction) OF PLATE

Figure 43: Deformed profile of blast panel together with connection movement for test C1806 (pulse pressure of 1.22 bar in B direction)

53


)ODWWHQLQJ�RI� FURVV�VHFWLRQ�

*URVV�URWDWLRQ�RI� SODVWLF�KLQJHV�


Figure 44: Deformed blast panel C1806 (pulse pressure of 1.22 bar in B direction)

54

Table 10: Summary of pulse pressure tests on ¼ scale blast panels

Connection Type

Test Reference

Ppeak

(bar) tm

(msec) tdur

(msec) max

(mm) perm

(mm)

60 m

m F

lexi

ble

Len

gth

(Sho

rt A

ngle

Con

nect

ion)

PREBLA2 + 0.51 16.7 38.0 4.8 0

60CORR6 + 0.57 30.7 57.5 4.9 0

C621-1 + 0.76 25.9 63.0 7.5 0

60CORR6 + 0.91 21.7 59.1 7.5 0

PREBLA4 + 1.04 31.0 83.0 9.0 0

60CORR5 + 1.21 26.1 73.4 - 4.0

C622 + 1.92 59.7 125.7 - 69

60CORR1 - 0.47 23.0 44.0 2.5 0

GCORR2 - 0.94 29.7 59.5 8.3 1

60CORR1 - 1.18 30.8/41.2 78.9 - 283

G2BARC - 1.33 30.8 > 200 - 315

60CORR4 - 1.34 30.2 > 200 - 310

120

mm

Fle

xibl

e L

engt

h (I

nter

med

iate

Ang

le C

onne

ctio

n)

C1201 + 0.43 16.6 47.8 4.5 0

C1211-3 + 0.53 17.1 39.4 3.4 0

C1202 + 0.99 26.2 68.5 13.0 2.0

C1211-4 + 1.02 24.6/40.0 80.2 - 0

C1211-5 + 1.05 31.2 72.6 9.3 0

C1211-1 + 1.02 31.7 72.7 0

C1212 + 1.48 40.2 102.3 - 100

C1215 + 2.00 47.5 119.3 - 133

C1211-6 - 0.52 24.4 42.2 3.3 0

C1211-7 - 0.97 33.9 63.0 9.3 2.0

C1213 - 1.26 27.2 123.6 - 476

C1214-2 - 1.30 25.0 120 - 469/483

180

mm

Fle

xibl

e L

engt

h (L

ong

Ang

le C

onne

ctio

n)

C1801-1 + 0.54 19.1 42.5 4.7 0

C1801-3 + 0.99 26.1/36.7 77.3 9.4 0

C1803 + 1.37 34.3 97.1 - 131

C1804 + 1.81 44.8/57.0 118.3 - 153

C1805 + 2.39 47.9/67.1 133.8 - 155

C1807 + 2.93 63.2 > 200 - -

C1801-2 - 0.47 20.4 38.5 3.9 0

C1801-4 - 1.00 41.0 81.4 - 144

C1806 - 1.22 26.6/37.0 56.1 - 602

55

Discussion

The pulse pressure test results indicate that the blast walls have a lower elastic limit in the B direction. The tests with small and intermediate size connections gave a B-direction elastic limit of 7.3 mm (estimated from Figs. 28 and 35) whilst the results indicate an elastic limit of 11 mm in the A direction. The directionality of the elastic limit displacement is due to the asymmetry of the corrugated profile and appears independent of connection type (the connections do not move while the corrugations deform elastically). The ‘yield pressure’, defined here as the pressure at which inelastic strains at the mid-point of the central corrugation occur or the pressure at which permanent displacement is produced in the panel (also at the panel centre as this is the point of maximum applied bending moment) varies with both load direction and connection type employed. The ‘yield pressure’ is lower in the B load direction and is also reduced by increasing the blast wall flexibility, i.e. by increasing the flexible angle length. As support restraint decreases (i.e. Lflex increases) the connections move inwards more easily and larger displacements are induced at the panel centre for a given pressure. Thus lower ‘yield’ pressures were recorded for longer connection details.

3.3.6 Failure Modes

A Direction

The progressive stages of failure of the blast walls in the A load direction are given below. The stage of failure attained by the blast wall depends on the pulse pressure and load duration as well as the connection type. The pressures required to progress failure were lower for the blast wall panels with longer angle connections. The same failure progression was observed in all the panels loaded in the A direction regardless of connection length. These observations were based on the transient displacement and post-test deformation measurements as well as the finite element models.

%� Elastic response

%� First plastic hinge formation at angle connection

%� Yielding of the corrugations

%� Localised buckling of the corrugations, in the bottom flange and web

%� Dishing of tension flange and flattening of corrugated profile, resisting large deformation of the panel

%� Stretching and rotation of the connections

56

B Direction

As in the A load direction tests, the same failure progression was observed for all types of connection detail as given below. Failure of the panels occurred at a lower pulse pressure for the panel types with longer angle connections.

%� Elastic response

%� First plastic hinge formation at angle connection

%� First yielding (flexural mode) in the corrugations

%� Buckling of the corrugation accompanied by large deformation of the panel as a whole

%� Collapse of the cross section, flattening of the cross-section at the centre of the panel

%� Large rotation of the angle connection

57

4 ANALYTICAL MODELLING

This section presents a proposed analytical model for predicting the elastic-perfectly plastic response of beams with different structural geometries and end conditions, which are subjected to varying pulse pressure loads. The analysis includes membrane forces and flexible boundary conditions. The main model examines the mode I response (large inelastic deformation) of the beam. This scheme can be used as a general tool for predicting the response of any beam of known cross-section and support conditions subjected to dynamic uniformly distributed loading.

4.1 BEAM MODEL

The main objective of this approximate method of analysis is to estimate the maximum transient displacement and final (permanent) displacement of a beam subjected to uniformly distributed dynamic loading. These two parameters are therefore the principal outputs of the analytical model. Damping is not included in the model and the permanent displacement is taken to be the mean of the residual elastic vibration.

Beams and springs are used to construct the model geometry so that all possible types of beam response to a transverse pressure pulse can be modelled, including the possibility of finite deformations. A list of assumptions is produced and the limits of the model applicability are outlined. This step is critical for assessing the validity of any results obtained. Mode shapes that represent the beam behaviour are carefully selected and checked to ensure that they satisfy the static model boundary conditions and the kinematics of the problem.

The energies of the system (strain energy, kinetic energy, work done by the loading, etc.) are calculated. Lagrange’s equation is formulated using the energy terms and equilibrium equations are generated. The equilibrium equations are solved numerically, in this case using Matlab software (FORTRAN has been used previously by Hsu [5] for similar work). The model outputs the maximum transient displacement, the final displacement and the displacement-time history for the beam at the mid-span.

4.1.1 Idealised Model

For loading of high magnitude, the stresses induced in a structure rise to levels sufficient to cause yielding, which is plastic flow in one or more regions of the structure. Menkes and Opat [6] were the first to define blast load induced failure modes as a result of experiments on impulsively loaded clamped aluminium beams: mode I – large inelastic deformation, mode II – tensile tearing at the support and mode III – transverse shear failure. It was observed that in some circumstances the plastic flow might localise and lead to failure by tensile tearing or shearing. Others have observed the same failure modes when studying the behaviour of flat plates [7, 8].

The proposed model examines only mode I type failures; the beam acquires a permanently deformed profile with maximum displacements being finite but moderate compared to the span of the beam. The beam is initially assumed to exhibit ductile behaviour throughout its response and not to shear or tear. Plastic deformation is assumed to occur in plastic hinges at points rather than in finite zones, as would be the case in reality. Plastic hinge progression, a localised response, is ignored. Springs are introduced to model the rotation at the plastic hinges and the in-plane axial restraint.

58

Due to the symmetry of the loading and the geometry of the model, only half the actual beam is modelled; therefore the model requires only one beam element and four spring elements as shown in Fig. 45, with the beam and springs connected as a continuous system. The total deformation of the beam consists of separate stages each with its own characteristic mode shape.

The three support springs are assumed to be elastic-perfectly plastic. The horizontal support spring has a bi-linear force-displacement function and is used to model the membrane resistance that becomes significant as displacement increases. The stiffness of the support spring, Kx, imposes axial restraint on the beam. Plastic membrane deformation is allowed at any stage of the response (when the axial force reaches the maximum resistance of the horizontal spring). The vertical spring also has a bi-linear force-displacement relation, and has a stiffness Ky, and is used to model the rigid body motion of the beam.

The rotation at the supports during elastic flexural deformation is dependent on the stiffness of the rotational spring, K q . For high values of rotational stiffness, fixed end conditions are

simulated and for low values of K , simply supported end conditions are simulated. The q

rotational support spring has a bi-linear moment-rotation relation. The other rotational spring is a rigid-perfectly plastic spring and is used to model the formation of a plastic hinge at the centre of the actual beam. The fully plastic bending moment of the two rotational springs is equal to the fully plastic bending moment of the beam.

The assumptions of the model are:

%� The beam is idealised as a one-dimensional structure.

%� The beam itself remains elastic throughout the response.

%� The deflections are finite but moderate compared with the beam span.

%� Hinges form at discrete points rather than finite regions and are assumed stationary.

%� Rotational springs at the supports are elastic-perfectly plastic.

%� The hinge at the beam centre is rigid-perfectly plastic.

%� The in-plane resistance of the beam is elastic-perfectly plastic and is modelled by horizontal translation springs at the supports.

%� Damping is neglected and the permanent displacement is taken to be the mean of the elastic residual vibration.

59

Figure 45: Idealised representation of the beam model (one-half symmetry)

4.1.2 Assumed Mode Shapes Method

The displacement for an n degree-of-freedom (DOF) model of a continuous system is approximated by

n

t x w ( ) , �-q i x t) ( C ) ( (1)i �i 1

where Ci (t ) = the generalised displacement of the system and qi (x ) = any admissible function expected to be similar to the deforming structure.

Different shape functions are used to represent the different phases of the beam’s response. Hence, the total deformation is then the combined deformation of the various stages. The choice of qi (x ) defines the model. The simple shape functions must satisfy static boundary conditions and the kinematics of the system. The function must form a linearly independent set of equations and possess derivatives up to the order appearing in the kinetic energy term.

In this case, the mode shapes must satisfy the kinematics and static boundary conditions of the displaced form of a beam, total length 2L, with partially fixed (or semi-rigid) ends in elastic flexural mode together with elastic or plastic membrane deformation. It must also model the formation of plastic hinges at the centre of the beam, and also at the beam supports.

A suitable shape function that fulfills these conditions is

tC 1 ) ( £ /x

L ²¤

cos ) ( £ /

t ¥ ¥

3 £² ¤ 1 ) ( t <

¥� � x

L

x C4 ) ( t (2) ²

¤ ³� 1 cos C2 C´

¦´¦

´¦

w � µ�2 2 L

It can be seen that the shape function consists of four parts, which represent different responses:

³�

tC 1 ) ( 1

¥� �(a) is the fundamental mode shape of a fully clamped beam ´

¦ ²¤

£ /x cos µ

�2 L

60

(b) C2 cos ) ( £ /x

t ²¤

¥´ ¦

is the fundamental mode shape of a simply supported beam 2L

(c) tC3 1 ) ( £² ¤ <

x

L¥´ ¦

represents the deformation when plastic hinges have formed at the centre

and at the supports

(d) C4 represents rigid body motion of the beam

There are four stages of response, each with different active velocity fields. These are shown in Fig. 46.

The results of the connection tests described in section 3.2 will be used to define the spring stiffnesses for the beam model. It will then be possible to compare the results of the panel tests described in section 3.3 with the beam model predictions of the panel responses for each type of panel. The SDOF model described in section 2 is incapable of predicting the panel response beyond collapse of the profile section, as it does not include the influence of large displacements or end effects.

61

t t & tStage I: w& I �

C& 1 ) ( ³� 1 cos

¤²£ /

L

x

¦´¥

�µ� C& 2 cos ) (

£² / x ´¥ C4 ) (

2 � ¤ 2L ¦

x x x

+ +

2L

1C&

2L 2L

x ¥Stage IIA: w& IIA �C& 2 cos ) (

£² / x ´¥ C3 1 ) ( < ´ C& 4 ) ( t & t ²

£ t

¤ 2L ¦ ¤ L ¦

+ +

2L

x

2L

x

3C&

2L

x

Stage IIB: w& IIB � C& 3 1 ) ( < x ´¥ C4 ) ( t ²

£ & t ¤ L ¦

2L

+

x

3C&

2L

x

4C&

Stage III: w& III � C& 3 1 ) ( < x ´¥ C4 ) ( t ²

£ & t ¤ L ¦

+

2L

x

4C&

2L

x

3C&

Figure 46: Velocity profiles for the beam model during each stage of response

62

4.2 CONNECTION MODEL

The pulse pressure tests have shown that the connections tend to form plastic hinge zones at two locations, namely (1) the rigid angle/flexible angle interface and (2) the flexible angle itself. The analytical approach described in section 4.1 in its current form is not able to model two plastic hinges at one support and hence a simplified approach is required that allows one of the hinges to be modelled using a rotational spring and the other using a translation spring.

The contributions of each spring to the response of the connection are as follows:

The rotational spring models the rotation of the plastic hinge at the flexible angle (the opening or closing of the angle). The angle, q, is defined in Figs. 47 and 48 for the two load directions, A and B, respectively.

The vertical translation spring (in the ‘y’ direction) models the stretching or compression of the flexible arm and will therefore have a high stiffness; the vertical movement of the wall due to change in geometry is added to the central displacement of the wall afterwards as this does not contribute to the strain energy absorbed by the connection. The stretching, 6 y, is defined in Fig. 47 for the A load direction.

The horizontal translation spring (in the ‘x’ direction) models the movement of the flexible arm due to plastic hinge rotation at the rigid angle interface, in a similar way to the displacement of a cantilever beam. 6 x is defined in Figs. 47 (A blast load direction) and 48 (B blast load direction).

From the connection test work (section 3.2), it can be seen that the behaviour of the connection, as part of the blast wall, during the A blast load direction tests can be represented by connection tests in the ‘V’ and ‘H’ directions as shown in Fig. 47. The behaviour of the connection in the B blast load direction can be represented, approximately, by connection tests in the ‘V’ and ‘H’ directions as shown in Fig. 48. The results from these tests, accompanied by the numerical analysis of the experiments, will be used to determine the spring constants, namely Kq , Kx, Ky,

M p , Rmx and Rmy for input to the beam model described in section 4.1. q

63

(a) Test direction ‘V’ (b) Test direction ‘H’

Figure 47: Idealisation of the connection response corresponding to the A blast load direction (showing definitions of 6x, 6y and q��

�

(a) Test direction ‘V’ (b) Test direction ‘H’

Figure 48: Idealisation of the connection response for directions corresponding to the B blast load direction (showing definitions of 6x, 6y and q�

64

5 NUMERICAL MODELLING

This section presents a numerical model employed to predict the failure of a 195 mm deep blast wall panel, subjected to pulse pressure loads varying from 0.5 to 1.92 bar, incorporating the end connection detail as part of the structure analysed. The commercially available finite element (FE) software, ABAQUS/Standard version 6.2, was used to perform the simulations.

5.1 FINITE ELEMENT MODEL

10

Fig. 49 is an illustration of the blast wall geometry, fully meshed and restrained, used by ABAQUS/Standard to simulate its response to pulse pressure loading. One half of a corrugation is modelled, due to symmetry of the blast wall panel profile, with connections at each end. The profiled panel is modelled using S4R shell elements and the connections are modelled using C3D8R solid elements. The mesh was refined in the centre of the panel to allow the mode of buckling to be represented accurately. Static stress analyses were performed, and due to the anticipated unstable nature of the buckling process, a small damping factor (equivalent to 2 x

-4 of the change in strain energy during the step) was applied to the model using the ‘stabilize’ parameter [9]. The connections were fully clamped along the bottom face (as indicated in Fig. 49) and the two edges of the strip were restrained from translating in the ‘z-direction’ (as shown in Fig. 49). The pulse loads were applied as uniformly distributed loads to the corrugated panel, and its time varying nature defined using tables based on experimental measurements. Runtimes for the final FE models were of the order of a few hours. To run the same model geometry (with the same level of mesh refinement) using ABAQUS explicit code would have taken a few weeks because of the relatively long load durations involved.

5.2 MODELLING PREDICTIONS – 195 MM DEEP BLAST WALL PANEL

The FE model predicted a maximum permanent displacement of 72 mm at the mid-span position for the test c622 with a pulse pressure of 1.92 bar. This compares with a corresponding experimental result of 69 mm. Fig. 50 shows displacement and stress (in the direction along the corrugation) contour plots after loading; the buckling behaviour is clearly visible in Fig. 51, which contains a close-up view of the deformed profile and the connection. One advantage of FE modelling is that it can often demonstrate the failure process in more detail than that which can be observed experimentally. For example, Fig. 52 shows that the flexible angle in the connection detail yields partway through its thickness before the corrugated panel yields at the centre, providing additional information on the failure progression of the panel. This means that the so-called ‘elastic’ pressure tests discussed in section 3 may have suffered some unobserved yielding at the connection angle.

65

Figure 49: Finite element model of a single corrugation and end connections

66

(a) Permanent transverse displacement (U2)

Buckle formation

(b) Stress S11 - along the corrugation (ranging from –600 MPa to 450 MPa)

Figure 50: FE predictions of permanent displacement and stress distribution

67

(a) Movement of the connections (b) Buckling at the panel centre

Figure 51: Enhanced views of the connection movement and profile buckling

Flexible angle

Flexible length / rigid angle interface

Figure 52: Yielding of the connection angle (t = 35 msec, applied pressure = 1.1 bar approx.)

68

6 CONCLUDING COMMENTS

%� An extensive programme of experimental work has been carried out on ¼ scale stainless steel blast wall panels with connections subjected to pulse pressure loading to determine their various modes of failure and blast resistance beyond the design limit. The panel design was based on the deep trough trapezoidal profile with welded angle connections top and bottom and free sides. The panels were approximately 880 mm wide by 1000 mm high. The profile depth was 40 mm and the overall depth of the panels including end connections was 195, 255 and 315 mm. The work has shown that the connection detail can significantly influence the response of the panel to pulse pressure loading. While the blast panels could withstand pulse pressures well in excess of the ‘rated’ design limit, the panels responded with large permanent plastic deformations up to 602 mm (ductility ratio 82.5 approximately) without rupture. The end restraint was a principal factor in the response of the panel. Consequently, the experimental work focused on the connection detail. Independent connection tests were used to characterise the support conditions for analytical modelling. The large database of experimental results can be used to develop pressureimpulse damage curves and more appropriate methods of assessment.

%� A comprehensive materials testing programme was carried out to characterise the material properties of the 316L stainless steel test specimens at strain rates ranging from 2.78 = 10-4

-1s (quasi-static) to 118 s-1. The data was used directly in the finite element numerical modelling work.

%� The performance of the ¼ scale panels was fully investigated using a pulse pressure test facility to generate pulse pressure loading in the range 0.5 – 3 bar peak pulse pressure (38 – 200+ msec load duration). Three types of panels were tested to compare the influence of the flexible angle length (60, 120, and 180 mm) on the overall performance of the panel/connection system. In general, the flexibility of the end connection and thus the panel increases as the angle length increases. This was observed in the yield pressure, defined as the pressure at which plastic strains at the mid-span of the panel occur or the pressure at which permanent displacement is produced in the panel. As support restraint decreases (flexible angle length increases) the connections bend more easily and larger displacements are produced in the panel for a given test pressure. For very large displacements, the panels adopt a membrane type mode in which high in-plane forces can be induced in the supports and consequently transferred to the primary framework with the risk of causing permanent damage to the framework. This will occur more readily with shorter angle connections. Thus it is important to optimise the design of the blast panel to absorb as much energy in bending and stretching and at the same time limit displacements that could affect other equipment and processes. The buckling capacity of the deep trough profile section is affected by loading direction. Thus tests were carried out in both transverse-loading directions. In the ‘design’ direction (A) the panels exhibited high postbuckling strength and deformation resistance due to the dishing of the flange in tension and subsequent flattening of the profile. It was found that, due to the non-symmetry of the profile about the plane of the panel, buckling of the section was initiated at a lower pressure in the opposite direction. In this direction (B), the connection geometry allows the flexible angle to fold back on itself thus offering less restraint and greater flexibility of the panel. No post-buckling strengthening mechanisms were observed in the B-direction tests.

%� The tests offered a unique opportunity to observe progressive failure of the panels at different pulse pressure loads in both the directions discussed in the previous statements. This data was used to refine the finite element numerical models of the panel/connection system. The ultimate strength of the panel, that is rupture, was never achieved although the panel tests produced deformations well beyond the ‘rated’ design capacity of the panel.

69

The design capacity of the panel was based on a simple bending mode of deformation and simple supports with no account for end restraint and large deformations. Consequently, the actual strength of the panel is substantially higher that the ‘rated’ design capacity. Thus, future design of blast walls should consider a more appropriate assessment of the panel’s resistance taking into account end restraint, connection flexibility and stretching modes of deformation as well as bending modes.

%� A simplified analytical model of the blast panel with connection detail was produced to enable a more appropriate assessment of the panel’s resistance to blast loading. This takes into account end effects and large deformations. The approach is based on the assumedmodes method of analysis of an elastic-perfectly plastic beam with springs for the supports subjected to dynamic pressure loading. The analysis includes membrane forces and flexible boundary conditions. This approach, which is more sophisticated than the SDOF equivalent spring-mass model, can be used as a general design tool for predicting the response of any beam of known cross-section and support conditions subjected to dynamic uniformly distributed loading.

%� Finite element numerical modelling work has been carried out to predict the response of the panel together with the connection detail. Good agreement has been achieved in both predicting the failure modes and the permanent displacements.

70

ACKNOWLEDGEMENTS

The authors wish to acknowledge the following sponsors of this work for their support:

%� Engineering and Physical Sciences Research Council

%� Mobil North Sea Ltd

%� Mech-Tool Engineering Ltd

%� Health and Safety Executive

71

REFERENCES

1. ‘Interim Guidance Notes for the Design and Protection of Topside Structures Against Explosion and Fire’, SCI-P-122, Steel Construction Institute, 1991.

2. ‘Design Guide for Stainless Steel Blast Walls’, Fire and Blast Information Group Technical Note 5, Steel Construction Institute, 1999.

3. Hsu S.S., White M.D., Schleyer G.K. and Birch R.S., ‘Pulse pressure loading of clamped mild steel plates’, Int. J. Impact Engng (in press).

4. Louca, L.A. and Pan, Y., ‘Effect of boundary conditions on performance of corrugated panels to blast loading’, Proc. 7th Int. Offshore and Polar Engng Conf, pp. 226-231, Honolulu, USA, 25-30 May, 1997.

5. Hsu S.S., ‘Response of stiffened and unstiffened mild steel plates to blast loading’, PhD Thesis, Department of Engineering, University of Liverpool, UK, 1999.

6. Menkes S.B. and Opat H.J., ‘Tearing and shear failures in explosively loaded broken beams’, Experimental Mechanics, 13, pp. 480-486, 1973.

7. Nurick G.N. and Shave G.C., ‘The deformation and tearing of thin square plates subjected to impulsive loads - an experimental study’, Int. J. Impact Engng, 18, pp. 99-116, 1996.

8. Langdon G.S. and Schleyer G.K., ‘Deformation and failure of clamped aluminium plates under pulse pressure loading’, (submitted for publication in IJIE).

9. ‘Abaqus/Standard Version 6.2 User Manual’, Hibbitt, Karlsson & Sorenson (UK) Ltd.

72

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Printed and published by the Health and Safety Executive C1.10 09/03

ISBN 0-7176-2706-3

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