transport and road research laboratory · test on the centre diaphragm, it was necessary to extend...
TRANSCRIPT
TRANSPORT and ROAD RESEARCH LABORATORY
Department of the Environment Department of Transport
TRRL LABORATORY REPORT 824
LOADING TESTS ON THE STIFFENED DIAPHRAGMS OF A TRAPEZOIDAL STEEL BOX GIRDER
by
C A K Irwin and J A Loe
Any views expressed in this Report are not necessarily those of the Department of the Environment or of the Department of Transport
Bridge Design Division Structures Department
Transport and Road Research Laboratory Crowthorne, Berkshire
1978 ISSN 0305--1293
Ownership of the Transport Research Laboratory was transferred from the Department of Transport to a subsidiary of the Transport Research Foundation on ! st April 1996.
This report has been reproduced by permission of the Controller of HMSO. Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.
CONTENTS
Abstract
1. Introduction
2. The model box
3. Loading arrangements
4. Instrumentation
5. Test procedure
6.
.
8.
Behaviour of the diaphragms under load
6.1 Introductory comments
6.2 Results of the loading tests: stresses and forces
6.2.1 Initial stages of loading
6.2.2 Shear flow from the webs
6.2.3 Stress flow in the diaphragms
6.2.4 Force flows from the stiffeners
6.3 Results of the loading tests: yield, buckling and collapse
6.3.1 End diaphragm 1
6.3.2 End diaphragm 2
6.3.3 Centre diaphragm
Comparison between experimental and analytical results
Discussion
8.1 Elastic behaviour
8.2 Transverse stiffeners and shear redistribution
8.3 Deformation and collapse
Conclusions
Acknowledgements
.
10.
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12.
13.
14.
15.
References
Appendix 1 : Materials
12.1 Yield stresses
12.2 Plate thickness
12.3 Lamination defects
Appendix 2: Fabrication of the model SBG
Appendix 3: Results of residual strain and imperfection measurements
Appendix 4: Instrumentation
15.1 Data logging system
15.1.1 Strain measurements
15.1.2 Displacement measurements
15.1.3 Load measurements
15.2 Other instrumentation
15.2.1
15.2.2
15.2.3
15.2.4
Closed-circuit television (CCTV)
Residual strain measurements
Initial imperfections and final distortions
Lamination inspection
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© CROWN COPYRIGHT 1978 Extracts from the text may be reproduced, except for
commercial purposes, provided the source is acknowledged
LOADING TESTS ON THE STIFFENED OIAPHRAGI~/tS OF A TRAPEZOIDAL STEEL BOX GIRDER
ABSTRACT
A large model trapezoidal steel box girder containing three stiffened diaphragms was tested in the Laboratory as part of the 'Merrison' programme of research. The diaphragms contained differing amounts of transverse stiffening. Each diaphragm region was tested separately and strains, deflections and modes of collapse recorded. The details of fabrication, initial measurements and test procedures are described and the behaviour of the diaphragm regions discussed. The elastic stresses are compared with the results of finite element analyses and the collapse loads with panel and stiffener strengths calculated using Part 3 of the 'Merrison' Interim Design and Workmanship Rules.
1. INTRODUCTION
This report describes loading tests on stiffened diaphragms in a large model steel box girder of trapezoidal
section. The tests were Carried out as part of the programme of research for the Committee of Investigation
into the Design and Erection of Steel Box Girder Bridges (the "Merrison Committee") and the design of
the box is based on the Committee's requirements.
The aim of the tests was to obtain a better understanding of the behaviour of stiffened diaphragms
in a trapezoidal box, to obtain quantitative data on the distribution of stresses, to determine the pattern
of buckling and areas of yield, and to determine the maximum sustained load and the mode of collapse.
A brief description of the tests has been given by Dowling, Loe and Dean 1 .
Tests were made on diaphragms at the centre and at each end of the model box. It was required that
all the principal details of design should be reproduced in the model and that the residual stresses due to
welding should be similar to those in an actual structure. These requirements necessitated the use of a
box having widths of 3.66 metres at top, 1.22 metres at bottom, a depth of 1.22 metres and a length of
9.30 metres. The model was fabricated by specialist model-makers.
About 500 channels of instrumentation were provided on each of the diaphragms and adjacent areas
of web and flange to provide information on strains and deflections occurring under load. Residual strains,
initial imperfections and profiles of the deformed box after loading were measured by manual metliods.
To conform with the investigations into steel box girders then being made, the model was designed
and fabricated to British (inch-pound-second) units of measurement, converted to SI (metric) units in the
• report.
2. THE MODEL BOX
The model box was designed by Dr J G M Wood of Messrs Flint and Neill and details are shown in
Figures 1 and 2. The design aimed at a diaphragm which was slightly weaker than the adjacent webs and
flanges so that failure of the diaphragm would lead to the collapse of the box. The box was fabricated from
high yield structural steel complying with grade 50B of BS 4360. The main features of the stiffened
diaphragm were a thicker plate for the lower part of the diaphragm, a one-sided load-bearing stiffener and
double-sided stub stiffeners over each bearing, and one-sided horizontal and intermediate vertical
stiffeners to form panels of suitable sizes. The stiffening of the webs and flanges included some fairly
heavy transverse stiffeners forming frames within the box. Steel frames were provided mid-way between
the centre and end diaphragms to provide reaction points when loading the end diaphragms in shear.
Tests to determine yield stress were made on samples of the steel plate and stiffeners used in the
model and the results are reported in Appendix 1.
The fabrication of the box was based on procedures which would be used on an actual bridge
structure and details are given in Appendix 2.
Manual welding was used. The imperfections resulting from fabrication (Appendix 3) were considerably less than the tolerance allowed by the current design rules 2.
3. LOADING ARRANGEMENTS
The loading tests were carried out in rigs formed from standard loading frames bolted to the strong floor
of the Structures Laboratory at TRRL. The arrangements of the loading points are shown in Figure 2.
The test rigs allowed reactions of up to 4000 kN to be transmitted from the strong floor to the box.
The beatings under the test diaphragm and the hydraulic jacks used to apply the load were supported on load spreading grillages (Plate 1).
The end diaphragms were loaded by jacks situated at the opposite end of the box from that under
test. Because the dimensions of the rig were such that the load at the jacks was only one third of that at
the test diaphragm, the load could be applied through the end diaphragm yet to be tested without risk of
damage. After the first test had been completed, the box was turned around and the collapsed diaphragm
strengthened by additional stiffeners before being used to transmit the load in the second test. For the
test on the centre diaphragm, it was necessary to extend the box by triangular frameworks to a length of
12.2 metres in order to provide moment and shear in the required proportions.
The bearings consisted of a pair of rockers and a layer of polytetrafluoroethylene (PTFE). Their
axes were in transverse and longitudinal directions and their centre of curvature immediately under the
bottom of the diaphragm. This arrangement was used to minimize the restraints on the box. Eccentric
(out of plane) loading of the diaphragm was reduced by careful alignment of the centre of the beating
with the plane of the diaphragm. For the end diaphragms a rocker-beam beating was used to equalise
loads through the two bearings. For the centre diaphragm this was unnecessary because of the low torsional
restraint of the triangular extensions. Rotation of the diaphragms out of vertical during the application of
the load was minimized by the geometry of the loading rig.
2
~lastomeric bearings were used to transmit the downward reaction from the loading frames to the box,
so as to allow limited horizontal and rotational displacement. A high degree of precision in defining the load
path at these points was not necessary.
The hydraulic jacks used in the tests were single acting with packless rams. For the end diaphragm
tests, a pair of 1000 kNjacks were used; these had spherical bearings at each end which allowed the jacks
to rotate as the box deformed during loading. For the centre diaphragm test two 3000 kN jacks with fixed
bases and spherical bearings at the top were used because no allowance for horizontal displacement was
necessary at the centre of the specimen. The normal load control systems were replaced by servo-controls
with deflection feed-back from displacement transducers near the jacks.
In order to prevent accidental overload of the model box, adjustable pressure cut-outs were provided
on each pump. As a safeguard against loss of load in the event of failure of the loading system, a push
button on the control console was provided to operate electrically actuated isolating valves on the hydraulic
line to each jack. The closely-spaced beating introduced some risk of overturning under load and, if
excessive tilt or torsional movement occurred, warn'rag lights operated. Mechanical restraints were provided
as an additional but unused precaution.
4. INSTRUMENTATION
The three diaphragms were instrumented with strain gauges and deflection transducers. The layout was
designed so that the mode of behaviour of each diaphragm could be established and data obtained for
comparison with the results of structural analyses. Strain gauges were also applied to the webs of the box
to establish the distributions of shear stress down the web/diaphragm junctions. The lower flange was
instrumented adjacent to the centre diaphragm to measure the flow of stress and out of plane distortions.
All strain gauge, deflection and load measurements were recorded by a data logger for subsequent analysis
by computer.
Closed circuit television and video tape were used to observe and record the behaviour of the model
in areas where direct observation would have been unsafe for personnel, especially within the box itself.
The residual strains and imperfections in the diaphragms were examined prior to the tests and the
permanent deformations afterwards.
Details of the instrumentation are given in Appendix 4.
5. TEST PROCEDURE
Preliminary loadings, well within the elastic range, were applied to check the functioning of the equipment.
For the centre diaphragm only, ten repeated loadings were then applied to relieve local stress concentrations
produced during fabrication.
It was intended that each diaphragm should be loaded incrementally until collapse occurred and that
each test, once commenced, should not be interrupted. This objective was achieved for the end diaphragms
but during the test on the centre diaphragm, when web buckling had commenced, the control equipment
developed a fault and the test had to be restarted on the following day.
3
The load was applied in prearranged increments by increasing the deflection of the specimen until
the required load was attained. The recording of the gauge outputs was delayed for 1 -2 minutes to allow
for some relaxation due to creep and it was found that strains then remained fairly constant during the 2 - 3 minutes needed for logging the results.
The first end-diaphragm tested was loaded in increments of 30 kN per bearing to 480 kN per bearing,
then in increments of 75 kN to 780 kN per bearing and finally in increments of 45 kN to failure. The
second end-diaphragm was loaded in increments of 30 kN per bearing throughout the tests. The centre
diaphragm was loaded in 120 kN per bearing increments initially; this was reduced to 60 kN per bearing at
780 kN and to 30 kN per bearing when non-linear deflections started to develop at 1080 kN per bearing.
As soon as there was any indication of yield or panel deformation, visual inspections were made and photo-
graphs taken when needed for record purposes. These inspections could increase the time interval between loading increments to about 10 minutes.
The use of deflection control enabled the deformation of the box to be held, so preventing the
sudden collapse which would otherwise have occurred at the maximum load and enabling the subsequent
further development of buckling to be followed during the "descending" part of the load/deflection curve.
6. BEHAVIOUR OF THE DIAPHRAGMS UNDER LOAD
6.1 Introductory comments
The loading of the diaphragms was marked by the following events:
(i) local redistribution of stress during "bedding down",
(ii) an elastic phase with (a) in-plane linear strains and (b) out-of-plane non-linear deformations,
(iii) a transition phase where behaviour became increasingly non-linear and merged into
(iv) an in-elastic phase dominated by yielding and buckling,
(v) collapse where, under deflection-controlled loading, progressive failure occurred with redistribution of load into alternative paths.
The distribution of forces and stresses was similar in all three diaphragms tested and these are conveniently
described together. Buckling and collapse differed for each diaphragm and separate descriptions are
therefore given. The non-linear behaviour of the diaphragms has been discussed by Loe and Irwin 3.
6.2 Results of the loading tests: stresses and forces
6.2.1 Initial stages of loading. Fabrication of the box was to a high standard of accuracy but
some variations in stress due to redistribution of local residual stresses could be expected. Thus, some non-
linearity in strain was found at a few of the strain gauges during the early stages of loading but this
disappeared later, probably due to redistribution of local stress concentrations by yielding. Apart from
this initial non-linearity, the measurements showed a uniform and symmetrical distribution of stress during the elastic stages of loading.
4
6.2.2 Shear f low from the webs. Shear was measured by strain-gauge rosettes attached to both sides
of the web plates but, because of congested steel work inside the box, the gauges had to be placed 125mm
from the web-diaphragm boundary. This meant that there was no indication of local stress variations along
the boundary. Each measurement depended upon six gauges and a six per cent failure rate in the gauges
led to a loss of about 30 per cent of the results. The distribution of shear was thus not defined as well as
would be desirable.
The shear flow was greater along the lower part of the web-diaphragm boundary (Figure 7 ,235 kN
per bearing). Some discontinuities appeared which might be associated with either stiffener positions or
changes in diaphragm thickness but there is no clear evidence on this.
The behaviour of the three diaphragms differed. In end diaphragm 1 the proportion of shear force
from the webs remained throughout the test at about 68 per cent of the load applied to the box (Figure 7).
The remainder of the shear force was transmitted by a secondary load path through the heavily stiffened
webs and lower flange (paragraph 8.2). At the web/diaphragm boundary some decrease in the proportion
of shear in the region of the joint between the 6 and 10 mm plates took place during the latter stages of
loading; this appears to have been counterbalanced by an increase in shear at the lowermost part of the web
boundary. In end diaphragm 2 the proportion of shear from the webs increased from about 63 per cent to
76 per cent of the load applied. Up to a load of 1175 kN per bearing this increase was spread fairly
uniformly along the boundary with the diaphragm but, at higher loads up to failure, some upward redistrib-
ution of shear took place, particularly on the side which failed (Figure 7).
The centre diaphragm showed a large redistribution of shear stress during loading and this was in an
upward direction. During the elastic stages it is estimated that about 40 per cent of the shear at the web/
diaphragm boundary was in the region of the 10 mm diaphragm plate but at 1135 kN per bearing this value
was reduced to about 30 per cent (Figure 7). The shear force applied to the diaphragm by the webs
amounted to about 50 -60 per cent of the total load applied to the box (paragraph 8.2).
6.2.3 Stress flow in the diaphragms. The distribution of stress in each diaphragm plate conformed
with the pattern to be expected. Shear forces at each sloping web were balanced by the vertical reaction
of the bearings and by the opposing horizontal forces from the other web. Although the main function of
the panels between the webs and load bearing stiffeners was to transmit shear, the stress pattern was strongly
influenced by horizontal compression. There were three exceptions where the shear pattern predominated.
These were in end diaphragm i after horizontal compression in the 6 mm panels had been relieved by
buckling (Figure 3), in the lower panels of end diaphragm 2 (Figure 3) where heavy horizontal stiffening
took most of the compression and in the lower panels of the centre diaphragm (Figure 4). In the latter
case, flexure of the box girder produced axial compression in the lower flange. By Poisson effects, this
tended to produce transverse tension in the diaphragm which reduced the horizontal compression in the
region of the 10 mm plate.
A zone of tension due to in-plane bending occurred near the top of each of the three diaphragms at
all stages of loading. The tensile stresses were smaller in the centre diaphragm because of the Poisson effect
from the flanges.
6 .2 .4 Force flows f r o m the s t i f feners . Except above the bearings, the forces along the vertical
stiffeners were small and these stiffeners appeared to have little direct influence on the in-plane stresses in
the plates. Near to the bearings the vertical forces were shared between the stub and load-bearing stiffeners
and the adjacent diaphragm plate.
In end diaphragm 2, large forces occurred in some horizontal stiffeners as buckling developed.
6.3 Results of the loading tests: yield, buckling and Collapse
For convenience, the three diaphragms are now discussed separately.
6.3.1 End d i aph ragm 1. Deflection gauges on the five central panels in the lower part of the 6 mm
plate showed that the elastic out-of-plane deformation commenced as soon as loading was begun (see
Figure 5). The pattern was alternately inwards and outwards in adjacent panels, the centre panel being out-
wards (an outward deflection was towards the face of the diaphragm carrying the vertical stiffeners). The
deflections were closely symmetrical about the centre line. These deformations became visible when a
deflection of about 1 mm was reached~ Thus, at a load of 360 kN per bearing (32 per cent of the ultimate
load) buckles were seen in the two panels to the outside of both the load-bearing stiffeners (see Figure 6)
and in the centre panel at 660 kN per beating.
Superimposed upon the panel deformation was a general inward bowing of both plate and stiffeners
across the three central panels of the 6 mm plate. Deflection gauges showed that this bowing commenced
at the start of loading (see Figure 5) but it was not observed until a load of 660 kN per beating (60% of
the ultimate load) had been reached. At the same load one of the adjacent outward deformations was seen to have extended upwards.
Whereas the panel deformations appear to have been influenced by horizontal compression, the
inward bowing was influenced by the vertical component of stress. The strain gauges indicated that, up to
this stage, the diaphragm was behaving elastically.
At a load of 1000 kN per bearing some shedding of millscale on the 10 mm plate marked the redistrib-
ution of high local stress. With further load, strain became increasingly non-linear until 1180 kN per
bearing which was the maximum load which could be sustained.
At the maximum load a large inward buckle formed across the compressive load path between the
web and adjacent bearing. This buckle extended across three panels causing bending of one vertical
stiffener and buckling of the other (Figure 6 and Hate 2A). An associated outward buckle formed above
on the same load path but was confined to one panel. Without deflection control of the loading jacks these
buckles would have caused collapse of the diaphragm. Gauges indicated that similar buckling had commenced
in the other half of the diaphragm.
The vertical shortening of the diaphragm due to the buckling had two effects. One was to cause the
lower flange to deflect upwards from a hinge line close to a transverse stiffener about 1.1 m from the bearing.
This deflection rotated the 10 mm diaphragm plate which further contributed to the buckling of the 6 mm
plate. The second effect of the vertical shortening was to distort a corner of the lower flange, the small
projecting web panels and the adjacent diaphragm plate (Plate 2A).
6
6.3.2 End d iaphragm 2. Deflection gauges showed that elastic inward bowing of the whole central
area of the 6 mm plate commenced as soon as loading was begun (Figure 5) but it was only about half
of that measured on end diaphragm 1. The two horizontal stiffeners prevented panel deformation at low
loads but, as the load increased, the gauges showed some slight evidence of inward panel buckling and this
became noticeable in the three centre panels at loads of 1070 to 1170 kN per beating (see Figure 6).
Shedding of miUscale from the 10 mm plate indicated some local redistribution of stress at 1000 kN
per beating. A small buckle formed in one of the lower web panels projecting beyond the diaphragm at
1040 kN per bearing and at 1250 kN per beating (94 per cent of the ultimate load) the two adjacent web
panels were similarly affected.
Failure occurred at a load of 1330 kN per beating when an inward buckle on the load path between
the bearing and web extended across adjacent stiffeners and a second parallel buckle formed just above it.
The failure was adjacent to the buckled small projecting panels. Strain gauges indicated that an upward
redistribution of shear stress had taken place (Figure 7, side A).
At failure two vertical and two horizontal stiffeners were buckled (Hate 2b) and a short length of
weld between the web and diaphragm was fractured at a point just below the cut-out for the lowest
longitudinal stiffener. Vertical shortening of the diaphragm caused the lower flange to deflect upwards
about a skewed hinge line (Figure 6). Buckling of the longitudinal lower flange and transverse stiffeners is shown in Hate 2b.
6.3.3. Cen t re d iaphragm. Elastic bowing of the middle area of the centre diaphragm commenced as
soon as loading was begun; the bowing was directed towards the vertical stiffeners (Figure 5). Tension
field buckling in the lightly stiffened areas of the upper part of the webs was observed (Figure 6) at a load
of 920 kN per beating (69 per cent of the ultimate load). At this stage the strain gauges showed that the
diaphragm strains were no longer increasing in a generally linear manner.
Buckling of the small web panels adjacent to the 10 mm diaphragm plate was observed at a load of
1010 kN per bearing. The stiffeners had been attached to the webs by intermittent welding and some
buckles extended to adjacent panels through gaps in the welding. Shedding of millscale from this diaphragm
could not be observed directly because the resolution of the closed-circuit television was inadequate.
At a load of 1120 kN per bearing the model had to be unloaded to allow a fault in the control system
to be rectified. On reloading, the tension field buckling in the webs extended to the small panels adjacent to
the diaphragm when a load of 710 kN per beating was reached and by 820 kN per bearing the remaining
small panels in the lower part of the web had buckled. The buckling of these panels contributed to the
upward redistribution in web-diaphragm shear flow which has been noted in paragraph 6.2.2.
The small panels in the lower flange, adjacent to the boundaries with the webs and diaphragm, buckled
• upwards during the second cycle of loading at loads of 1000 kN and 1090 kN per bearing respectively
(Figure 6). These deformations appeared to be associated with a shortening of the diaphragm.
At a load of about 1200 kN per bearing buckling started in the 6 mm plate across the load path
between both webs and their adjacent beatings. These buckles were away from the vertical stiffeners and,
in both cases, a horizontal and a vertical stiffener buckled. At the same time the bowing of the middle area
7
of the diaphragm towards the vertical stiffeners increased considerably (Figure 5) and this caused some
distortion of the upper part of the 10 mm thick plate (Figure 6). The development of these buckles led
to failure (Plate 3A). The maximum load of 1330 kN per bearing was sustained only momentarily but
steadied at a lower value of 1250 kN per bearing. The higher load (1330 kN) should be regarded as the
collapse load. The post-collapse behaviour of the box was studied by increasing the deflection imposed by
the loading jacks. The load that could be sustained decreased and at 1010 kN per bearing the lower flange
buckled downwards, its five stiffeners buckling at a distance of about 0.7 m from the diaphragm. On the
same side of the diaphragm two welds between the lower flange stiffeners and the diaphragm stub stiffeners
fractured. Loading was then discontinued. The deformed shape of the unloaded diaphragm is shown in
Figure 8.
7. COMPARISON BETWEEN EXPERIMENTAL AND ANALYTICAL RESULTS
Finite element analyses of trapezoidal diaphragms in box girders with webs at 45 ° to the flanges have been
made by several authors 4'5'6'7. Three of these dealt specifically with the centre diaphragm of the test
model: Simonian 5 made a finite element buckling analysis of the stiffened diaphragm using data from a 3-
• dimensional elastic analysis. Jones and Irwin 6 made a linear elastic 2-dimensional analysis for comparison
with the elastic stresses measured during the test and Wood and Flint a 3-dimensional analysis 7, the results
of which were used in diaphragm strength calculations by Wood.
The 2-dimensional analytical model was developed to give a satisfactory but conservative representation
of the 3-dimensional structure in the diaphragm region of this particular box girder. The development of
the model highlighted the complex structural interactions which occurred during loading. Particularly
important were (a) the effect of the framing formed by the transverse stiffeners on the flanges and webs in
transferring load into the stiff lower flange, thereby bypassing the diaphragm, (b) the stresses induced in
the diaphragm by Poisson's ratio effects in the flanges and webs due to longitudinal bending of the box, and
(c) the enhanced effective width o f the lower flange acting with the diaphragm in resisting transverse stresses.
It was necessary to include in the effective width the whole of the lower flange as far as the first transverse
stiffeners and wedge-shaped parts beyond (Figure 9). This was subsequently confirmed by the stress
distributions given in reference 7. The calculated stresses for this model were in good agreement with the
measured stresses (Figure 10) except at the centre-line where the vertical stresses were approximately half
the measured values. The measured stresses were obtained over a load range in which the behaviour of the
structure was predominantly elastic.
The 3-dimensional elastic analysis 7 was made in two parts: analysis A used elements with 6 degrees of
freedom, ie including plate bending, and analysis B used elements with 3 degrees of freedom. The results
from these analyses are compared with the 2-dimensional analysis and with measured stresses in Table 1
for several stations on the diaphragm. Analysis A gave results in close agreement with the measured values.
Methods for the calculation of the collapse loads of panels and stiffeners in diaphragms are given in
Parts 2 and 3 of Appendix 1 of reference 2. However, restrictions in the Rules, on the arrangement of
stiffeners and the web slope angle, prevented the application of the Part 2 method to the test diaphragm.
The strengths of the plates and stiffeners were calculated using the stresses from the 3-dimensional
elastic analysis with 6 degrees of freedom (Analysis A). The strengths are given in Figure 11 in terms of
the bearing reaction at which each part would collapse (Rult), on Part 3 criteria. Although the strength
appraisal was based on an analysis shown above to be satisfactory (Analysis A), it did not allow for redistribution
8
of shear up the web due to yielding and buckling. This redistribution affected the actual collapse
behaviour. Had it been considered in the strength appraisal it would have (a) reduced the values of Rul t
for the vertical stiffeners and the 6 mm plates in the middle and upper parts of the diaphragm and (b) incr-
eased the Rul t in the 10 mm plate at the bottom.
The calculated values of Rul t were obtained firstly (a) on the basis of nominal yield, thicknesses and
Part 4 imperfections 2 and secondly (b) on the basis of measured values. These strengths are compared with
the failure loads in paragraph 8.3.
The finite element elastic buckling analysis 5 gave a critical load about 25% greater than the measured
collapse load. Simonian noted that the difference may have been due to the omission of flange shear
forces from the analysis and to imperfections and residual stresses in the test model. Additional factors
not taken into account were (i) the upward redistribution of shear in the webs, which would have tended to
reduce the collapse load, and (ii) the effect of the alternative load path through the lower flange and
transverse framing which would have tended to increase it.
TABLE 1
Comparison of Emite element results with elastic experimental stresses. Centre diaphragm at 500 kN per bearing
Position on diaphragm Stress Analysis (see Figure 10, Section 2)
6
Vertical o 1 N mm "2
Transverse o 2 N mm 2
Shear r N mm 2
Equivalent effective o e
A B C
Exp
A B C
Exp
A B C
Exp
A B C
Exp
18 22 19 17
22 29 16 19
31 40 24 30
57 75 44 55
7 8
33 13 41 21 51 34 36 15
37 52 52 72 40 63 33 48
48 65 62 82 33 34 51 66
91 123 118 156 67 81 95 122
Analysis A B C
Exp
3-D, 6 degrees of freedom, with bending stiffnesses 3-D, 3 degrees of freedom, without bending stiffnesses 2-D Experimental results from Figure 8 Of reference 6
Based on Table 1 of Wood and Flint 7
9
8. DISCUSSION
8.1 Elastic behaviour
The loading of a steel box girder produces the following forces in a support diaphragm:
(i) a vertical component of the shear force from the webs,
(ii) a horizontal component of the shear force from the webs (in trapezoidal boxes only),
(iii) in-plane bending due to the diaphragm behaving as a loaded beam supported at the bearings,
(iv) transverse forces from the flanges due to the Poisson effects from longitudinal flexure of the girder,
(v) out-of-plane moments due to longitudinal eccentricity of the bearings.
The vertical shear forces from the webs are transmitted through the diaphragm by shear panels between
the webs and load-bearing stiffeners. Strain measurements show that, in the absence of horizontal stress,
these panels carry only shear, eg the middle lower 6 mm plate of end diaphragm 1 (Figure 3) where the
occurrence of panel deformation due to the absence of horizontal stiffeners has almost eliminated transverse
compression. Generally, however, the shear is modified by horizontal direct stresses produced by the forces
and moments listed in (ii), (iii) and (iv) above and the resultant, as indicated by the strain measurements,
shows that large compressive load-paths exist between webs and bearings (see Figures 3 and 4). It is across
these load-paths that the buckles which initiated failure later developed.
The horizontal component of compression due to web shear tended to flow through the lower part of
tile diaphragm and the associated area of lower flange. This was partly due to a greater acceptance of compre-
ssion by this very stiff zone and partly because of the larger flow of shear in the lower webs. The horizontal
compression arising from web shear was augmented by compression from in-plane bending (Figure 3) but,
for the centre diaphragm, was decreased by Poisson forces from the lower flange (Figure 4). There was
minimal horizontal reaction at the bearings under the diaphragm as these were free to slide.
At the top of the diaphragm the tensile stress due to in-plane bending predominated and the values
shown in Figure 3 are the amount by which this stress exceeded the compression from web shear. For the
centre diaphragm the Poisson compression was also deducted and Figure 4 shows the resulting reduced tensile
stress.
The centre portion of each diaphragm (bounded approximately by the outer stub stiffeners) provided
the reaction for the shear panels. The vertical compression in this central portion was zero at the top and
equalled the total force flow through the diaphragm at the bottom, most of, thi s force flowing in near the
bottom. The panels between the load-bearing stiffeners in the lower part of the diaphragm were in biaxial
compression.
The out-of-plane moments from longitudinal eccentricity of the bearings (v), were virtually eliminated
in the tests by the setting and geometry of the bearings. However, some out-of-plane moments arose as the
collapse loads were approached due to bottom flange deformations. It is thought that these had only a
minor influence on the diaphragm collapses.
8.2 Transverse stiffeners and shear redistribution
Instrumentation showed that only part of the applied test load was being transmitted through the
diaphragm. A secondary load path was provided by the heavy transverse stiffeners on the webs and flanges
10
which formed frames about 230 mm away from the diaphragm plates and by the lower flange with its five
89 mm deep by 6 mm longitudinal stiffeners. These stiffeners were welded both to the frames and to the
diaphragm so that a very rigid assembly with longitudinal continuity was formed which transmitted the
shear force to the bearings. This secondary path took up to 30 per cent of the load applied to the end
diaphragms and 40 per cent (shared between the frames at each side) of the load applied to the centre
diaphragm.
The forces following the secondary load path induced out of plane bending stresses in the lower flange.
These would have tended to destabilise the flange when it carried longitudinal compression due to bending
of the box.
The redistribution of shear along the web/diaphragm boundary during loading appeared to be.
influenced by the relative stiffness of the adjacent web and diaphragm panels. The upward redistribution
at the centre diaphragm (Figure 7) was due primarily to deformation of the adjacent web panels. The slight
downward redistribution in end diaphragm 1 was probably due to progressive deformation of the diaphragm
in the absence of horizontal stiffeners. No redistribution occurred until a late stage in end diaphragm 2 and
this may have been associated with a weld fracture near the bot tom of the web which was found after the
diaphragm failure. Web deformations were comparatively small.
The non-linear strains observed at 920 kN per bearing in the centre diaphragm were probably due
primarily to the upward redistribution of the web shear rather than to non-linearity in the diaphragm stiffness.
8.3 Deformation and collapse
All diaphragms commenced to bow at the start of loading. The bowing was mainly in the 6 mm plate
with some rotation of the 10 mm plate. End diaphragm 1 (vertical stiffeners only and an in-out pattern of
distortion described in paragraph 6.3.1) showed more deformation than the end 2 and centre diaphragms.
The bowing was elastic and is to be distinguished from the in-elastic buckling which led to collapse. The
direction of bowing was independent of the stiffener arrangement and the plate and stiffener imperfections
were small.
In the small web panels adjacent to the centre diaphragm, buckling started in the lowest panels and
later appeared in the higher panels. In similar panels at the end diaphragms only slight indications of buckling
appeared in the projecting webs. Because of flexure in the girder, the lower small panels would be under
combined compression and shear at the centre but under shear alone at the ends. This is the probable
explanation of the differences in behaviour. Variations in web panel geometry are unlikely to have affected
the resistance to buckling under shear because, for the same bearing reaction, the shear stress in the centre
panels was similar to that at the ends (both shear force and web thickness were halved at the centre) and the
panel depth to thickness ratios (b/tw) were similar. The use of chain welding allowed most buckles to
extend through the 'miss' lengths to cover two panels (Plate 3b).
In the centre diaphragm test the large web panels between the transverse stiffeners showed tension
field action, unlike the panels in the end diaphragm tests. The stresses in the two groups of panels were
similar because the longitudinal stresses due to flexure of the girder were small at that depth. The b/t w
ratios for the panels near the centre were twice those for the panels near the ends and this is likely to have
been the main cause of the difference in behaviour.
11
The buckling in the upper small web panels adjacent to the centre diaphragm appeared to be associated
with the tension field action in the large panels.
The bottom of the diaphragm, being thick and heavily stiffened, formed a comparatively rigid base
and most of the deformation was forced into the adjacent lighter components. Calculations for the centre
diaphragm showed that yield in the bottom part would have been reached at about the load at which collapse
occurred by buckling. Experimental evidence showed that at the gauge positions (ie at the centre of the
panels) yield was approached in end diaphragm 1 at the collapse load but not in the other diaphragms.
The use of deflection control meant that collapse in the normal sense did not occur. The collapse
load would however be the maximum load reached since there would then be no further beneficial
redistribution of stress.
Collapse occurred by buckling across the load paths between web and bearings. In the end diaphragms
collapse occurred on one side only although strain gauges showed symmetrical behaviour up to a late stage.
In the centre diaphragm both sides buckled together. The collapse occurred as the vertical stiffeners
buckled and failed. The mode of failure did not appear to be influenced by the horizontal stiffeners. This
was consistent with the results of the strength calculations for the centre diaphragm which showed that the
capacities of the load bearing and full length vertical intermediate stiffeners were close to exhaustion at
the collapse.
The use of rockers to equalise the loads at the bearings under the end diaphragms may have resulted
in failure of only the marginally weaker sides of the diaphragms. At the centre diaphragm, rockers were
considered to be unnecessary because of the low torsional resistance of the triangular extensions. There
may however have been sufficient torsional stiffness to prevent marginal differences from showing and to
cause both sides of the diaphragm to collapse together. These differences would not effect the failure loads.
The calculated strengths 9f stiffeners and plates (Figure 11) indicated a collapse by stiffener failure at
an Rul t of 1150 to 1200 kN for the centre diaphragm. This compares with observed buckling of the outer
panel and intermediate stiffeners at 1200 kN and total collapse of the diaphragm at 1330 kN. The lower
pair of 6 mm outer plate panels had calculated strengths Rult, on actual properties of 1790 to 1870 kN.
Even if the effect of redistribution of shear were considered, there would have been reserves of strength at
the failure load provided the stiffeners had remained unbuckled. The predicted failure load of the load
bearing stiffener at about 1150 kN, compared with its actual failure load of 1330 kN, was probably due to the
partial rotational restraint at the bearing provided by the flange but which is discounted in the Part 3 analysis.
The above collapse estimates were based on the elastic stresses developed in the diaphragm due to part
of the reaction; the remainder of the reaction was carried by the flange transverse and longitudinal stiffener
system. Although the balance of the load sharing between the diaphragms and flange stiffener systems would
have changed as the structure approached its collapse loads the estimated divisions at collapse were:
Diaphragm 1 Total reaction per bearing
carried by the diaphragm
carried by the flange stiffeners
1180 kN
800 kN 68%
380 kN 32%
12
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Diaphragm 2 Total reaction per bearing
carried by the diaphragm
carried by the flange stiffeners
1330 kN
1000 kN 75%
330 kN 25%
Diaphragm 3 Total reaction per bearing
carried by the diaphragm
carried by the flange stiffeners
1330 kN
800 kN 60%
530 kN 40%
9. CONCLUSIONS
The observed distributions of strain in the diaphragms were compatible with the loadings applied
ie vertical shear and horizontal compression from the webs, in-plane bending and Poisson forces
from the flanges.
The horizontal component of force from the sloping webs had an important influence: it super-
imposed direct stress on the shear stresses in the panels between the webs and load-bearing stiffeners,
it produced deformations in panels without horizontal stiffening and it produced a large transverse
stress flow in the thicker lower panels and adjacent flange.
The stress distributions obtained from the fully developed finite element analyses were in good
agreement with the measured elastic stress distributions.
The results do not enable the Poisson effects from longitudinal flexure of the box to be isolated but
they confirm analytical results suggesting that the effect is important.
Elastic bowing of the diaphragm commenced as soon as loading was applied. The direction of bowing
was independent of the stiffener arrangement; plate and stiffener imperfections were small.
The distribution of shear at the web/diaphragm boundary was influenced by buckling of adjacent
panels. Thus, buckling of the small panels in the web caused an upward redistribution at the centre
diaphragm while deformation of the upper part of end diaphragm 1 caused a downward redistribution.
In the design of the model box transverse stiffeners were provided adjacent to the diaphragms on the
webs and flanges to take'transverse compressive stresses and to help the redistribution of the shear
"boot" in the web panels. It was found that these stiffeners also served to transfer shear from the
webs, through the lower flange, to the bearings thus reducing the loads on the diaphragms. If this
arrangement of transverse stiffening is used the lower flange should be designed either (a) to accept
the additional out-of-plane loading or (b) to follow the Interim Design and Workmanship Rules.
These Rules require the flange to remain stable under displacements which occur when the webs and
diaphragm carry all of the shear.
The chain intermittent welding used on the web longitudinal stiffeners provided inadequate restraint
to the boundaries of some of the panels adjacent to the centre diaphragm. In consequence the buckling
passed through the "miss" lengths and combined with that in contiguous panels. This has led to the
recommendation in Clause 14.4 of Part 2 of the Interim Design and Workmanship Rules that all welds
in areas of plastic redistribution should provide continuous connections.
13
(9) Collapse in all three diaphragms was primarily by buckling across the diagonal compressive load paths
between the webs and bearings. These buckles passed through the stiffeners and calculations for the
stiffeners on the centre diaphragm, using Part 3, indicated that they were at, or close to, their
collapse loads.
(10) In the 10 mm plate adjacent to the bearings, the panels whose calculated failure load was close to the
measured collapse load participated little in the mode of collapse.
(11) The highest diaphragm load was carried by end diaphragm 2 (1000 kN per bearing) and failure was
due to exhaustion of the strength of the stiffened panels of the diaphragm. The balance of the
reaction (330 kN per bearing) was carried by the flange stiffeners. End diaphragm 1 failed at a lower
diaphragm load (800 kN per bearing, with 380 kN per bearing in the flange) due to the effect of the
large deformations in the diaphragm plate which had developed as a consequence of the lack of
horizontal stiffening in the middle-upper part of the diaphragm. The centre diaphragm also failed
at a lower load (800 kN per bearing, with 530 kN per bearing in the flange) than end diaphragm 2 and
failure was influenced by the upward redistribution of shear from the webs resulting from web panel
buckling.
10. ACKNOWLEDGEMENTS
This work was undertaken in the Bridge Design Division (Head of Division: Dr G P Tilly) of the Structures
Department of TRRL. The authors acknowledge the contributions of Dr J G M Wood (of Messrs Flint and
Neill) for the design concept of the model box and for the strength calculations, Dr P C Das for the detailed
design of the model and for monitoring the fabrication, Mr P J D Guile (of Research Models and Equipment
Ltd) for manufacturing and instrumenting the model to the exacting standards required, and
Mr M D Macdonald, Mr D A Ives and others for their assistance with the loading equipment and
instrumentation.
11. REFERENCES
1. DOWLING, P J, J ALOE and J A DEAN. The behaviour up to collapse of load bearing diaphragms
in rectangular and trapezoidal stiffened steel box girders. Paper 7, Steel Box Girder Bridges. Proc
of the Int Conf organised by the Inst. of Civ. Engrs. in London, 13-14 Feb 1973, Thomas Telford Ltd,
London 1973.
. DEPARTMENT OF THE ENVIRONMENT, SCOTTISH DEVELOPMENT DEPARTMENT,
WELSH OFFICE. Inquiry into the basis of design and method of erection of steel box girder
bridges. Report of the committee; Appendix 1, Interim design and workmanship rules, parts 1-4.
London, 1973 (H M Stationery Office).
. LOE, J A and C A K IRWIN. Non-linear behaviour of stiffened diaphragms in a steel box girder.
Paper 15, Structural analysis non-linear behaviour and techniques. Department of the Environment, TRRL Supplementary Report SR 164 UC, Crowthorne, 1975 (Transport and Road Research
Laboratory).
14
4. ROCKEY, K C and M A EL-GAALY. Stability of load-bearing trapezoidal diaphragms. Int. Assoc.
for Bridge and Structural Engineering, Zurich, !972.
5. SIMONIAN, W S S. Investigation into elastic and buckling behaviour of trapezoidal support diaphragms
in steel box girder bridges. PhD thesis, University of Liverpool, 1975.
6. JONES, J P and C A K IRWIN. Analysis of the centre diaphragm of a trapezoidal steel box girder.
Department of the Environment, TRRL Supplementary Report SR 101 UC, Crowthorne, 1976.
(Transport and Road Research Laboratory).
. WOOD, J G M and A R FLINT. The design of box girder diaphragms. Paper 18, Int. Conf. on Steel
Plated Structures, Imperial College, London, 1976.
15
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Fig. 2 DETAILS OF STIFFENED FLANGES A N D WEBS A N D A R R A N G E M E N T OF LOADING POINTS
Principal stress flows
Shear f low in webs
Force f low in stiffeners
,~x,/Compression
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Fig. 6 DEVELOPMENT OF BUCKLING IN DIAPHRAGMS, THE ASSOCIATED LENGTHS OF WEB AND BOTTOM FLANGE ARE SHOWN AS VIEWED EXTERNALLY
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Fig. 11 RESULTS OF PART 3 STRENGTH CALCULATIONS ( CENTRE DIAPHRAGM Para. 7)
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Plate 2a BUCKLE IN END D I A P H R A G M 1, OUTSIDE VIEW
Neg. no. R1455/72/6
Plate 2b BUCKLE IN END D IAPHRAGM 2, INSIDE VIEW
Axis of pP!tographic lighting
Neg, no. R1421/73/2
Plate 3a CENTRE DIAPHRAGM AFTER THE TEST (Instrumentation has been removed)
Plate 3b BUCKLES IN WEB PANELS ADJACENT TO CENTRE DIAPHRAGM AFTER REMOVAL OF INSTRUMENTATION• (The web is viewed from below• Note marks indicating diaphragm weld and longitudinal
stiffener intermittent welding)
12. APPENDIX 1
MATERIALS
12.1 Yield stresses
The steel box girder model was constructed of Grade 50B weldable structural steel to BS 4360:1972.
The nominal minimum yield stress of the material was 355 Nmm "2. Tensile test specimens were obtained
from off-cuts or, after the tests, from plate cut from the model in areas which had been subjected to low
stresses during fabrication and the loading tests. Each test specimen had a machined test length of 65 mm
and width 12.5 ram. The tensile tests were made in a 600 kN hydraulic testing machine having servo-control
of load with a displacement feedback transducer attached to the ram. Elongation was measured with a 50 mm
gauge length transducer and recorded, against load, on an X-Y plotter.
The specimens were tested using a constant rate of ram displacement giving a rate of strain increase
in the specimen of 100 microstrain per minute and maintained until the X-Y plotter indicated that strain
was increasing at an approximately constant load, ie along the yield "plateau". The displacement was then
held constant and the load allowed to fall towards a "static yield" value. After two minutes the load was
observed and the movement of the ram recommenced to give a rate of strain increase of 1000 microstrain
per minute until ultimate load was achieved. The rate of strain increase of 100 microstrain per minute and
the 2 minute fall in load were selected as equivalent to the conditions during the box test.
The mean static yield stress for each box component is given in Table 2; the mean stress over all the
test specimens was 415 Nmm "2 (the static yield stress measured after a two minute fall in load is approx-
imately 3% below the conventional lower yield stress).
12.2 Plate thicki~ess
The thickness of the plates was measured at twenty eight stations on each diaphragm and on the
adjacent plates and stiffeners after the tests. The mean thicknesses of the nominal 3, 6 and 10 mm plates
were 3.4, 6.4 and 9.8 mm respectively. The plates were supplied as 1/8, 1/4 and 3/8 in. thicknesses.
12.3 Lamination defects
The diaphragm plates were examined with ultrasonic equipment at points on a 225 mm grid and along
the edges. No lamination was detected. The other plates were examined visually along the edges and no
lamination was found except on one of the six 5 mm plates used to form the upper flange. Ultrasonic
inspection showed that the lamination was confmed to a small triangular area 37 nun wide by 470 mm long
at one corner of the plate. The plate was positioned in the model so that the laminated area was remote
from the diaphragm to be tested and from other areas of high stress.
32
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13. A P P E N D I X 2
FABRICATION OF THE MODEL SBG
The fabrication of the model, which was made by specialist model makers, has been described by
P J D Guile 8. The diaphragms, flanges and webs were first constructed separately as stiffened sub-assemblies
and then fitted and welded together to form the box girder. Manual welding techniques were used, mainly
by covered electrodes but some inert gas metal arc (MIG) welding was employed. Chain intermittent welds
were used extensively to rninimise residual stresses. Structural steel to Grade 50B of BS 4360:1972 was used
except in the mild steel loading frames.
The steel plates were first marked out with the relevant fabrication details, strain gauge positions and
residual strain measurement positions. The 10 mm (3/8 inch) thick plates needed for the lower part of the
diaphragm and the lower flange were flame cut to size; all the other plates, which were of 6 mm (1 [4 inch)
thickness or less, were sheared to size.
Fabrication of the diaphragm commenced by milling the slots needed in the 10 mm plate for the lower
flange stiffeners. The 10 mm and 6 mm plates were then butt welded together. The 'U' slots needed for the
top flange stiffeners were flame cut on a profding machine and similar slots for the web stiffeners were cut
by drilling and hacksawing. Lastly, the various diaphragm stiffeners were fdlet welded to the plate according
to a sequence designed to minimise weld distortion. This sequence consisted of vertical stiffeners (working
from alternate sides to centre), horizontal stiffeners (bottom to top) and stub stiffeners (centre outwards,
vertical stiffener side first).
The bottom flange was made from a single piece of 10 mm thick plate. Transverse and longitudinal
stiffeners were shaped and slotted where required and welded to the flange plate. The transverse flat
sections of the loading frame were tacked in position.
The central lengths of the webs were each made from two pieces of 3 mm thick plate joined by a
longitudinal butt weld 200 mm from the upper edge. These were then attached to the end sections of 6 mm
plate by a transverse butt weld. Shaped and slotted transverse stiffeners were welded to the webs at positions
• locatedby the completed bottom flange so as to ensure a good fit on final assembly. The longitudinal
stiffeners were then welded in position. All welding was carried out in a pre-arranged sequence.
The top flange was made from six separate sheets of 5 mm thick plate joined by transverse welds at
1.2 m (4 ft) on either side of the transverse centre line and by a central longitudinal weld. The transverse
welds were made first, forming two lengths of plate. The longitudinal stiffeners were then welded to the
plate and, to ensure a good fit, temporarily attached transverse stiffeners were located from corresponding
stiffeners on the already completed webs. The two halves of the flange were then butt welded together and
the transverse stiffeners were refitted and welded. The manholes in the top flange were afterwards flame cut.
Final assembly was commenced by clamping the top flange, stiffener-side uppermost, on the welding
platform. The diaphragms and loading frames were then positioned and fully welded. Next, the webs and
bottom flange were fitted in position and a number of the transverse stiffener intersections were partially
welded. The longitudinal welds between the webs and the top flange were then completed. The box was
placed on its lower flange and on each of the webs in turn so that welding to these components could be
completed in the downhand, or fiat, position.
34
Weld sequences, currents and voltages were recorded.
Reference
8. GUILE, P J D. The construction and instrumentation of a trapezoidal box girder model.
report supplied to the Transport and Road Research Laboratory. Unpublished
35
14. APPENDIX 3
RESULTS OF RESIDUAL STRAIN AND IMPERFECTION MEASUREMENTS
Measurements to determine residual strains were made before, during and after fabrication and transportation
of the box girder model (see Appendix 2). The residual strains in the centre diaphragm, a web and the bottom
flange, after fabrication and transportation of the model, are shown in Figure 12. The strains are typical of
an end-diaphragm except that the transverse strains tended to be lower in the 6 mm plate. Full details of
the residual strains at intermediate stages in the fabrication have been given by Guile 8.
All plates and stiffeners were flat when checked on a surface table prior to fabrication. The geometrical
imperfections of each of the diaphragms, including associated areas of webs and flanges, were examined
immediately prior to that diaphragm being tested. For the two end diaphragms the examinations were made
visually, with the aid of straight-edges. This was sufficient to establish that the imperfections were small
compared with the fabrication tolerances given in Appendix 11 of the Interim Design Appraisal Rules 9.
The timing of the testing programme permitted detailed measurements to be made at the centre diaphragm.
The initial imperfections for the centre diaphragm are shown in Figure 13. Profiles of the imperfections,
relative to a common plane surface, are plotted along the lines of the stiffeners and along hnes passing through
the centres of the panels. Figure 13 also shows the imperfections on the lines of the stiffeners on a web
and On the bottom flange, adjacent to the centre diaphragm. The imperfections on the diaphragm stiffeners
were all within 1/800, where l = length of stiffener.
The imperfections measured in the area of the centre diaphragm were Checked against the fabrication
tolerances laid down in Appendix 11 of the Interim Design Appraisal Rules. In the diaphragm all of the
panel imperfections were less than 50 per cent, and in many cases less than 10 per cent of the specified
tolerances. None of the web and bottom flange panels exceeded their tolerances and in the direction of their
shortest dimensions the imperfections were all less than 50 per cent of the tolerances.
All of the stiffeners were within tolerances except for some longitudinal stiffeners on the south web,
as measured on the plated side. The largest imperfections occurred at the boundary between the bottom
flange and south web; if the stiffener tolerance is applied to this boundary, then the tolerance would be
exceeded by 38 per cent. The north boundary was well within this tolerance. All of the stiffened panels
were within tolerance.
Subsequent to the testson the model the Interim Design and Workmanship Rules 2 have been published;
Revised closer and morestringent tolerances are given in Section 23 of Part IV, but all of the panels and most
of the stiffeners of the experimental model were within these stricter tolerances.
Reference
9. DEPARTMENT OF THE ENVIRONMENT, SCOTTISH DEVELOPMENT DEPARTMENT, WELSH
OFFICE. Inquiry into the basis of design and method of erection of steel box girder bridges: Interim
Report; Appendix A - Interim design appraisal rules (SBG-6A). London, 1971 (H M Stationery Office).
36
15. APPENDIX 4
INSTRUMENTATION
15.1 Data logging system
A 600-channel data logger was used to make and record all measurements of strain, deformation
and load during the tests. The logger provided a resolution of + 0.01% of full scale and an accuracy of
+ 0.02%. The data were recorded on 8-hole punched paper tape for subsequent analysis on the TRRL
ICL 4 - 7 0 computer.
15.1.1 Strain measurements. For the centre diaphragm test, measurements were made at 477 gauge
positions and for the end diaphragm tests at 342 positions. The distributions of strain gauges on the
diaphragms were similar for the three tests but more gauges were placed on the webs and lower flange at
the centre diaphragm. The gauges were of the electrical resistance, post-yield type (maximum working
strain 5%) and of 10 mm gauge length. Dummy strain gauges, one for each active gauge, were mounted on
unstressed, 6 mm thick steel plates. The overall accuracy of strain measurements was +-- 3 microstrain.
Errors due to electrical noise were minimised by the high noise rejection characteristics of the data logger
and the use of a strain-gauge system balanced about the electrical earth.
15.1.2 Displacement measurements. Three types of transducers were used for the displacement
measurements; linear variable differential transformer (LVDT) transducers of + 50 mm and + 2.5 mm
travel (overall accuracies + 0.03 mm and + 0.006 mm respectively) and potentiometers of 250 mm travel
(overall accuracy + 0.2 mm). Forty + 50 mm LVDT transducers were attached to a frame suspended from
the top flange and parallel to the diaphragm under test. These were connected through universal couplings
to the diaphragm to measure out-of-plane deformations. For the centre diaptiragm test an additional seven
+ 50 mm LVDT's were connected to the diaphragm and twenty seven were attached to a frame outside the
box girder. The latter were connected to the upper and lower flanges. Two of the transducers were placed
so that the position of the frame within the box girder could be related to that outside, four were arranged
in pairs to measure the vertical displacements and rotations of the bearings under the diaphragm and the
remainder were positioned to measure lower flange deformations. Two more were positioned to measure
the compression in the rubber bearings at one end of the model. The outside frame was located vertically
with respect to the frames (on the box) used for reacting load in the end-diaphragm tests, and longitudinally
at the plane of the centre diaphragm. A potentiometer transducer was connected between the outside frame
an~, the [abo, atory floor to measure the vertical displacement of the frame.
For the end-diaphragm tests the outside LVDT's and frame were not used. In-plane diaphragm
distortion was measured by eight potentiometers, two per corner, supported on a floor-mounted frame.
Potentiometers were attached to the loading jacks to provide displacement feedback signals to the
loading-control system and a + 2.5 mm LVDT was mounted horizontally betweenthe two box-girder
support bearings at the centre diaphragm to measure changes in the spacing between them.
15.1.3 Load measurements. The load in each hydraulic jack was determined from the oil pressure.
The pressure was measured by a strain-gauge transducer mounted on the jack and connected to the data
logger and a digital display. The jacks were of a low-friction type designed for structural testing and the
pressure-measuring system was calibrated against a pendulum system similar to that used in materials
37
testing machines. The overall accuracy of load measurement was better than + 1% of reading for loads above
20% of the collapse load of the box-girder.
15.2 Other instrumentation
15.2.1 Closed-circuit television (CCTV) . CCTV was used to observe and record, on a video-tape
recorder, the behaviour of selected areas of the model during the tests. This was especially important at
the centre diaphragm and the support bearings because safety considerations prohibited close inspection by
personnel. The video-tape recording enabled the development of any transient phenomena which might have
occurred, such as sudden collapse, to be examined subsequently. One face of each vertical stiffener on the
diaphragms was painted white to make out-of-plane distortions easier to observe. Preliminary tests had been
made to determine the best form of lighting to use for CCTV and general photography. Fluorescent tubes
were selected as providing sufficient light whilst minimising heat input to the model. Heat input was
particularly critical during the tests on the centre diaphragm where both radiant and convective heat transfer
occurred within the box-girder. The radiant heat input was checked on the first diaphragm tested, using
thermocouples and a multi-channel chart recorder.
15 .2 .2 Residual s t ra in m e a s u r e m e n t s . During the fabrication of the model residual strain measure-
ments were made close to the locations of the electrical resistance strain gauges. Measurements were made
at 104 positions on each diaphragm, 128 positions on each web and 24 positions on the lower flange. At
each position the residual strain was determined on both sides of the steel plate. 50 mm, 100 mm and
200 mm gauge length Demec mechanical strain gauges were used and measurements were made at three
stages of the fabricationB; the unworked steel plate, the plates cut to size and with stiffeners welded into
place, and the completed model. An additional set of measurements were made on the diaphragms after
the completion of the butt weld between the 10 mm and 6 mm plates. The measurements on the completed
model were made immediately prior to each test.
Invar bars and strips of steel plate, of the same material as the model, were used as references to
correct the Demec gauge readings for temperature effects. The plate was kept in the same environment as
the model and supported in an unstressed condition during measurements.
15 .2 .3 Initial i m p e r f e c t i o n s and final d i s to r t ions . The out-of-plane deformations of the centre
diaphragm were measured before and after testing using a reference plane and internal dial calipers. The
reference plane was provided by a stiff beam sliding on a frame attached to the model. Plate panel
imperfections and distortions on the lower flange and webs adjacent to the centre diaphragm were measured
in a similar way but the reference was a 2m long, stiff beam on magnetic clamps. This was traversed across
the sections. The straightness and squareness of stiffeners were checked with straight edges and protractors.
The end diaphragms were checked visually using straight edges.
15 .2 .4 L a m i n a t i o n inspec t ion . To check that no significant lamination was present in the diaphragm
plates the three diaphragms were inspected with ultrasonic equipment after they had been cut to size.
Inspections were made along lines adjacent to the edges and at the intersections of a 225 mm grid over the
plates.
The upper flange plates were also examined following visual detection of a small area of delamination
near the edge of a plate.
38
(800) Dd0536316 1,400 5/78 HPLtdSo ' ton G1915 PRINTED IN ENGLAND
ABSTRACT
Loading tests on the stiffened diaphragms of a trapezoidal steel box girder: C A K IRWIN and J ALOE: Department of the Environment Department of Transport, TRRL Laboratory Rep- ort 824: Crowthorne, 1978 (Transport and Road Research Laboratory). A large model trap- ezoidal steel box girder containing three stiffened diaphragms was tested in the Laboratory as part of the 'Merrison' programme of research. The diaphragms contained differing amounts of transverse stiffening. Each diaphragm region was tested separately and strains, deflections and modes of collapse recorded. The details of fabrication, initial measurements and test proced- ures are described and the behaviour of the diaphragm regions discussed. The elastic stresses are compared with the results of finite element analyses and the collapse loads with panel and stiffener strengths calculated using Part 3 of the 'Merrison' Interim Design and Workmanship Rules.
ISSN 0305-1293
ABSTRACT
Loading tests on the stiffened diaphragms of a trapezoidal steel box girder: C A K IRWIN and J A LOE: Department of the Environment Department of Transport, TRRL Laboratory Rep- ort 824: Crowthorne, 1978 (Transport and Road Research Laboratory). A large model trap- ezoidal steel box girder containing three stiffened diaphragms was tested in the Laboratory as part of the 'Merrison' programme of research. The diaphragms contained differing amounts of transverse stiffening. Each diaphragm region was tested separately and strains, deflections and modes of collapse recorded. The details of fabrication, initial measurements and test proced- ures are described and the behaviour of the diaphragm regions discussed. The elastic stresses are compared with the results of finite element analyses and the collapse loads with panel and stiffener strengths calculated using Part 3 of the 'Merrison' Interim Design and Workmanship Rules.
ISSN 0305-1293