Mechanisms of energy absorption in special devices for use in earthquake resistant structures

A structure designed to resist earthquake attack must have a capacity to dissipate kinetic energy induced by the ground motion. In most structures this energy absorption is developed in the vicinity of beam to column connections. Recent research has shown that connections are not reliable when subject to cyclic loading, such as results from earthquake attack. Connections in steel frames deteriorate due to local instabilities in adjacent flanges, and in reinforced concrete frames alternating shear loads produce diagonal tension and bond failures which progressively reduce the strength of the connection. 
Much work in building research and earthquake engineering in laboratories throughout the world is directed toward increasing the reliability and energy absorption capacity of structural connections. In this paper an alternative approach to this problem is described. This approach is to separate the load carrying function of the structure from the energy absorbing function and to ask if special devices could be incorporated into the structure with the sole purpose of absorbing the kinetic energy generated in the structure by earthquake attack. 
To determine whether such devices are feasible a study has been undertaken of three essentially different mechanisms of energy absorption. These mechanisms all utilized the plastic deformation of mild steel. They included the rolling of strips, torsion of square and rectangular bars,  and the flexure of short thick beams. These mechanisms were selected for intensive study since they were basic to three different types of device each of which was designed for a separate mode of operation in a structural system. 
The characteristics of these mechanisms which were of primary importance in this study were the load displacement relations, the energy absorption capacity and the fatigue resistance. This information was obtained with a view to the development of devices for specific structural applications. 
This report describes the tests used to explore the basic mechanisms and the data obtained. It also include s a brief description of tests on scale models of a device which was designed to be located in the piers of a reinforced concrete railway bridge. 
It has been shown by the tests that the plastic torsion of mild steel is an extremely efficient mechanism for the absorption of energy. It was found that at plastic strains in the range 3% to 12% it was possible to develop energy dissipation of the order of 2000-7500 lb in/in3 per cycle (14-50 x 106 N/M2 per cycle) with lifetimes within the range of 1000 to 100 cycles. It was also shown that the mode of failure in torsion is an extremely favourable one for use in an energy absorbing device in that it took the form of a gradual decay. The other two mechanisms studied were both less efficient and less reliable than torsion and had capacities of 500-2000 lb in/in3 per cycle (3.5 - 14 x 106 N/M2 per cycle) and life times of around 200 to 20 cycles. Nevertheless they lend themselves to more compact devices than does the torsional mechanism and furthermore the devices may be located in regions in a structure where they are readily accessible for replacement after attack.


INTRODUCTION
The attack of an earthquake on a structure is through the interaction of the oscillatory ground acceleration and the inertia of the connect ions provides adequate f1exibility but doe s so at the expen se of large interstory drift in the lower floors. The energy absorpti on is developed entirely in the be am column co nnections whi ch are difficult to de sign f or cyclic loading.
The high eg st associated with steel frame construction has led to the development of reinforced concrete frames using what Blume (?) has called ductile concrete.
Thi s type of de sign suffers from a reduced flexibility and an increased weight leading to high internal forces ana, although it is possible by careful de sign and high quality construction techniques to enhance the energy absorbing capacity of the structure, it is not possible to provide very many cycles of plastic action without damage to the concrete.
In addition all structural frames in which the energy absorbing capacity of the system is provided by plastic action at connect ion s have the di sadvantage that the presence of plastic hinges at the joints can allow a severe interaction of non-earthquake 1oads and the earthquake generated displacements.
Composite buildings in which a 1ight frame is braced against lateral forces by a core or a system of shear walls have at first sight a number of di stinct advantages over moment resisting frames. However, the concrete core and the steel frame are badly matched in terms of st iffness and interstory deflect ion.
The different patterns of displacement require that the lateral loads, apportioned to each element to produce equal displacements, .are carried mainly by the core in the 1ower storeys and by the f rame in the upper storeys.
It has been pointed out by Newmark ( 1) that thi s can lead to a structure which is insufficiently flexible in the lower storeys. Also the energy absorbing capacity of the core is uncertain and that of the f rame cannot be developed.
There are al so problems of detailed de sign and co nstruet io nal pract ice to ensure the adequate interact ion of the core and the frame.
Other structural forms such as those with prestre ssed members and those of shell form have a 1imited capacity for energy absorption, as have bridge pier bearings.
In view of the difficulty of providing re liable energy absorbing capacity in mos t structural forms it seems logical to ask if special device s could be built int o the structure with the purpose of providing solely for the absorption of kinetic energy generated in the structure by earthquake induced ground mot ion. The provi sion of a system of such devices separate from the main load-carrying capacity of the structure would have a number of advantages to offset the additional cost of the devices. The main structure would operate under simpler and le ss severe conditions and its static and dynamic response could be analysed using elastic methods. A reduction in de sign effort and construetio nal cost is also possible through the use of simpler beam column connections which would not now be called upon to provide the energy absorbing capacity of the structure.
A better distribution of deformation might be possible wi th such a design approach.
The energy absorbing devices couId be de signed to operate at 1evels of seismic intensity lower than those at which structure s de signed according to current practice are damaged and could be replaceable when subject to a major earthquake.
The necessity to design for large plastic deformation s of structural component s and permits def1ections which exceed those of elastic design.
The damping provided by the yielding of some elements in the structure prevent s a resonant build up of deflection thus limiting the maximum deformat ions to less than would occur in a conventionally damped system.
The current approach to design is to attempt to combine this pla st ic action, usually referred to as ductility, with a certain degree of flexibility.
Flexibility is considered necessary to reduce the internal forces produced by the ground acceleration and to reduce the aceelerations imposed on the contents and occupants of the structure. Ductility is defined to be the ratio of the maximum deformation prior to collapse to that at initial yield.
In a sense it represents the re serve deformability beyond the elastic range be fore unacceptable damage occurs.
Thus in general terms we may say that the de sign philosophy is to combine flexibility and ductility to minimize the internal forces and to prevent collapse if the elastic deformation of the system is exceeded.
The design approach on the basis of most building codes is to replace the earthquake attack by nominally equivalent lateral loads derived by the use of empirical formulae and to proportion the elements of the structure particularly the moment resisting beam column connections to carry the se horizontal loads• The structure resists the earthquake attack in an entirely different way.
As the ground mot ion f eeds energy into the stru cture, energy dissipating elements act to minimize the excursions and prevent collapse.
Thus the concept of ductility based on unidirectional loading is unsatisfactory.
It is important to emphasize the cyclic nature of the earthquake attack on a structure.
In the 196^ Alaskan earthquake for example, the ground mot ion had a predominant period around 1 sec, which is also a typical fundamental period for a high rise building and a duration of at least three minutes, In such a case the energy absorbing mechanisms in the structure could be subject to around 200 cycle s of loading.
The Alaskan earthquake was, of course, an example of an earthquake of exceptionally long duration, the number of cycles for a more typical major earthquake and accompanying aftershocks would be perhaps 100 cycles.
Recent tests involving cyclic loading on standard beam-column connections for steel frames by Popov et al (k, 5) have shown that plastic instability in flange s adjacent to the connections has the effect of reducing the energy absorbing capacity of the connections and that thi s instability does not appear in unidirectional loading but only after reversal. Test s by Bre sler and Bertero (6) on cyclic loading of reinforced concrete beams have shown that their stiffness and strength decrease when subject to cyclic loading. The implication of these re suit s is that reinforced concrete structure s designed according to conventional practice suffer from a rapid deteriorat ion under cyclic loading.
Thus ductility, reflecting as it doe s re serve under unidirectional loading, does not adequately repre sent the re serve against cyclic loading if the system contai ns element s which deteriorate under cyclic loading.
The steel frame with moment resisting imposes severe constraints on the designers in terms of materials, detailing and structural forms, A source of difficulty is the imposed loads which components must withstand while undergoing pi as tic deformations.
When special structural components are introduced with the primary function of absorbing energy there may be increased reliability, lower costs, and a wider range of design possibilities. The basic attraction of the concept lies in concentration of the inelastic deformation in a replaceable device specifically designed to provide energy absorption.
The specificat ion for such a device might be expressed in the following way.
It should not be involved in transmitting the static loads of the st rueture; it should operat e only under earthquake attackj it should perform at least 100 cycle s of energy absorption without deterioration and should be replaceable when subject to a major earthquake.

THE ENERGY ABSORBER AS A STRUCTURAL ELEMENT
An approach to structural design somewhat similar to that proposed here has been used in Japan, where a number of tall buildings have been designed with reinforced concrete panels. Each panel ha s a set of vert ical slits as a re suit of which the panel act s as a series of reinforced concrete columns. When a pane1 is deformed by inter story deflection, hinge s are formed at the top and bottom of each effective column thu s absorbing energy (8). Thi s appears to be the first use of components with the primary functi on of absorbing earthquake induced energy, and while constituting an advance in aseismic de sign the use of the se slit panels doe s entail certain di sadvantage s. They add substantially to the weight of the structure and consequently to the internal forces generated by the earthquake motion.
More over, as mentioned before, reinforced concrete suffers a rapid deterioration under cyclic plastic def ormat ion.
It would seem more logical to use reinforced concrete to carry vertical loads and use plastically deforming steel to dissipate energy.
In the course of the present project a number of basic mechanisms of energy absorption have been studied.
In each case these utilized the plastic deformat ion of mild steel, and included the rolling (with bending) of f1 at strips, torsion of square and re ctangular bars, flexure of beams of rectangular section and combinations of the se.
The aim of the tests was to determine the energy absorption capacity, the fatigue resistance, and the stability of the material when 1oaded in the above ways. A description of the test procedure s and re suIts will be given in later sections.
On the basis of the results of these tests three main type s of energy absorbing device have been developed and tested.
The se three type s use e s sent ially different mechani sms of energy dissipation and are envisaged as being applicable to three di st inct situations in structural systems. The devices are as follows; TYPE A. Thi s device make s use of the rolling (bending) of f1 at stri ps of mild steel.
It is designed to be 1ocated between f1exibly based shear walls in a composite buildi ng.
The device operat e s between adjacent surf aces who se relative motion is directed parallel to each other.

TY P E B. This devi ce uses a combination of torsion and bending (with torsion predominating) of square or rectangular bars.
It operate s be tween surface s mov ing to ward and away from ea ch other.
The load capacity of thi s device can be made very high and it is designed to be used in foundat ions or in association with a shear wall system, TYPE C. This device utilizes the flexural behaviour of short rectangular beams and the phy s ical dimen si ons of the device make it su i table for insertion in diagonal bracing in steel or re inf orced concre te frame s to pr ovide the energy absorpti on normally developed in t he vicinity of the be am column conne c t i ons. In addition to those shown other combinations are po ssible in which all t hree devi ce s are used concurrently.
The present report wi 11 be c oncerne d wi th the study of the basic me chani sms of energy absorption from which the above device s will be developed.
The development of the devices wil 1 be reported in a subsequent paper.
To obtain an estimate of the magnitude of the energy absorpti on which the se devices could be called upon to provide in a typical structural situation we consider here a very simple model of a vibrating sy stem including hysteretic damping.
We con sider f urther that the system, of mass M and period T, is subject to impulsive e xcitation which is synchronous with free vibrations of the system ana that the damping mechanism which f or simplici ty will be assumed to be of Coulomb type, is large enough to damp out each impulsively generated oscillation in e xactly one cycle. This is not intended to be a repre sentation of an earthquake induced motion but is used to avoid the difficulties of numerical integrat ion nece ssary if actual earthquake excitation is used.
It is considered that if the damping is adequate to kill each vibration in one cycle it will be adequate to prevent th e resonant build-up of earthquake induced vibrations in an actual attack.
It is usual to specify a maximum level of acceleration in the asei smic design of a structure. We note that an oscillator of period T experiencing a maximum accelerat ion a develops a maximum velocity aT/gTT* The free vibrations of an oscillator damped by coulomb friction are conveniently repre sent ed by a phase plane plot as shown in Fig. 3. The axes are displacement and velocity/frequency and a solution whi ch takes the system from init ial condi t ion s of specif ied ve1ocity and zero displacement to the final conditions of zero velocity and displacement is shown in the figure.
The quantity r Q which defines centres in the hodograph is given by where F q is the frictional force and K the elastic stiffne ss. For the purpose of this example we take T = 1 sec, typical of a 20-storey high rise structure and assume a floor weight of 10 lbs (k5Q,000 kg). The design acceleration for a building of this period may be around 0.2g. Thus the required F Q is ^0,000 lbs ( 180,000 N) and the displacement 1^ inch (3-8 cm). The total energy dissipation requirement per cycle is of the order of 12F Q r 0 = 180,000 lbin {6800 NM) .
The displacement of l£ inch is somewhat large as an interstory drift; on a 10 ft storey weight it repre sents a relative displacement of 1 in 80• Taking 1 inch (2,54 cm) as a more reasonable number this would increase the required force to 60,000 lb (2?0,000 N). If this capacity were to be provided using devices of type C inserted in diagonal bracing it is probable that two devices would be used; if it were provided by a device of type A located at each storey level the force required would be reduced in the ratio of the shear wall width to the storey height which ratio might be of the order of one half.
Thus for these devices 30,000 lb (135JO00 N) would seem to be a reasonable estimate of tne magnitude of the forces required.
It is not so easy to estimate the requirement s for a device of type B which might be used in foundations or in seismic gaps between non-synchronous parts of a st ructure.
However, the use of a device of this type has been proposed for a bridge project of the New Zealand Railways.
For this reason a detailed analysis ot the structural system proposed for the bridge and including an energy absorbing device of this type has been made and is given in detail by J. L. Beck and R. I. Skinner (9). to which reverence may be made for the details of the analysis.
A brief summary of those aspects of the project which relate to energy absorption devices will be given here• The New Zealand Railways is at pre sent engaged in a program intended to replace conventional steel railway viaducts with low maintenance reinforced concrete structures• The example shown in Fig. k  As point ed out earlier in this report, a disadvantage of reinforced concrete is its inability to provide plastic action without rapid deterioration.
To provide some plastic action in the system the Railways engineers suggest ed that steel pins be included in the pier legs near the base• The full loads, static and dynamic, in the legs would be transmitted through the pins and overload inducing yielding of the pins would provide the plastic action. A detailed dynamic analysis of the sy stem including the pins enabled the response of the system to a typical earthquake to be computed ( 10) and it was found that there were certain difficultie s in prov iding adequate energy absorpti on and that exce ssi vely high tension stre sse s could be developed in the legs. These difficultie s are largely due to the f act that the pins have to be able to tran smi t the entire static load.
A modificat ion of the sy stem to allow the leg to step off its base was proposed.
Here the problem of tension in the leg is removed but the sys tem is almost ent irely without energy absorption or even normal levels of damping.
Under certain e xcitations excessively high displacements could be developed and the st ructure could vibrate for a considerable period of time after a di sturbance.
To provide energy absorption in the stepping bridge it was proposed by engineers at PEL to use torsional energy absorbers in the legs of each frame. The devices would be arranged in pairs on each side of a central guide pin, and would be located in such a way that they were operative only when the leg was stepping of f it s base. A computer analysi s (9) of the proposed sy stem has shown that two devices per leg, each providing around 30,000 lbs (135*000 N) with a di splacement of around 1 H (2.5 cm) would be required to bring the earthquake induced oscillations to an acceptable 1evel.
It will be shown in the later sections that the energy absorbing capacity (in terms of energy dissipated per unit volume of material) of mild steel is so large that the se energy absorption requirements can be developed by devices of fairly modest dimensions,

TEST RESULTS ONi BASIC MECHANISMS OF ENERGY ABSORPTION (a) Rolling (Bending) of Thin U-shaped Strips
The mechanism of energy absorpti on in the U-shaped strips is very simple. The strip is initially in a semi-circul ar form with two equal straight sections on either side• When one side is moved relative to the ot her the semi-circular portion rolls along the strip and work is done at the two point s where the radius of curvature is changed from straight to the radius of the semi-circle and then from this radius to straight.
Thus at any instant the energy dissipation is concentrated at two transverse surfaces but the se two surface s move along the strip.
The maintenance of the semi-circular shape can be enhanced by including a roller held in position in such a way that it can move with the semi-circular port ion but this is not essential for the energy dissipation process.

The investigation of the energy absorption of the U-shaped strips utilized the test set-up shown in Fig. 5«
Alternating tension and compression loads were applied to the central bar of the double strip system, by a standard Instron te st ing machi ne.
For the purpose of interpret ing the result s it is convenient to refer to Fig. 6 which shows the loading device in detail.
The steel strips te sted were of a variety of different types of st eel ranging from ordinary mild steel to special deep drawing steels and in addition strips of stainless steel were also tested.
The width (b) of the strips was 9 mm and they ranged in thickness (t) from 0.75 mm to 2.00 mm.
Four spacings were used namely, 9 > 11> 13 > 15 mm allowing a wide variat i on in the rat io t/R where R is the average bend radius. The strips were cold bent from flat around a mandrel of roughly 1.5 mm less than the spacing.
Each specimen was tested under controlled displacement cycling, hysteresis loops being recorded during the test.
A wide range of preset di splacement s were used.
The result s of immediate interest are the peak load, the energy dissipated per cycle, and the to tal number of cycle s to failure. The mode of failure for this mechanism took the form of a localized kinking of the st rip foil owed rapidly by complete transverse fracture.
It was observed that be f ore the initiat ion of kinking the initial semi-circular shape was fairly well maintained even at relatively large di spla cement s (e.g.

cm).
In al1 situations involving reversed loading the usual theory of perfectly plastic behaviour doe s not repre se nt the response with any degree of accuracy.
In general the initial yield follows the elastic plastic model but on reversal and on subsequent cycles the well defined yield point disappears and the response curves differ substantially from the elastic plastic idealization.
Nevertheless a rigid plastic analysis is of considerable value in identifying relationships.
Thus we consider first the plastic analysis of a typical specimen.
An upper bound to the yield load is given by assuming a velocity field the simple st of which is to as sume that the strip re tains its circular shape.
The load applied to the centre post of the double strip system does work at a rate Pa where A is the di spla ceme nt rat e . The rate of dissipation of energy D in each strip is given by where M is the moment, K the curvature rate and ds the element of length along the strip. The curvature rate is singular; the lengths over whi ch it var ies are zero but these lengths move along the bar with speed A . Writing the integral in the form 2 and noting that M = + M Q j(defined below), that K changes from 0 to 1 / R to 0, we have D = |s J^K dt * f (n Q ± * <-M 0 )(-|)J Thus an approximation to the yield load for two U-strips is This re suit does not take into account the influence of the force P on trie yield load moment M Q and due to the method of loading such an interaction is possible.
The yield condition for combined axial force P and bending moment M on a rectangular beam (see prager and Hodge (11) is the yield moment in the absenee of axial load and P Q the yield axial load in the absence of bending. Thu s the above re sult shou1d be replaced by -£ 6 -l^f) 1 2 Since M Q = TJ0^b t and P q = (f y bt for a rectangular cros s section, where is the yield stre ss in simple tension the correction term In the most extreme case tested namely t = 2 mm and R = 5•5 mm thi s rat io is less than 1 .0% and the average over all specimens is around 0.3% so that interaction of thi s kind need not be taken into account.
The yield load is not a quantity of particular intere st in a cyclic te st since after a very few cycles no well defined yield point exists.
Neverthele ss it suggest s correlations between quantities which can be useful in the design of devices based on the particular mechanism under study.
In the present case the result suggests that the maximum load for two U-strips wil1 be given by a formula The strain which is developed during a test does not depend on the stroke; on the assumption of plane sections in the deformed region and circular curvature it is given by and this ranges from 5.3% to 17%.
Since the object of these devices is to dissipate energy, the energy dissipated per cycle is a result of some importance.
This can be estimated from the hysteresis loops recorded during each test.
Due to the fairly substantial strains which are developed and the fact that cycling to spread from the points at whi ch it is theoretically located and thus invo1ve s more material in the doubly 1oaded region than the above calculation predic ts..
The implications of thi's re sul t f or the de sign of a device are that the st roke shou1d be selected to be not more than ITR but should not be much less than this value in order to minimize the amount of material which is undeformod during a cycle of load ing, and that the st rain level be kept to a low enough value to en sure that the specified life is achieved. A large number of tests at different strain levels using several different stroke to radius ratios we re carried out.
The re suit s sho w a certain . amount of scatter but gener ally reflect the trends indicated abov e.
The re sult s hav e been used to prepare the diagram of cycles against st rain and stroke shown in Fig. 8.
In the course of the test program a number of different approache s were used in an at tempt to overcome the problem of kinking of the strip which led to it s final collapse.
The onset of kinking generally took place several cycle s be fore final collapse but duri ng these terminal cycles the peak load and the shape of the 1oad displacement curve became very unpredictable. A specified peak load and a reliable hysteresis loop are, of course, a prerequisite for a successful working device.
To a11empt to overcome these difficult ies, con straining roller s were used in some te st s and rollers with guide s in other s. The con straining rollers worked satisfactorily giving a somewhat increased peak load, and a longer life, but required adjustment during the test to maintain contact with the strip whicn tended to increase somewhat in length.
Thi s slight increase in length prevented the system with bo th roller s and guide s from working satisfactorily.
An alternat ive to the roller system was to use stainle ss steel for the strip material.
Stainle ss steel strips gave consistently life times which were longer than the mild steel strips; the work hardening properties of the mater ial appeared to prevent the localization of deformat ion which produced the kinking in the mild steel.
Although the use of rollers and the use of stainle ss steel led to an improvement, they are not con sidered to be use f ul for the design of a full scale device• The expense and complication of the roller design together with the need to adjust it in operation, are major disadvantages and the expen se of the stainle ss steel in comparison to mild steel is a handicap as also is the fact that for a ful1 scale device the f or c e s required to form the originally straight strip into the required semi-circular shape would be much larger than those needed for mild steel.
It appears that simplicity of the mild steel, unrestrained device can be achieved if the strain level and the stroke are kept wi thin the limits required to produce lifetimes in excess of the specified minimum (e.g. 100 cycles). In view of the fairly smal1 structural displacements which wil1 be developed in a building under earthquake loading these may be expected , to be in the range 2. 5 to 5.0 cm. and the fairly high forces required of the device (e.g. 150, 000 N) means it is likely that the ratio of stroke to radius will be such that life time s in the range 100 -200 cycles could be reliably guaranteed with useful values of the plastic strain.
For example, a single strip device required the st rain level is constant but the de forming region move s along the strip the 1oad dis placement curve of the deviee is very rectangular and the enclosed area was found to be consi stent ly 90% to 9k% of the rectangle based on the peak load.
Thu s an average value of the energy di ssipated per cycle is given by c (fbt 2 s/R A where c i s a f ac tor of the range . 90 to . 9 ^, <T is the effective cyclic stress and S is the stroke.
The lifetime of an energy absorbing device is naturally of considerable importance and it is useful to identify the factors which contribute to the failure of the device.
In the case of the double strip system the quantit ie s which appear to influence the result s mo st strongly are the stroke and the level of maximum strain.
It is generally accepted (see e.g. Morrow {12) ) that the life of a structural element subject to cyclic 1oading is controlled by the amount of energy di ssipated per unit volumei of the material.
In the case of the U-shaped strips the volume of material involved in the deformation depends on the length of the st roke. When trie half stroke is less than the original bent length i.e. TfR the length of deformed material in each strip is just the stroke length itself.
When the half stroke exceeds T7 R the length involved is (j| + Jff R).
The energy dissipated per unit volume per cycle, e, is given by A e * c (Tt/2R for S < 2 7Tr and 6 " c * t/2R s-rrm for S< 2 TTR In bending and unbending wi th maximum strain.t/2R the work done per unit volume would be 2c g t/2R, but without unbending ( S < 2 TfR) the deformed portion is loaded only in one direction.
In the second case (S > 2 7/R) a portion of the strip of length s/2 -JfR is subject to bending and unbending.
The second result is A thus only an average and the dissipation is cft/2R in the two regions each ^>f length TFR whi ch are def ormed only once and cfft/R in the central region of length 5/2 -TfR between the se which is loaded twice.
The f inal collapse of the system, generally took the form of the development of a region of highly localized deformation, the format ion of a kink on one or both of the strips, followed by rapid transverse fracture thus tending to corroborate thi s pattern of energy di ssipation; for small strokes the final fracture occurred in one of the lateral regions and for large strokes in the central region.
This suggests that the number of cycles to failure wouId decrease very rapidly for stroke s greater than 2TfR and would tend to decrease* with increasing strain.
In principle the life of the device should be independent of stroke when the stroke is less than 2 TTR.
In fact it is found that the life increases with decreasing stroke even in thi s range.
The rate of decrease of cycle s wi th stroke appears to increase markedly when the. stroke is greater than fl R whi ch is probably due to the fact that the deformati on tends with to develop a peak load of 25,000 lb (112,000 N) might have the following dimen si on s. We as sume that a strain of 10% is po ssible and using thi s we obtain b = 20 cm, t = 2.7 cm and R = 13.5 cm, the total width of the device is s = 19 Three materials were used in the tests, as follows : (a) Cold rolled mild steel as delivered (severely cold worked) (b) Cold-rolled mild steel annealed (c) Hot rolled mild steel from J", 1" and 2j» sizes.
In each te st the bar was cycled at the maximum rate of the Instron machine, (equivalent to 1 cycle per minute in the case of a 5 inch lever and.a + 5 cm stroke). A typical set of re sults are shown in Fig. 10.

For each test a few complete torque twist loops were drawn to determine the initial hardening behaviour then the di splacement axis was replaced by a time axis and a plot of maximum torque as a function of cycles was obtained.
Reduced torque vs cycle curve s for several materials are shown in Fig. 11.
The cold rolled material shows an exponent ial decrease in maximum torque beginning from the first cycle• The hot rolled material from the J w size work hardens during the first few cycles then shows a linear decrease in peak torque with cycles. The hot rolled material from the 2^" size work hardens somewhat less, exhibit s a fla t portion and then a 1inear decay.
A few similar test s were carried out on bars of circular section. To facilitate gripping these specimens they were machined from square stock, a smooth transition region being provided.
The se bars were tested in 69 both the annealed ana unannealed state s and in al1 cases failed due to transverse cracking at the transition region. The unannealed bar s failed during the first reversal and the annealed af ter se veral rever sals.
It is not believed that the se tests constitute an adequate test of the application of bar s of circular cros s section.
However, the difficulty of providing grips whi ch do not introduce stress concentration problems remains and is a substantial factor in favour of square bar s. Ther e are sever al observation s of a general nature whi ch we should mention he re. Al1 materials tested exhibited on fir st yield a flat portion on the torque twist curve followed by a 1inear hardening port ion. On reversal the torque twist curve doe s not e xhibit a flat port ion and is in fact curved over the ent ire region of reversed torque. The deviat i on from elastic behaviour begins in general before the torque changes sign. The torque twist loops rapidly reach a st eady state shape whi ch is very different from the elastic perfectly plastic idealization.
The area within a typi cal loop was e st imat ed from a number of example s to be in the range 60 _ 65% that of the rectangle defined by the extremities of the loops. Further it is clear from thi s set of re suit s that cyclic loading is producing le ss har den ing than monotoni c 1oading, and is more damaging to the materi al.
For example, the cold rolled mat erial in the unannealed con dit i on could be twi sted unidirectionally to a twi st of about one revolution per inch on a \* squar e or circular bar while continuing to harden. With cyclic loading on the other hand, for a maximum rotation of + 22J° the square bar progressively softened and the circular bar failed during the firs t reversal. A comparison of unidirectional as opposed to cyclic 1oading for hot rolled mild st eel is shown in Fig. 12 in which curves of torque versus cumulative plastic twist are shown.
There the hardening during the first few cycles is particularly severe, but is not comparable to that for unidirectional loading.
It was also noted that even at the very substantial twi sts ther e was no apparent change in length of the bar. Also noted during the unidirectional tests was the fact that there were no apparent cracks along the length of the bar. However, reversal from any substantial level of twist produced immediately a pattern of longitudinal cracking.
The pat tern of failure in the cyclic torsion of square bar s is di fferent from tha t experi en ced by the U-shaped strips. The peak torque achieved at the end of each stroke remains constant for a number of cycle s whi ch may range from less than 10 for high s t ra in s to more than 100 for low strains. A progressive drop in the peak torque follows, the rate of the decay depending on the strain, and associate d with this is a pat tern of longitudinal cracks extending the ful1 length of the bar. No precise point of failure can be determined as the bar continues to dissipate energy at a progressively decreasing rate as the torque falls off. This pat tern of progressive failure is felt to be a con si derable advantage of torsion in square bars as a mechanism of energy absorption in that at all times the integrity of the bar is maintained, and the collapse of the bar occurs in a con trolled non-catastrophic manner.
Since the primary purpose of the devices wil1 be to absorb energy it is useful to 70 thi s var iat ion in the maximum shear strain due to bending is to maintain the length £ and vary the 1 ever arm s while maintain ing the same nominal angle of rotation. 'The result s of such tests are shown in Fig. 1^ (a) and 1^ (b). In Fig. 1^(a) we plot torque against cycles for \ square bar s of annealed bright mild steel with J = 2**5 whi ch corresponds to a nominal shear strain of 3.75%, and S = 1", l|" and 2" corresponding to £/s = 2, 1.33, 1.

00.
There is very little difference between the lJ M and 2" curves but the 1 M lever curve shows a very rapid drop in torque after 300 cycles• In Fig.  1^ (b) the same results are plotted for clear lengths of 1", corresponding to a nominal 7 • 5% strain.
Here the curve s do not differ very much one from the other.
The result s of a series of tests on square hot rolled mild steel bars is shown in Fig. 15.
In this case the lever arm was maintained constant at 2 M an d the clear length increased in steps from 1* through 2", 3" to k>\»». As noted in the previous section the re is evidence that this steel is inferior in it s cyclic plastic fatigue re sistance to the annealed bright mild steel, (comparison of the case £ -2" and s = 2 M with the equivalent case £ -1", S -1" for the \" squar e bars shows that the decay is more rapid).
However, the failure mode pattern is the same. For £ f $ -1.50 and less, there is a gradual decay associated with longitudinal cracking of the bar; for £/ s = 2.00 and above, the torque remains con stant followed by a rapid drop associat ed with transverse cracking of the bar.
In repeated tests the decay curve when longitudinal cracking occurs is repeatable, whereas when transverse cracking occurs the number of cycles at which the rapid collapse occurs varies widely from test to test.

A curious and somewhat unexpected phenomenon associated with the combined torsion and bending is a lateral displacement of the center of the bar toward the loaded side.
This appears to be due to the interaction of the rotation of the center portion of the bar and the applied force.
The machine applie s a vertical for ce so that when the lever is near the lower extent of the travel and moving downward the bar is yielding and experiences a force component which for the central portion at least is in the originally horizontal direction.
When the lever is moving up and near the top there is again a force component in the originally horizontal direction.
The plastic part of the downward displacement produced by the downward force is cancelled by that produced by the upward force. How ever, the displac ements produced by the force components in the originally horizontal direction are additive and a cumulative lateral drift of the center of the bar results. Roughly then the initiation of peak 1oad decay appears to be around k 105 lb. in/in 3 (2.a x 10* N/M 2 ) accumulat ed di ssipation for thi s material. This does not of course mean that the material cannot dissipate more energy, the linear decrease in peak torque with cycles implie s that the total energy dissipation capacity of the material is of the order of 9 x 10-5 to 13 x 10-5 lb. in/in 3 {7*7 x 10 9 to 9*0 x 10 9 N/M 2 ) .
The results of this test series indicate that the hot rolled mild steel in the 2^w size has highly favourable behaviour from the point of view of an energy absorbing devi ce in a structural system, if used at st rain range s around At this range, cyclic hardening is small and achieved wi thin the fir st few cycles, and a range of 20 0-300 cycle s of uniform peak load follows with a substantial reserve of strength left.
On the basi s of the se result s the de sign of a sui table device incorporating torsion as the primary mechanism was explored. It was found that a substantial simplification of design could be achieved if the load was applied to the torsion bar in such a way as to develop flexure in addition to torsion.
To determine that the energy absorption properties wore not adversely affected by the addition of flexure the foil owing tests were carried out•

(ii) Combined Torsion and Bending
As pointed out in the previous section the design of a torsional energy absorbing device can be greatly simplified if it is possible to apply the torque through a single lever at the center of the bar.

13•
Although a certain amount, of vertical deflection occurs under the mid-point of the bar and thi s has the effect of reducing the total angle of twist applied to the bar the deflection at the end of the lever arm was taken to be the specified quantity in the series of te sts.
This vertical displacement has no effect on the torque at which yield is initiated but since it reduces the maximum shear strain to which the bar is subject it tends to reduce the maximum torque in the bar• This is particularly noticeable in bars with long clear lengths.
One way of minimizing

(iii) Tor si on Tests on Rectangular Bars
Following the tests involving torsion of square bars which were de scribed in the previou s two sec t i ons, 3 (i i) (a) and (b), a number of scale model devices were designed based on the results of these tests.
During the te sting of the scale mode1 devices it became clear that gripping of the square bar in the device constituted a more substant ial problem than it had done in the pre 1iminary tests. The difficult ies wh ich arose and the several approaches to their solution wi11 be outlined in the fol1owing section.
One approach was to consider the use of a torsion bar of rectangular cross section and to thi s end a series of tests on combined torsion and bending of rectangular bars was undertaken.
The apparatus, (see Fig. 16) used in the t orsion te st ing of rectangular bars had be en devel oped for 1 11 square bars and using packing pieces of various thicknesses in the grips it was possible to test bars of 1 M width and varying thickness.
It was a feature of this apparatus that the bar could be loaded wi th the wider f ace either hor izontal or vert ical.
Thus two bars each of cross sections 1" x £ H (2.5k cm x 1.2? cm), 1" x |" (2.5k cm x .95 cm), 1" x (2.5*4-cm x . 6k cm) were tested, one of each pair having the wider face horizontal and the other having it verti cal.
The lever arm, angle of rotation and bar length were the same in each te st. A summary of the test results together wi th tho se for a square bar of 1" (2.5** cm) side of the same length, lever arm and maximum angle of rotation, is given in Table I. There are two points which are immediately apparent from thi s table. The first is that the rate of decay of the rectangular bars is less than that of the square bar, and is increasingly less as the bar width to thi ckness increases. The second is that there are no out standing dif ferences between bar s in the horizontal or verti cal positio n. The peak loads and decay are the same within the rather large variability common in the se tests. This latter re suit is somewhat unexpected since the elastic bending stiffne ss and the plastic yield moment when the wider face is hor izontal are both much less than when it is verti cal.
The explanation for thi s re sult appears to be that the bending response, both elastic and plastic, is of negligible importance in the case of such large torsional displacements f or the se ratios of length to lever arm.
To gain an insight into the improved decay behaviour of the rectangular bars, we consider the perfectly-plastic analysis of the torsional response.
The torque T in the case of a rigid perfectly-plastic material is given by, (13) where a is the longer side and b the smaller side of the rectangular cross section, andf is the yield stress in shear. We assume that the same f o rmula wilj^ apply with replaced by an effective stress "J? dependent on the strain. The energy dissipated per cycle per unit volume of material is thus: For the 1" x |*», 1" x 1" x -\" bars this rat io is 0.625, 0.^9, 0.^1 respectively. If we accept that the primary factor in the damage of the system is the energy di ssipated per unit volume of the material, the explanati on for the reduction in the decay of the peak 1oad is clear. The rectangular bar is less efficient in its energy absorption capacity than the square bar and becomes increasingly less efficient as the ratio of the long side to the sho rt side increases. Thus if a certain energy absorption per cycle is specified it is necessary to use more material if rectangular bars are used.
On the other hand, the amount of active material in the energy-absorbing devices is not great and increasing it by a factor or two, f or example, may in mo st circumstance s be an acceptable penalty to pay for the increased ease of gripping the bar.

( c) Tests on Flexural Energy Absorption
An obvious application of the energy absorbing device approach is to use them to replace the energy absorptio n which takes place in a multi-storey frame at the beam column connections by that from devices located in a system of diagonal bracing.
A design in which the frame is required to resist vertical and wind load and the bracing provide s the energy absorption capacity could lead to a lighter and less expensive structure if suitable energy absorbers were available.
The bracing need not be over the entire frame. A computer study of the effect of yielding of bracing in mult istorey frames was carried out by Hanson and Fan ( ik).
The basic structure under study was a single-bay multi-storey rigid-jointed frame with a variety of bracing configurations ranging from f ully braced, through two con figurations of partial bracing, to fully unbraced. They found that early yielding in the bracing re suit ed in energy di ssipation requirement s for the girders significantly below those needed f or the unbraced frame s.
In addit ion the energy dissipation appeared to be more uniformly distributed throughout the structure.
The difficulty of designing such a device lies in the fact that it mus t be able to fit wi thin the thi ckness of a wall panel.
The torsional device by its nature is three dimensional in that the load is applied in one plane while the active element, the torsion bar, lies in another plane. However, flexure is an e ssentially planar mechanism and the device developed f or thi s appli cation has be en based on this principle.
The anticipated working form of the device has been shown in Fig. 1 (c). A simplified form of the device was used to study the re sponse of the basic mechanism, to determine its energy absorbing capacity and fatigue characteristies. Thi s is shown in Fig. 17 In each of the f1exural tests the peak load was achieved at around the second cycle and maintained con stant until one or two cycle s before failure which was rapid and due to a t ransverse crack acros s one of the beams at one of the four point s of maximum moment. There appears to be considerable scat t er in the results but the trend appears to be that the lifetime reduces rapidly wi th increasing stroke. Table II shows a summary of the results.
The int ere s ting conclusion is that, in terms of total energy dissipat ion per unit volume during the lifetime of the system, the short span beams are superior. The explanation f or this may be the fact that for a short beam ( ^/Jt < 10) the thickness of the beam and the pre sence of the guides tends to spread the plastic deformat ion more uniformly along the length of the beam, thus using the material wi th greater efficiency.
In an actual devi ce it would be an advantage to keep the elast ic deformations of the device to as low a value a s po ssible whi ch is compat ible wi th the other requ irements of the system, ana since the elastic def ormat ions will increase with increasing slenderne ss of the beams, this is another factor in favour of using short beams in a device of this type. It is clear f rom the test re suits that thi s mechani sm i s not so efficient in ene rgy absorption nor so fatigue resistent as is the torsi on of square or rectangular bars, but its advantage is that it can be conveniently located and that it can be readily replaced in the event of earthquake damage.

CONTINUING RESEARCH
The most important area of continuing re search on this approach to earthquake-resistant design is the development of full scale devices which wi11 develop energy-absorption capacities of the order of magnitude requi red for actual structural systems. A certain amount of work along these 1ines has already be en carried out with a vi ew to providing a torsi onal device for the piers of the re inforced concrete bridge described in Section 2. The general form of the device is shown in Fig. 1 (b) and a number of models which used 1* square torsion bars were construe ted and tested.
The testing of these models brought to 1ight a number of problems which were not apparent from the test series on the basic mechanism.
Details of the development work needed to overcome the se prbblems will be given in a later report.
Briefly the major problems arose out of the transmission of the forces from the levers into the torsion bar. To simplify the construction technique, the square hoies in the levers were roughly cut to shape and the levers welded to the bar by fillet welds on both sides. This meant that the weld was used to transmit the torque into the bar and it was found that the device failed at a lower number of cycles than predicted by the basic tests due to a transverse cracking at the welds.
To attempt to alleviate this the entire system was heat tre ated after welding but no improvement was achieved.
A further approach was to machine the 1 M square bar to £ n square between levers and width b. These beams are located in such a way that they can be de formed to subs tant ial plastic st rai ns without the de ve 1 opmen t of 'forces in the originally axial direct ion. The device is subject to a cyclic di splacement with stroke S. The maximum central displacement of one beam, assuming symmetric response,i s s/^.
The di splacement s used in the tests are of the order of the thickness of the beams, The maximum angle of the def ormed beams middle surface is of the order of 30° and thus an axial f orce in the beam is developed, the magnitude of this force is nevertheless sufficiently smal1 to have a negligible effect on the bending response.
A series of devices of the type shown in Fig. 4? were tested under di splacement-controlled cyclic loading.
It was found from an initial series of tests that the life time of the beams could be considerably enhanced by the use of a system of re straining guides.
The guides are clearly seen as the short cantilevers with rounded ends in Fig. 17.
They were short lengths of mild steel of the same width and somewhat thinner than the beams and struck out a di stance of half the ir width from the clamping edge. The se guides had the effect of distributing the deformation in a more uniformmanner near the clamped ends, The criterion which was used to determine the optimum dimensions of the guides was the point on the beam at which the final crack developed.
If this point lay directly under the clamping edge the guide was considered to be insufficiently rigid and if at the edge of the guide s the se were taken to be too rigid. The re sult s quoted in what f ollows pertain to those test s in which guides adjusted according to the above criterion were used. A typical hysteresis loop is shown in Fig. 18. These loops are qui fee different from those obtained for the U-shaped strips or for the torsional device.
On first loading a well marked yield point is noted but it is followed by rapid linear hardening.
This rapid 1inear hardening has the effect that the peak load and the energy absorption per cycle are strongly dependent on the stroke. The use of the guides makes it difficult to accurately assess the maximum strain level reached in the te st but the strain like equivalent parameter /jfi can be used in interpret the results.
Plots of peak load as a function of ^$$f2 are shown in Fig. 19• The straight line drawn through the points indicates that for the purpose of design the peak 1oad can be estimated from p * 5^2 (i +<* st / /2) with jp * 320 x 10 6 N/M 2 and ®& = 20 The yield load predicted by a rigid plastic theory for this situation is weld the levers again on both sides to the 1 M square portion. Again transverse failure with a lower number of cycles than predicted occurred.
A satisfactory system was finally achieved by machining V-notches in the levers and bolting them to the bars using high tensile bolts.
In this approach the forces are transmitted to the bar through surface contact pressures.
In order to keep the contact pressure below the yield point of the material fairly thick levers are required or, alternatively, the cross-section of the bar may be shaped down as before to reduce the moment to be transmitted.
Both of these approaches were used and worked.
However an alternative approach which was found to lead to a simpler form of device was to use a rectangular bar as the torsional element.
In this case the bar produces, for the same surface area per unit length, a much smaller moment than the square bar and thus the gripping pressures are less critical.
The final device is shown in Fig. 20.
It will be noted that there are two central levers. Using this the welding can be confined to the outside of the outside levers and to the inside of the inside levers. The moment is transmitted into the bar through contact between the machined surfaces of the slots in the levers, the welds being used only to maintain the levers in place on the bar. This device using a 2 M x J" bar developed a force of 2 tons (20,000 N) with a displacement of 1 cm, developed an energy 2 absorption per unit vol of 11.6 x 10 N/M per cycle and maintained this for 200 cycles with a subsequent very gradual decay.
At 500 cycles the peak load had reduced to 80% of the maximum.
Accompanying this decay were the predicted pattern of longitudinal cracks. The device is thus entirely satisfactory and on scaling up by a factor of 2.5 should provide the requirements for the railway bridge.
Such a full scale model is under development.
Full scale devices for using the other mechanisms are also under development and it is anticipated that it will be possible to test devices by subjecting them to the time history of displacement that they might be called upon 'to undergo in an earthquake attack.
The testing of the devices at the earthquake frequencies is considered to be a matter of priority for future research in this project.