V 
 
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LIBRARY 
 
 UNIVERSITY OF CALIFORNIA 
 
 OF" 
 
 Received 
 Accession No. J / J 
 
 . Class No. 
 
On Some Common Errors in Iron Bridge Design. 
 
ON SOME COMMON ERRORS IN 
 IRON RRIDGE DESIGN, 
 
 BY W. C. KERNOT, M.A., C.E., 
 
 \ i 
 
 Professor of Engineering, Melbourne University. 
 
 FORD & SON, PRINTERS, 372 & 374 DRUMMOND STREET, CARLTON. 
 
 lA 
 
7/ 
 
ON SOME COMMON ERRORS IN IRON 
 BRIDGE DESIGN. 
 
 In the Australian Colonies, as in other parts of the world, 
 there is a large and increasing number of iron (in which is 
 included steel) bridges. These bridges are of ages varying up 
 to about fifty years. Many of them were designed at a time 
 when the proper mode of proportioning the various parts was 
 but imperfectly understood, while in some the material and 
 workmanship is by no means up to the modern standards. Unlike 
 wine, bridges do not improve with age on the contrary, corrosion 
 is always going on, sometimes rapidly, but generally very slowly, 
 but no less surely, and is bound sooner or later to cause a 
 perceptible diminution in strength. It is also thought by many 
 that there is a tendency for the metal in course of time to 
 become hard and brittle and so less able to endure shocks. 
 Thus the bridges are without doubt growing weaker with 
 effluxion of time. Meanwhile the loads they have to endure 
 show a distinct tendency to increase. Steam rollers, traction 
 engines, and other specially heavy loads, undreamt of at the 
 time our earlier bridges were designed, are now common, while 
 locomotives, with the universal call for more power, become 
 constantly larger and heavier, and powerful continuous brakes, 
 unknown when the earlier bridges were built, introduce longi- 
 tudinal stresses of serious magnitude. From these combined 
 causes it is plain that the margin of safety is steadily diminishing, 
 and it is only a question of time for the point of absolute danger 
 to be reached. 
 
 Again, there is reason to believe that many parts of the older 
 bridges are excessively and unnecessarily strong while other 
 portions are weak, and that the general arrangement of parts is 
 often far from the most economical. 
 
It appeared, therefore, that a criticism of existing bridges 
 would be useful not only to the designer of new structures 
 anxious to avoid the defects of the older ones, but also, and 
 perhaps in an even greater degree, to the man who has received 
 a legacy of imperfect structures from his predecessors, which he 
 is desirous of utilizing as far as possible by judicious repairing 
 and local strengthening, for it is to be noted as a good point of 
 many of our defective bridges that they are like chains, most of 
 the links of which are abundantly strong while occasionally a 
 very weak one is found, which governs the strength of the whole 
 and that thus a comparati\ 7 ely inexpensive local reinforcement 
 may improve the whole structure to a very large and valuable 
 extent. 
 
 I shall now proceed as briefly as is consistent with clearness to 
 point out what I consider to be the principal errors in structures 
 that have come under my notice, and indicate how their defects 
 may be remedied, if remediable, in existing and avoided in future 
 structures. 
 
 1. Disproportion of joundation area to load carried. If a 
 foundation is too small it gives way partially or wholly, injuring 
 or destroying the structure ; if too large it stands but represents 
 waste of money. In every instance however some slight yielding 
 when the load is applied takes place, and it is desirable, espe- 
 cially if continuous girders are employed, that all the supports 
 should yield equally. Hence all foundations should be propor- 
 tioned to the load carried that is to say, under full load the 
 pressure per unit area on the supporting material should be 
 throughout equal. In calculating this pressure, it is to be 
 remembered that it is not the total load on the foundation surface 
 that is to be considered, but the excess over the load that existed 
 previously. For example, at the great Hawkesbury Bridge, 
 N.S.W., it has been stated, that the pressure on the foundation 
 is 10 tons per square foot, and this is obtained by dividing the 
 total weight of the structure by the area of foundation. But in 
 order to reach the depth required a very large quantity of 
 earth had to be removed, and the foundation was relieved to 
 that extent. The true or effective pressure on the foundation 
 is therefore the difference between these two amounts, and 
 actually is only 5 tons per square foot. This I submit is the 
 correct way of stating foundation pressure. 
 
There is a further qualification, however, and that is the allow- 
 ance for the effect of friction of earth upon the sides of a bridge 
 cylinder or caisson, and if this be taken into account, the pressure 
 on the base is still further reduced. This friction is somewhat 
 variable and has been stated as high as 800 and as low as 50 Ibs. 
 per square foot in different strata. 
 
 Directing our attention to existing structures, great discrepan- 
 cies appear in the size of cylinder foundations, not only between 
 one structure and another, but between different piers of the 
 same structure. For example the Intercolonial Railway Bridge 
 at Albury consists of two continuous spans of 160 feet each, 
 carried on three piers, each consisting of two cylinders of 10 feet 
 diameter. The centre pair of these cylinders carry -J-J of 
 the load, while the two end pairs together carry only T <] F . 
 Thus, while two cylinders carry a load represented by the 
 number 10, four of equal size are provided to carry a load 
 of 6 only, and these four are further surrounded by earth 
 to a much greater height than the central ones, and therefore 
 receive greater frictional support. It cannot, I think, be 
 disputed that the bridge would have been both cheaper and 
 safer had the end cylinders been reduced to 6 feet diameter, 
 or even less, for then any yielding would have been approxi- 
 mately equal throughout, and the distribution of bending 
 moment in the continuous girders consequently undisturbed. 
 Similar remarks will apply to the Railway Bridges at Wagga, 
 Bathurst, and Aberdeen, described in the Report of the Royal 
 Commission on Railway Bridges, N.S.W., 1886. In all of these 
 the terminal cylinders though carrying less than half the load, 
 and more favourably circumstanced in other respects, are just as 
 large in diameter as their heavily loaded companions, see Fig. 1, 
 which represents to scale the railway bridge at Aberdeen, N.S.W. 
 A reference to numerous successful cylinder and caisson bridge 
 foundations leads to the conclusion that the subjoined are safe 
 foundation pressures, the most unfavourable combination of load, 
 wind and flood, being employed in the calculation. Rock 10 tons 
 per square foot at least. Fine compact sand at considerable 
 depths, 6 tons per square foot. Very good clay 5 tons per square 
 foot. Ordinary sand, clay, or loam 1 to 3 tons per square foot. 
 Knowing then the superincumbent load and the nature of the 
 
6 
 
 material there should be no difficulty in proportioning the 
 cylinders of future bridges. As for those in existence, nothing 
 can be done, but as they usually err on the side of excess there 
 is not much cause for alarm. 
 
 2. Excessive and disproportionate size of columns. By the 
 term column is meant that part of the structure extending from 
 the foundation to the girder seat. Its size is often made equal 
 to that of the foundation, but there is no necessity that this 
 should be the case, for while the size of the foundation depends 
 on the resistance of the material upon which it rests, that of the 
 column depends upon the material of which it is made and which 
 sometimes offers a greater resistance per square inch than the 
 foundation does per square foot. For the sake of lateral and 
 frictional support, the cylinder is usually, and properly carried up 
 the full size from the foundation to the surface of the ground. 
 Above this, however, there is no reason why it should not be as 
 economically designed as any compression element of the super- 
 structure. In many of the older bridges the columns are of most 
 unnecessary size, adding seriously to the cost of the structure, and 
 impeding the flow of water in the case of river bridges in an 
 undesirable manner. This is certainly the case with the older 
 New South Wales railway bridges already referred to, and also 
 with some in Victoria. As examples of what has been success- 
 fully done in the way of reducing this part of the structure to 
 reasonable and economical proportions, two structures may be 
 cited. The first is the Johnston Street Bridge, Collingwood, near 
 Melbourne, shown in Fig. 2. This is an iron bridge built about 
 20 years since by C. Rowand, Esq., C.E., to replace a large timber 
 arch that failed through decay. It consists of three spans of 
 nearly 60 feet each, extending between the stone abutments of 
 the old timber arch, and having as intermediate supports wrought 
 iron columns filled with concrete, which for slightness present a 
 most extraordinary contrast to the usual practice at the time 
 it was built. Their dimensions are as follow : 
 Height from top of cast iron cylinder 
 
 to girder seat ... ... 45 feet 
 
 Diameter ... ... ... 2 feet 
 
 Thickness of metal ... ... T 5 F inch 
 
 Dead load for each column... ... 40 tons 
 
 Live load for each column .. 50 tons 
 
Each pair of these columns supports an area of bridge decking 
 70 feet long and 32 feet wide. 
 
 The proof of the practical success of these columns is in every 
 way most conclusive, for not only is the bridge on an important 
 main road with heavy traffic, but it is also at the part of the 
 Yarra where the hydraulic conditions are of the severest kind. 
 During the great flood of July, 1891, when two iron bridges were 
 washed away and hundreds of suburban dwellings inundated, the 
 water stood at the level shown in Fig. 2. The gradient of the 
 flood surface for 50 chains above the bridge was at the rate of 
 over 5 feet per mile, the hydraulic radius about 30 feet, and 
 floating timber and other wreckage abounded. Nevertheless 
 these slender columns stood absolutely uninjured, and that, 
 although the bracing between them is by no means as massive as, 
 in my opinion, it should be. 
 
 The second example is the bridge carrying the North-Eastern 
 Railway over the Racecourse Road, Flemington, near Melbourne. 
 The railway is double line and is traversed by a busy suburban 
 traffic propelled by tank engines of 49 tons weight. The bridge 
 is situated at the entrance of the Newmarket Station and is 
 exposed to the constant action of the Westinghouse brake. There 
 are two spans of 51 feet each (discontinuous), four main girders 
 to each span, and the central support consists of four columns 
 each made of four 3J x 3J x J angles of mild steel, with single 
 rivetted lacing. The foundations are of Victorian bluestone, a 3 
 inch cube of which crushes with 40 tons pressure, and are 2J feet 
 square for each column. The compressive stress on the metal of 
 the angles is 4 tons per square inch. The columns are 15 feet 
 high from stone foundation to girder seat and are 18 inches 
 square. 
 
 Strange to relate a second railway, carrying a practically 
 identical traffic crosses the same road at a short distance, 
 and here the columns are of cast iron filled with cement, 
 2ft. Sin. diameter, 1 inch thick, and the girders 44 feet 
 span. Judging from experiments made with the University 
 testing machine it would take 300 tons to crush a column 
 of the former bridge and 4000 tons to crush one of the 
 latter, and yet the latter carries a smaller load than the 
 former. 
 
8 
 
 There is no doubt whatever that considerable economies are 
 to be effected in the design of columns of future bridges by 
 abandoning old arbitrary methods, and treating the problem 
 scientifically. 
 
 As a further instance of economical design, Kinzua Viaduct, 
 New York State, U.S.A., may be quoted, a section of a wrought 
 iron column of which is shown in Fig. 3. Two of these columns 
 form the support intermediate to a span of 61 and one of 38 feet, 
 carrying a main line of railway 4 ft. 8J in. gauge. Each column 
 is 279 feet high and is braced laterally at intervals of 31 feet. 
 Further comment is needless to show how excessively wasteful 
 bridge columns in Australia have been in cases too numerous to 
 mention. 
 
 3. Girders supported in an unfavourable manner. Under 
 this heading come many defective arrangements. The fiist of 
 these is when a girder is supported at the extreme end, it being 
 possible to support it at a more favourable point. It does not 
 seem to have been generally recognised by engineers that the 
 extremity of a girder is a most unfavourable point of support, 
 giving rise to bending moments and shears of maximum value, 
 and therefore should not be adopted except under the most 
 cogent conditions. If the points of support of a uniformly 
 loaded beam are moved towards the centre, the most surprising 
 diminution both of bending moment and shear takes place, and 
 when the supports are distant from the ends by -207 of the length 
 the maximum bending moment is reduced to '172 and the maxi- 
 mum shear to -59 of what it is when the supports are terminal. 
 As in the great majority of beams including rectangular sections 
 of timber and rolled girders of usual proportions, the strength is 
 regulated by the moment and not by the shear, this means that 
 a uniform beam supported at what I propose to call the "efficient 
 points," is very nearly six times as strong as a similar one 
 supported at the ends, the load being uniformly distributed. 
 With a live or variable load, such as a crowd, the advantage is 
 not so great, the stress range being somewhat increased, but even 
 allowing for this in accordance with the Weyrauch vibration 
 formula, the strength of a beam carrying an equal* live and dead 
 load a very usual case is increased about threefold by its 
 being supported at the efficient points instead of the ends. Thus 
 
8 
 
OF THE 
 
 UNIVERSITY 
 
it will be seen that there is an enormous advantage in supporting 
 both main and cross girders at their efficient points, or as near 
 to those points as is possible, and this is true in all cases but 
 most especially so when the dead load is large. 
 
 Should it be obligatory to support the beaiap-ftt one extremity, 
 
 0ffift^rt*4fZ . 
 
 the position of the other support being /Sotainoa, the efficient 
 point is found to be -29 of the length from the other end, and 
 the maximum bending moment is almost exactly one-third of 
 what it would be were both supports terminal, the load being 
 uniformly distributed. 
 
 Should it be inconvenient to adopt so large an overhang as 
 above mentioned, considerable advantage may still be obtained 
 with a very moderate amount. For example, a uniform beam 
 uniformly loaded and supported at points one-eight of its 
 length from the ends endures a maximum bending moment of 
 only one-half of what it would if supported at the extremi- 
 ties. 
 
 As an instance in which an overhanging end might have been 
 advantageously applied certain bridges on the Melbourne and 
 Coburg Railway may be cited. Here, as shown in Fig. 4, the 
 terminal support of the girder is a brick pier imbedded in the 
 embankment, and the girder seat is surrounded with earth in 
 an undesirable way. By moving the pier to the position shown 
 in Fig. 5, the bending moment would be reduced, and the 
 girder seat rendered accessible. 
 
 A case of unfavourably arranged support is illustrated in Fig. 
 6, which represents two bridges each crossing six lines of railway 
 in Yarra Park, Melbourne. The girders are of the lattice type, 
 supported at the ends by a double system of standards or legs. 
 Calculation shows that the compressions on the diagonals AB 
 and CD are equal. But the tension on AC is equal to the 
 compression on AB as their horizontal resolved parts balance at 
 A. Hence the vertical resolved part of AC balances that of CD 
 at C, and the leg CE carries no weight whatever, except the 
 actual small floor load at C. 
 
 Now, had the bridge been arranged as at Fig. 7, the main 
 girder would have been shortened by ten per cent., the stresses 
 throughout the remainder would have been reduced considerably, 
 the leg FG would have been saved and the whole structure 
 
10 
 
 largely reduced in length, thus economising flooring, hand-railing 
 and area of ground occupied. This, it may be added, has been 
 done in several more recent structures of a similar kind. 
 
 A third case of unfavourable support is where the girder seat 
 is not placed centrally to the cylinder or column. This causes 
 the stress to be greater on one side of the column than the other, 
 and involves a tendency for the column to lean over if in soft 
 ground. An instance of this is to be seen in an important 
 bridge illustrated in "Engineering," vol. 43, p. 117. 
 
 Such errors as these are usually irremediable in existing 
 structures. It is desirable, however, to guard against their 
 repetition in future designs. 
 
 4. Imperfect expansion apparatus. Variations of temperature 
 affect all metal structures, and unless properly provided for 
 may cause extra stresses of serious amount in the metal work 
 and dislocation of the brickwork or masonry of the supports, 
 such dislocation unfortunately being only too apparent in not 
 a few existing structures. The extreme temperature range in 
 Melbourne from the Observatory thermometer records is about 
 150 Fahrenheit, but it is not probable that the change of 
 temperature of considerable masses of metal work such as used 
 in bridges will be more than 120. As iron and steel expand 
 not quite one part in 800 between freezing and boiling, a range 
 of 180, the expansion for 120 will be one part in 1200 or 1 inch 
 in 100 feet. This simple and easily remembered rule is safe for 
 the Victorian climate, but would not suffice for places such as 
 New York, where the temperature range is greater in both 
 directions than in Melbourne. 
 
 A metal structure then should be anchored or fixed at some 
 definite point and be allowed free movement everywhere else. 
 The point of anchorage may advantageously be near the centre, 
 so as to divide up the motion. If this is not convenient the 
 anchorage should be at the firmest' or most solid support. If for 
 example one end of a bridge be on solid rock and the other on a 
 tall and somewhat flexible support, the former should be made 
 the anchorage. At the Victoria Street Bridge, near Melbourne, 
 the opposite course was adopted and the whole bridge was 
 thrown somewhat out of position by movement of the support 
 and involved the necessity of its being detached and moved 
 back to its original position a troublesome operation. 
 
11 
 
 Girders of less than 100 feet span are usually supported on 
 planed surfaces of metal which slide one upon the other. In 
 some cases pressures of over a ton per square inch have been 
 imposed on such surfaces with success, but usually the pressure is 
 much less. Larger bridges are as a rule supported on rollers and 
 it is desiraMe that these be of ample diameter and so placed as 
 not to be choked up with dirt or injured by moisture. Rollers 4 
 inches diameter are allowed J ton load per inch length by good 
 American authorities, but this pressure is often exceeded in 
 English practice and apparently with impunity. Whether the 
 sliding plates or rollers should be surmounted by a rocking 
 arrangement is a point on which practice varies. In theory the 
 rocker is undoubtedly correct, giving a perfectly definite point 
 of support, and obviating the unequal pressure on the rollers 
 due to the slope of the deflected girder. Many excellent and 
 experienced authorities however omit it. The Great Hawkes- 
 bury Bridge, N.S.W., for example, has no rockers, though 
 carried out in the best possible style in other respects. On the 
 other hand, the bridge over the Yarra, carrying the Port 
 Melbourne and St. Kilda Railways is carried everywhere on 
 rockers. The fact that in the former case the girders are very 
 deep and therefore stiff, while in the latter they are shallower, 
 may perhaps justify the difference. 
 
 It is often forgotten by bridge designers that expansion takes 
 place transversely as well as longitudinally, and that roller 
 systems should be arranged accordingly. One point of support 
 being fixed, all the others should be provided with rollers acting 
 in directions radiating from the fixed point. 
 
 Tall thin columns, such as those at Johnston Street Bridge, 
 previously referred to, do not need expansion arrangements as 
 a rule, the column itself being capable of springing an inch or 
 two without injury. In dealing with the expansion arrange- 
 ments of existing structures, 1 would suggest that they be kept 
 clean and lubricated and protected from dust arid moisture, and 
 that all impediment to free motion be removed. 
 
 We next have to consider the main girders constituting a large 
 and costly part of the structure. These are of various types, 
 including plate girders, box or tubular girders, closely latticed 
 girders of the type used 30 years ago, and the many modern 
 
12 
 
 forms of open girders including the X girder, the N girder, the 
 W or Warren girder, the Pratt tfe Whipple girders so deservedly 
 popular in America, and of late years, frequently adopted by 
 English engineers, and other forms too numerous to mention. 
 Some of them are of equal depth throughout, the top and bottom 
 surfaces being parallel, while others vary in depth, having one 
 or sometimes both surfaces curved. To discuss all these various 
 forms in detail would require a very large volume indeed, far 
 beyond the dimensions of the present brochure. All that can be 
 here attempted is to clearly state the leading principles of strong 
 and economic construction, and indicate how they have been 
 transgressed in times past. These are as follow : 
 
 (a) In beams or girders having continuous plate webs the 
 
 material should be concentrated as far as possible 
 from the neutral axis so as to give a maximum 
 moment of resistance, and only sufficient material be 
 left in the connecting web to enable the whole mass 
 to act as one beam. 
 
 (b) The web should be sufficiently stiffened or reinforced so 
 
 as to enable it to bear transverse compression at 
 points of support, or of heavy isolated load. 
 
 (c) In open web girders the structure should consist of a 
 
 continuous series of triangles connecting the points 
 of application of external force, the sides of which 
 should be perfectly straight, and the angles common, 
 and which should be so arranged that determinate 
 equations of equilibrium may be obtained for every 
 angular point. 
 
 (d} The various bars composing the frame should be propor- 
 tioned to the stress they undergo, should be efficiently 
 jointed, and if in compression should be of such a 
 section as not to evade their duty by lateral bending 
 or wrinkling. 
 
 (e) In all forms of girder no unnecessary material should be 
 used in any part, and the proportions and arrange- 
 ments of parts should be such as to give the greatest 
 possible strength for a given amount of material and 
 work manship. 
 
angle iron double 
 '. d. 
 
 bars- X-^ r"** 
 
 rig. 9. 
 
13 
 
 Let us now see how existing structures fail to comply with the 
 above conditions. In connection with main girders the following 
 errors have come under my notice. 
 
 5. Insufficient depth. The extreme top and bottom elements, 
 or chords as they are generally called, of all structures performing 
 the functions of a beam are stressed in inverse proportion to their 
 distance apart. Hence the deeper the girder the less the stress 
 upon and requisite sectional area of these parts. As a matter of 
 pure and bald theory the quantity of material in the web is 
 independent of the depth, so that the most economical girder is 
 one infinitely deep with chords infinitely small and web infinitely 
 thin. Such a result as this is of course valueless as a guide to 
 practice except as showing that as ample a depth as other 
 considerations permit should be chosen. 
 
 For many years English engineers, following apparently the 
 example of Fairbairn, adopted depths of T \r to T V of the span 
 involving very heavy chord sections. The Americans however 
 showed that it was possible to follow theoretical indications much 
 more closely without incurring practical difficulties, and erected 
 many efficient and economical structures with depths of \ to T ^, 
 the average being about ~. Of late years English practice has 
 been approaching to American, though somewhat hesitatingly. 
 This is of course in cases when the depth is not restricted by 
 such considerations as head way or flood level. 
 
 As practical illustrations of the defect of insufficient depth, I 
 could refer to, first, the earlier foot passenger bridges over the 
 railways in the vicinity of Melbourne. These are excessively 
 shallow Warren or lattice girders surmounted by gas pipe hand- 
 rails, which in no way add to the strength. A model of one of 
 these at the Prahran Railway Station was made and broken down 
 at the University, and also a model containing the same metal, 
 of decidedly simpler construction and double the depth. The 
 latter was found to be 70 per cent, stronger than the former, and 
 further, had the advantage of dispensing with the handrail, being 
 itself deep enough for the purpose of a parapet (see Figs. 8 and 9). 
 
 The cross girders of the recently erected Tower Bridge London, 
 constitute another example of the same peculiarity, having a 
 depth of only ^ of the span. Consequently the chords are 
 enormously massive, consisting of, in some places, seven layers of 
 
14 
 
 plates rivetted together, an undesirable arrangement, as it is very 
 difficult to effect satisfactory rivetting through so many super- 
 posed layers of metal, and, further, there is some doubt as to 
 whether the outer layers really do their fair share in resisting 
 the bending moments. 
 
 Had the Tower Bridge cross girders been supported at the 
 efficient points, which lie at the edge of the footpath, the reduction 
 in material and weight required would have been enormous, and 
 it is not clear that there is any insuperable objection to this being 
 done. As examples of excessive shallowness and most unfavour- 
 able mode of support these girders are very notable. 
 
 This defect is obviously incurable in existing structures. 
 
 6. Unfavourable disposition of material for enduring bending 
 moment. This is an infraction of requirement a on page 12, and 
 is occasionally seen in the older type of box girder. A notable 
 example is the Railway Bridge at Penrith, N.S.W., the section 
 of which is shown in Fig. 10. Here there are four chords 
 instead of two, and those nearer the neutral axis represent a 
 most unfavourable disposition of material. The intermediate 
 chords are 10 feet apart and the extreme ones 13. Consequently, 
 tirst, the stress on the intermediates is only \^ of that on the 
 extremes, and as it acts at only -J-J of the distance from the 
 neutral axis, the value of every square inch of metal is only 
 liifH or n t much more than half of what it would have 
 been if placed at the extreme distance. In this way the bridge is 
 loaded with a vast quantity of metal which performs only about 
 60 per cent, of the duty it should. Further, this arrangement 
 involves the existence of cells 18 inches square, and nearly 600 
 feet long, which are most objectionable from the point of view 
 of inspection, painting and repair. Fortunately, this form of 
 girder is now quite obsolete, and the error is not likely to be 
 repeated. 
 
 7. Uniformity of chord section throughout the length. This 
 uniformity is justifiable on grounds of simplicity in rolled beams 
 and the smaller varieties of built girders when a pair of angle 
 bars of convenient size suffices for the maximum chord section. 
 But when one or more plates have to be added, to carry these 
 throughout the whole length regardless of variations of chord 
 stress is absurd. In some of the earlier plate girder bridges on 
 
15 
 
 the Victorian Railways this has been done to a most remarkable 
 extent. At Kororoit Creek, on the Geelong Railway, there is a 
 double line bridge of 80 feet span, the chords of the girders of 
 which consist of two 3J x 3J x J angles and three 24 x f plates 
 continuous throughout, and representing an enormous waste of 
 metal towards the ends of the girders. As a pleasing contrast 
 to this the new steel bridges over the Inkermann and Balaclava 
 Roads 011 the Brighton Railway,- near Melbourne, may be noted. 
 Here the plates are arranged just as the stress requires and for 
 the last few feet of each end are omitted, the angle bars forming 
 the whole chord. Figs. 11 and 12. 
 
 8. Insufficient connection between chords and web. The stress 
 in the chord of a plate web girder is given with approximate 
 accuracy by dividing the bending moment by the depth. If this 
 stress be determined at two points say one foot apart, different 
 values will be obtained, the difference between which will be the 
 horizontal or longitudinal shear for that foot in length tending 
 to separate the chord and web. This has to be resisted by the 
 rivets. As the bending moment varies rapidly near the supports, 
 and slowly near midspan, this shear will vary correspondingly. 
 Hence, for equal strength throughout, the pitch of the connecting 
 rivets should vary from the centre to the ends, being very large 
 at midspan, and becoming smaller and smaller as the supports 
 are approached. To carry this out exactly as calculation requires 
 would involve too much complicated measurement for practical 
 conditions, hence one or at most two variations of pitch must 
 suffice, portions of the work being a little over-rivetted to secure 
 uniformity. The great Penrith Railway Bridge, N.S.W., shows a 
 notable neglect of this requirement. The rivetting at the point 
 A in Fig. 10 being small and uniformly pitched throughout, the 
 rivets are seriously over-stressed for a distance of 40 feet on each 
 side of the piers, and for 10 feet at each end of the bridge (which 
 is continuous over three equal spans). This grave defect was 
 discovered by Professor Warren of Sydney University and 
 verified by the writer. It is fully dealt with in the Report of 
 the Royal Commission on Railway Bridges of N.S.W., 1886, and- 
 the proper remedy, viz., the replacement of the f inch rivets by 
 1 inch rivets for the distances mentioned, pointed out. But 
 
16 
 
 though this effective remedy could be applied at a mere nominal 
 cost and without any interruption of the traffic, the N.S.W. 
 Railway authorities have persistently refused to yield to the 
 urgent representations of the Royal Commission, of Professor 
 Warren, and of the writer. Should disaster ensure the responsi- 
 bility rests with them. 
 
 In the later work of the Victorian Railway Department this 
 variation of horizontal shear has been consistently recognised as 
 is evidenced by the varying pitch of the rivets in the girders on 
 the bridge over the Yarra on the Port Melbourne Railway and 
 elsewhere. The considerations applying to the row of rivets con- 
 necting the web and chord angles of these girders also apply to 
 those connecting the chord angles with the chord plates, and a 
 similar variation of pitch is required here. It is to be noted, 
 however, that these latter rivets perform a smaller duty than the 
 former and so may be smaller, or at larger pitch without uiiiifar- 
 pg the strength of the girder Strange to say in Penrith Bridge 
 these rivets, B in Fig. 10, are larger than those at A, though 
 dealing with the shear consequent upon the stress variation in a 
 portion of the chord only, while those at A deal with the whole 
 a notable anomaly. It is to be added that the stress on the 
 vertical rows of rivets in a plate web is identical with that in the 
 contiguous portions of the horizontal rows, and that the diameter 
 and pitch should be the same for both. To illustrate this point 
 Fig. 13 has been prepared, representing a theoretically rivetted 
 girder with terminal supports and uniformly distributed load. 
 Existing girders ought to be examined and computed to see if there 
 is any weakness as to horizontal and vertical shear, and, if there is, 
 rivets should be cut out a few at a time, holes enlarged and bigger 
 rivets inserted, as recommended by the Royal Commission in the 
 case of Penrith Bridge. 
 
 9. Vertical stiff eners absent or wrongly placed, Requirement 
 {), page 12. These vertical stiffeners are added at intervals 
 along the web of a plate or box girder for one of the following 
 purposes : 
 
 1. To prevent the thin web from being crushed by the local 
 
 vertical pressure due to the reaction of a support or a 
 
 concentrated load. 
 
17 
 
 2. To check the tendency of the web to buckle under the 
 diagonal compression that pervades it, being most 
 intense near supports and least midway or there- 
 abouts between them. 
 
 To comply with the former condition we need a mnrjruiqc mas- 
 sive vertical pillar at the end of every ordinary girder, and a 
 .still more massive one at the piers of continuous girders or those 
 with overhanging ends. Strange to say, however, these verticals 
 .are often seen inserted when there is 110 need for them, and 
 omitted where there is the maximum stress. A notable instance 
 is to be seen in a small continuous three span bridge on the 
 North-Eastern Railway about two miles from Melbourne. 
 
 Should a very heavy concentrated load, as for example a large 
 column in a building, be imposed at any particular point, this 
 column should be continued as a vertical stiffener to the bottom 
 of the girder. This case does not however often occur in bridge- 
 work. 
 
 These stiffeners are usually made of uniform section from top 
 to bottom of the girder. Jhis may be justified by convenience 
 of construction, but is not required for strength. As we pass 
 from the bottom to the top of the girder at a point of support, or 
 from the top to the bottom at a point of concentrated top load, 
 the compression in the vertical gradually discharges itself into 
 the web in the form of a shear, or its equivalent, a set of diagonal 
 compressions and tensions, and thus dies away. Hence the 
 vertical at a support should be of the full section required by the 
 reaction of that support at the bottom and diminish to nothing 
 at the top, and that at a concentrated top load of full section for 
 the load at top diminishing to nothing at the bottom. In large 
 girders this fact may be made use of to save material. The other 
 use of verticals in plate girders is to prevent the web from 
 buckling or being thrown into waves by the diagonal compression 
 due to the shear. 
 
 Rankine in his "Civil Engineering" treats the web as a long 
 column tending to buckle under the diagonal compression, and 
 measures the length on an angle of 45 deg. between top and 
 bottom chords, or between vertical stiffeners, whichever happens 
 to be the smaller. He then applies the excessively high safety 
 factor of six. There are two most serious errors in this treat- 
 
 2A 
 
18 
 
 ment. First, the diagonal tension, which is approximately equal 
 to the diagonal compression, has a powerful tendency to prevent 
 buckling or undulation and so improve matters, and second, to 
 apply a safety factor of six to a long column, whose failure is due 
 to lack of stability and not of strength is unscientific as is shown 
 in my paper on this subject in the " Transactions of the Royal 
 Society of Victoria," Vol. XV., p. 14. There is no doubt that 
 the resistance of such a web to buckling is at least five times as 
 great as the Rankine treatment will allow, and this conclusion 
 is confirmed by Professor Warren's elaborate analysis of the web 
 stresses of Penrith bridge, in the Royal Commission Report 
 previously quoted. It is there shown that, according to Rankine, 
 the safety factor of some parts of the web is less than unity under 
 ordinary traffic, and yet this bridge has now been in existence for 
 more than thirty years and has shown no sign of weakness. 
 
 To determine the exact strength of a thin plate web against 
 buckling is a question of much difficulty and obscurity, but there 
 is no possible doubt that it is immensely greater than Raiikine's 
 imperfect method of computing indicates, and that in a vast 
 number of instances the thinnest metal that it is desirable to use 
 from the point of view of corrosion, and practical convenience of 
 construction is abundant to resist the tendency to buckle due to 
 the shear. 
 
 The following rules may be laid down as sound for arranging 
 verticals, and proportioning webs. 
 
 1. A vertical pillar at each point of support of section pro- 
 
 portioned to the reaction of that support should 
 extend from bottom to top of the web, but it needs 
 the full section only at the bottom and may taper to 
 nothing at the top. 
 
 2. This pillar should be placed fairly on the centre of the 
 
 support and not as is sometimes seen at or near one 
 edge. 
 
 3. The web should have a vertical sectional area of one 
 
 square inch for not more than 2 tons of vertical shear 
 for wrought iron, and 2 tons for mild steel. 
 
 4. Vertical stiffeners of T section should be placed wherever 
 
 any considerable concentrated load is imposed on the 
 top chord. 
 
19 
 
 Bridges defective in these respects should be reinforced by 
 rivetting on the necessary additional parts. 
 
 Leaving the girders with continuous plate webs we next have 
 to consider those in which the chords are connected by some 
 arrangement of bars forming an open lattice or trellis work of 
 some kind. These have enjoyed a great popularity for bridges of 
 the largest size, and also for smaller ones, where the load being 
 light it was difficult to design an economical plate girder without 
 using a web undesirably thin for practical conditions. 
 
 In these as in the plate web girders the fault of insufficient 
 depth and consequently needlessly large chord sections has been 
 very prevalent. At Oemorne on the Melbourne and Brighton 
 Railway there is a lattice girder bridge 140 feet span and 10 feet 
 deep, built about forty years ago. Some ten years since, it was 
 required to build a second bridge at one side of it to carry the 
 Oippsland Railway, and, although there was a desire for the sake 
 of appearance to keep the two structures of uniform depth, the 
 advantage of increasing it was so great that the new bridge was 
 made 20 feet effective depth for the same span. 
 
 Apart from this defect the principal faults to be found in 
 girders of this class are 
 
 10. Incomplete triangulation. As stated on p. 12 require- 
 ment c, every framed structure should consist of a complete and 
 continuous series of triangles, the triangle being the only 
 polygon whose figure is fully determined when the length of its 
 sides are tixed. Such a structure is subject to longitudinal 
 tensions and compressions only, and is free from bending moment 
 and shear, and so utilizes most advantageously the material of 
 which it is composed. Now in actual existing structures glaring 
 departures from this rule are sometimes seen, as in the case of 
 the shore girders of the old footbridge over the Yarra at the 
 Botanical Gardens, Melbourne (Fig. 14). Here it must be 
 obvious to anyone having the slightest knowledge of the subject 
 that a single strut, as shown by the dotted line, would have 
 carried the triangulation to its proper termination, and been far 
 cheaper and in every way better than the complex and costly 
 arrangement of plates, angles and rivets actually employed. As 
 this structure is about to be removed its defects have no further 
 interest. In future structures they should, however, be avoided. 
 
20 
 
 11. As an error in the opposite direction to the last redundancy 
 may be next quoted. This fault is very wide-spread, and has 
 received a good deal of defence from influential quarters. But 
 such defence has usually been more in the direction of palliation 
 than- justification. Redundancy may be defined as a duplicate 
 system of triangulation connecting identical points. In such a 
 case the stresses in the bars become indeterminable by statical 
 calculation, and can be computed only by a much more complex 
 and less satisfactory method based upon the elastic deformations 
 of the various parts, and the result is likely to be vitiated by 
 variation in the coefficient of elasticity, and to a still more serious 
 degree by imperfections of workmanship invisible in the com- 
 pleted structure. To explain more fully, a redundant structure 
 minus certain of its bars presents a complete system of triangu- 
 lation. Suppose now that the remaining bars are by accident 
 made a little too long or too short, and are forced into their 
 places with violence, a set of stresses of possibly great severity 
 is induced throughout the structure which may modify profoundly 
 the result of any calculation. Hence redundancy, while rarely, 
 if ever, of any real advantage, may lead to most undesirable 
 consequences. As a gigantic example of this defect, the Charing 
 Cross Railway Bridge over the Thames at London, illustrated in 
 "Humber's Iron Bridges," and shown in outline in Fig. 15, may 
 be noted. 
 
 Minor instances of this fault are very common, and to forbid 
 redundancy absolutely would mean condemning many otherwise 
 meritorious designs. We may, however, I think, say first, that 
 other things being equal or nearly so, preference should always 
 be given to non-redundant arrangements, and second, that if 
 for sufficient reasons redundant ones be adopted special care 
 should be taken that they are put together in a perfectly 
 unstressed condition. In French practice this fault is very 
 prevalent, and a gigantic example of it is to be seen in the- 
 Eiffel Tower, a structure which, like the Charing Cross Bridge, 
 would undoubtedly be much improved by the removal of 
 numerous costly parts. 
 
 12. Curvature of members. Considering that every part of a 
 properly designed framed structure is a simple strut or tie subject 
 to longitudinal stress only, the necessity of absolute straightness 
 
21 
 
 is an immediate consequence. Strange to say, however, owing 
 to some peculiar warp of the human mind, many persons persist 
 on fanciful grounds in increasing the cost and diminishing the 
 strength of structures by the introduction of curved members. 
 A curious example of this is to be seen in the evolution of the 
 frame of the modern bicycle. For years this vital part was 
 made of ridiculous shapes presenting complex curves utterly 
 contrary to scientific principles, and the result was, despite the 
 most liberal employment of material, straining, weakness, and 
 frequent fracture. The modern diamond frame, every part of 
 which is perfectly straight, is thoroughly scientific, and, with 
 half the material of the earlier frames, is far more rigid and 
 absolutely free from fracture under ordinary and reasonable 
 use. 
 
 Perhaps the most extraordinary and inexcusable instance of 
 this fault in modern times is to be seen in the huge and costly 
 Jubilee Bridge over the Hoogly in India, described and discussed 
 in the " Proceedings of the Institution of Civil Engineers," 
 Vol. XCII., 1888, an outline of the terminal panels of which 
 is given in Fig. 16. Here one of two things ought to have been 
 done, either AB should have been made perfectly straight, or the 
 space C should be plated over, the latter being the only practic- 
 able remedy now. This grave fault was animadverted upon by 
 myself in the " Engineer" of 5th June, 1885, and afterward by Pro- 
 fessor Max am Ende before the Institution of Civil Engineers, 
 London. A second and still more recent example is seen in the 
 Warburton Bridge over the Manchester Ship canal, illustrated in 
 "Engineering" of 26th January, 1894. 
 
 But while condemning as strongly as possible such designs as 
 the Jubilee and Warburton Bridges, I would make an exception 
 in favour of many bowstring and hogback girders such as the new 
 Cremorne Bridge on the Gippsland Railway near Melbourne. 
 Here the top chord forms a bold and graceful curve, very pleasing 
 to the eye, but the panel points where the web members come in 
 are so numerous that the curvature i8 each panel or length of the 
 chord is imperceptible. If the chord was made polygonal, each 
 panel being straight, its outline would not differ visibly from 
 what it is at present. A chord curved at a large radius and 
 divided into panels so short as to be practically straight, cannot 
 
22 
 
 be reasonably objected to. From this point of view also, the 
 magnificent 350 foot span girders at Indooroopilly, Queensland 
 are justifiable. 
 
 13. Eccentricity. The condition laid down on page 12 that a 
 properly designed framed structure should consist of a series of 
 triangles having common angles, involves the necessity of any 
 three or more bars meeting at a point being so arranged that 
 all their mean fibres pass accurately through that point, the 
 mean fibre being defined as the line passing through the centre 
 of gravity of the cross section of each bar. If these mean fibres 
 or gravity lines, as they are sometimes called, do not meet truly, 
 bending moments and shears are set up in the bars, and loss of 
 strength ensues, unless obviated by the introduction of additional 
 material. "Very great laxity is sometimes shown in this respect, 
 as may be seen from Fig. 17, representing portion of a large 
 girder recently erected over Primrose Street, in connection with 
 the enlargement of the Liverpool Street Railway Station, 
 London, illustrated in the "Engineer," of 21st August, 1896. 
 Here it is to be noted that the end pillar, instead of being placed 
 centrally over the rocker support, is placed most eccentrically so 
 as to concentrate the stress on one edge instead of distributing it 
 equally, and further, that the mean fibres of the last diagonal and 
 end pillar meet far above the upper surface of the top chord, 
 instead of as they ought in its mean fibre. Another glaring case 
 is shown in Fig. 18, representing part of a bridge near Windsor, 
 N.S.W., inspected some years ago by the writer. Recent 
 Australian practice appears fairly free from these inexcusable 
 faults, which is more than can be said for English practice. 
 
 A most disastrous accident took place ten years ago near 
 Boston, U.S.A., causing the destruction of a train, the loss of 
 twenty-five lives, and injury to about one hundred persons. This 
 all started from the failure of the improperly designed bridge 
 hanger shown in Fig. 19. This hanger had ample sectional area 
 for the direct pull, but that pull was imposed so eccentrically as 
 to give rise to a bending "moment which increased the stress 
 several times. This and other cases show the necessity of 
 guarding most carefully against this fault. Few persons realise 
 that in a rectangular section a deviation of the centre of stress 
 
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 UNIVERSITY 
 
23 
 
 from the centre of figure by one-sixth of the width of the bar, 
 doubles the stress on one side and reduces that on the other to 
 zero. 
 
 Eccentricity should be most carefully avoided in designing 
 new structures, and when it exists in old ones, special local 
 strengthening should be applied, unless computation shows the 
 parts to contain a sufficient excess of material to resist the 
 moments and shears involved as well as the direct stresses. 
 
 14. Unscientific and wasteful end pillars. There are multitudes 
 of girders in existence which are reasonably and consistently 
 designed as far as chords and web members are concerned, 
 but which have the terminal verticals of excessive size, and 
 most complicated construction involving great and altogether 
 unnecessary increase in the weight and cost of the girder. No 
 defence or excuse for this anomaly has ever reached the writer's 
 ears, but its vitality is remarkable, as it appears not only on 
 bridges built thirty or forty years ago, but even in quite recent 
 structures, including some of those crossing the Manchester Ship 
 Canal. One example is shown in Fig. 14, where the end pillar 
 or box contains at least three times as much material as would 
 be needed for a proper terminal diagonal or " batter brace," to 
 use the American term. A second example is shown in Fig. 20, 
 representing part of a bridge over the Rio Verde, South America, 
 the work of a late president of the Institution of Civil Engineers. 
 Here the end pillar AB has 98 square inches sectional area 
 against 21 square inches in the adjoining diagonal BC, which 
 bears 40 per cent, more stress, and 20 square inches in the 
 vertical CD, which endures a compression three-fourths of that 
 on AB. Were AB reduced to 25 square inches area, which 
 would be most abundant, 11 per cent, of the weight and cost of 
 the whole girder would have been saved. There is, however, a 
 still better arrangement originated by Whipple, an American 
 Engineer, and used in America for nearly half a century past. 
 It is to abolish the bars AB, BC, BD, and insert a compression 
 diagonal AD as shown by dotted lines. This will leave the 
 compression on the top chord unchanged, and the stress on all 
 except the end panel of the bottom chord, which at present is 
 unstressed, though of massive section, and will reduce the stress 
 on CD largely, thus saving no less than 17 per cent, of the 
 
24 
 
 weight of the girder. The remarkable economy due to replacing 
 the clumsy end vertical by a sloping compression piece or 
 "batter brace " of theoretical section is now somewhat tardily 
 being recognised by English Engineers. It has been universal 
 practice in America since the time of Whipple. 
 
 This is an error to be avoided in future designs. In existing 
 bridges it simply means waste of money, but does no further 
 harm. 
 
 15. Unduly numerous systems of triangulation This is a very 
 common fault of the lattice girders of 30 or 40 years ago. A 
 multiplicity of small bars, many of which for practical reasons 
 have to be much larger than calculation requires, which involve 
 a large amount of complicated workmanship and often are 
 not placed in proper relation to the points of attachment of the 
 cross girders, constitute a usual characteristic of early practice. 
 Modern work, however, usually avoids this fault, and as it in 
 most cases where it exists means waste and not weakness, it is 
 not a matter needing any present action. 
 
 16. Inefficient forms of compression member. In consequence 
 of the high compressive resistance of iron or steel the transverse 
 dimensions of compression parts of girders have to be compara- 
 tively small relatively to their length, consequently the tendency 
 is to fail by buckling or long column action, rather than by 
 direct crushing, and the strength attained depends largely on 
 the success with which this tendency is combattecl. When the 
 column is so short as to fail by true crushing, the form of section 
 is immaterial, provided only the required area is present, but 
 when it is longer the form of section has a most profound influence 
 on the resistance. The best form is that which presents the 
 greatest resistance to bending laterally, either of the column as a 
 whole or of any constituent part. Hence a good compression 
 member must approach in form to an efficient beam, but as it 
 may bend in any plane and not in one only, it must be an efficient 
 beam in every direction. The ideal long column is a hollow 
 cylinder which is a fairly and equally good beam in every direc- 
 tion. The greater the diameter the greater the resistance to 
 bending as a whole, but there is a limit to desirable increase of 
 diameter and consequent reduction of thickness owing to the 
 tendency of very thin tubes to give way by wrinkling or 
 
25 
 
 corrugation of the thin metal. Figure 21 shows a full size 
 sample of bicycle tube that has been crushed in the University 
 testing machine, its original dimensions being shown by dotted 
 lines the metal is '035 thick and the ultimate load 4400 
 Ibs. Unfortunately the circular tube is very unsuitable for the 
 convenient attachment of other parts, and consequently has 
 been generally rejected by the designers of framed structures, 
 although the great Forth Bridge and the modern bicycle frame 
 are instances to the contrary. A further reason for rejecting 
 the circular tube is, in structures of ordinary size, the 
 inaccessibility of the interior for purposes of inspection, clean- 
 ing, painting, and repair. To describe and discuss all the 
 sections that have used for compression members for chord and 
 web purposes would extend this paper far beyond permissible 
 limits. It must therefore suffice to enunciate general conditions 
 to be complied with, and point out instances of conspicuous 
 transgression of these conditions. 
 
 () A good compression section should have a large radius 
 
 of gyration in every direction. 
 
 (b) If the column is prevented from bending in one plane 
 by the attachment of other parts, and is not so pre- 
 vented, or not so effectively prevented from bending 
 in a plane at right angles to the first, it should, if its 
 radius of gyration varies, be placed with its maximum 
 radius of gyration in the second plane. 
 
 (<:) Thin unsupported edges should be avoided, or, if unavoid- 
 able, should not be counted as part of the effective 
 section, as they are very liable to buckle. 
 
 (d) Flat surfaces should not be made too thin in proportion 
 
 to their width. A proportion of 1 to 30 is quite 
 small enough. If this be passed the central part of 
 the flat face becomes of little value for resisting 
 compression. 
 
 (e) If two compression members be connected together with 
 
 the object of preventing their bending in the plane 
 of the connecting pieces, those pieces should be 
 arranged so as to constitute an efficient web system, 
 forming with the two compression pieces a complete 
 girder designed for resisting bending. 
 
26 
 
 AVe now proceed to cite cases of infraction of these rules, with 
 consequent loss of strength. 
 
 Figure 22 represents one girder of a small over bridge at the 
 Spencer Street Railway Station, Melbourne. It is 45 feet span 
 and about 4 feet deep. All the diagonal web members are of 
 3 x | inch iron. These are suitable enough for tension purposes, 
 but most inefficient in compression, having a radius of gyration 
 across the plane of the girder of only -1 inch or about 3^ of the 
 length. This unfortunate girder further presents the faults of 
 redundancy, owing to the presence of unnecessary verticals, and 
 of absurdly heavy and complicated end pillars. 
 
 Fig. 23 represents an amended design in which the more 
 heavily stressed compression diagonals are made of angle iron 
 having a radius of gyration many times greater than that of the 
 flat bars, and in which the faults of redundancy and dispropor- 
 tionate ends are avoided. 
 
 Inch to the foot models in iron of each of these girders were 
 constructed at the University and tested to destruction, with the 
 following results: The amended design contained 16 per cent, 
 less iron than the original owing to the omission of the massive 
 end plates and intermediate verticals. It involved much less 
 workmanship owing to there being less than one-third the 
 number of rivets, and the time taken in making it was less than 
 half that of the other. Its actual breaking load distributed 
 along the bottom chord as in the actual bridge was 77 libs, 
 as against 208 for the original structure. Thus with identical 
 external dimensions, and very little change in appearance, the 
 cost of the structure was largely reduced, and its strength 
 increased nearly fourfold. The mode of fracture of this defective 
 design was, as was predicted by calculation, the buckling or side 
 ways bending of the weak compression diagonals near the end. 
 There would be no difficulty and but little expense in increasing 
 the strength of this structure threefold by simply clamping 
 angle irons to the most heavily stressed compression diagonals 
 so as to prevent their bending, and this ought to be done, and 
 was long ago urged by the writer, but without result. 
 
 Fig. 24 represents the section of a large buttress or inclined 
 strut, erected at great cost on the down stream side of the 
 Victoria Street Bridge, near Melbourne, for the purpose of 
 
i/A 
 
 angle iron double 
 
 r 
 
 zj. 
 
 anqle iron double 
 
 | 
 
 angle iron, 
 fig. S.3 
 
remedying an entirely imaginary lack of lateral stability. Its 
 radius of gyration is 3 '9 inches in the plane of its web, and 1 inch 
 at right angles to that plane. It is 25 feet long and is regarded 
 as fixed in direction at the ends, though whether this fixing is 
 perfectly reliable is not altogether certain. It is braced against 
 lateral bending by a costly system of bars in the plane* oi the web. 
 Taking the most favourable view, calculation shows that it would 
 give way under a compression of 98,000 Ibs., whereas if it were 
 turned the other way, as it easily might have been, so as to be 
 braced in the direction in which it was weakest, its resistance 
 would be more than 200,000 Ibs. This is an instructive 
 example of the neglect of condition b, p. 25. 
 
 Fig. 25 represents a very usual section of compression chord 
 of the earlier types of lattice girder bridges in England and 
 Australia. Here the side plates are so thin and so liable to 
 buckle or wrinkle at the edges that it was decided in the calcula- 
 tions made by Professor Warren and the writer, and published 
 in the Report of the Royal Commission on Railway Bridges, 
 N.S.W., 1886, to ignore the outer half of their width as contri- 
 buting anything to the compressive resistance of the chord. As 
 an example of improved practice, Fig. 26 is given, representing 
 the upper chord of the very fine steel bridge over the Yarra, on 
 the Gippsland Railway. 
 
 Of transgression against condition d, I am happily unable to 
 quote a case. 
 
 Condition e applies to very numerous cases of compression dia- 
 gonals, where two parallel angle, T or channel bars are braced 
 together. Fig. 27 represents an arrangement that has been 
 adopted on the two most recently erected bridges over the Yarra, 
 and shows that the latest practice is not always the best. The 
 only function that the cross connections perform is to ensure 
 that the two main bars bend the same way, and if they are of 
 themselves inclined to do so no gain of strength ensues as 
 compared with entirely disconnected bars. Fig. 28 shows a vast, 
 improvement with the same amount of iron and rivetting, and 
 the dotted lines show how any lateral bending must be of a very 
 different character to that of Fig. 27. In fact the shorter curves 
 and more numerous nodes in the latter case are equivalent to a 
 reduction to the effective length of the column to the distance XY, 
 
28 
 
 which means a valuable gain in strength. There would be no 
 difficulty and but little expense in altering these structures now, 
 removing the cross pieces one or two at a time when the bridge 
 was free from live load, and replacing them by square plates as 
 in Fig. 28. An even better but slightly more expensive arrange- 
 ment would* be to insert a complete triangulation similar to that 
 shown for a different purpose in Fig. 8. 
 
 Fig. 29 represents a type of braced strut appearing in the late 
 Sir John Hawkshaw's great railway bridge over the Thames at 
 Charing Cross, Fig. 15, and copied thence extensively in Europe 
 and in New South Wales. It requires but little consideration 
 to detect the weakness of this arrangement. Suppose there is a 
 tendency for the member to bend to one side, the rectangular 
 panels will become rhomboidal, one diagonal being extended, and 
 the other reduced in length. Now if these diagonals are straight 
 they will oppose the maximum resistance to such distortion, 
 but if bent or crooked, as in the Charing Cross Bridge, the 
 extended one will tend to straighten, and the compressed one to 
 become more crooked. Experiments have been made at the 
 University on different types of compression members, and have 
 shown that great advantage ensues from replacing this unsatis- 
 factory double system of crooked flat bars, by a single diagonal 
 system of straight bars, as shown in Fig. 30. This improvement 
 might easily be applied to actual structures, taking advantage of 
 times when they are free from live load to remove the one and 
 insert the other. 
 
 Fig. 31 is a photograph of a number of experimental com- 
 pression pieces tested at the University, arranged in order of 
 merit. The best of these carried, in proportion to the metal it 
 contained, rather more than twice the load that the worst did. 
 These specimens were free to bend in their own plane, but braced 
 at three points in a direction at right angles to their own plane, 
 and represented compression diagonals in closely latticed girders 
 intersected and kept from bending in the plane of the main 
 girder by the tension diagonals. The figures at the bottom 
 indicate the ratio of the load carried, to the weight of the 
 structure, and thus express the relative values of the various 
 systems. The first and third of these models have angle bars 
 and the second and fourth channel bars for their sides. 
 
n g .z 5 . 
 
 .26. 
 
 o o 
 
 
 \ 
 
 
 
 
 
 o 
 
 1 
 o 
 
 \ 
 
 
 
 \ 
 
 
 
 \ 
 
 
 
 
 
 1 
 
 o 
 
 / 
 
 1 
 
 c 
 
 o 
 
 (V 
 
 / 
 
 
* 
 
 
 Fig. 31 
 
29 
 
 1 7. Imperfect jointing of tension members. The form of section 
 and ratio of length to transverse dimension of a tension member 
 are immaterial as regards strength, and so may be arranged 
 according to convenience. The joints, however, are the points of 
 vital consequence, and malformation of these often leads to 
 serious loss of strength and efficiency. Of these joints there are 
 two principal classes, ri vetted joints and eye-bar and pin joints. 
 The first of these is most usual in European, and the second in 
 American bridge work. 
 
 In rivetted work, the metal is used as it comes from the rolling 
 mill and the attempt to utilize the full section for strength is not 
 made. A rivetted joint, in other words, never claims perfect 
 efficiency, but is always subject to some percentage of loss as 
 compared with the pieces connected. To minimise this percen- 
 tage of loss is the object in arranging the joint, and it is possible 
 to reduce this to the proportion of area cut away by one rivet 
 hole. Fig. 32 shows a properly rivetted joint, which should 
 fracture at the line AB, passing through the leading rivet and 
 giving an efficiency less than unity by the fraction represented 
 by the diameter of one rivet hole divided by the width of the bar. 
 It will not fracture through the following pair of rivet holes, 
 because the tension is too much reduced by the action of the 
 first rivet to permit it, nor through the third row for a similar 
 reason. All this has been verified by careful experiments at the 
 Melbourne University and elsewhere. In contrast with this, 
 Fig. 33 shows a tension member weakened by no less than three 
 rivet holes in one leading row, and many similar cases might be 
 quoted. There are many more complicated forms of tension 
 joint met with in girder work to discuss which would occupy 
 too much space here. Suffice it to say that the same general 
 principles apply as in the simple cases. 
 
 The leading rivet ought to to placed in the mean fibre of the 
 bar, which in an ordinary rectangular section is the middle of 
 the width and the other rivets arranged symmetrically behind. 
 Sometimes it is convenient to place the leading rivet near one 
 side, and, as far as the writer's experiments go, the loss of 
 strength due to such an unsymmetrical arrangement does not 
 seem to be serious. Still it is a departure from what is obviously 
 the right arrangement, and is therefore not to be encouraged. 
 
30 
 
 In arranging rivetted joints it is recommended that there 
 should be a width of solid metal at least equal to 1 J diameters of 
 a rivet between each rivet hole and its neighbour or between a 
 rivet hole and the edge or end of the plate, for drilled work, and 
 1J for punched work, that the shearing area of the rivets be 20 
 per cent, in excess of the tearing area of the plate, and that the 
 aggregate diametral bearing area or sum of the products of the 
 diameters of all the rivets piercing a given plate into the 
 thickness of such plates shall be not less than half the tearing 
 area of that plate. 
 
 If a weak rivetted joint be discovered in an existing structure, 
 and it is not possible to increase the number of the rivets, an 
 improvement may often be made by removing the rivets one or 
 two at a time, carefully enlarging the holes with a suitable cut- 
 ting tool, and inserting larger rivets. This may be done very 
 advantageously in punched work, for the metal removed is that 
 which was damaged in the process of punching, and therefore of 
 little value. 
 
 In eyebars the attempt is usually made to secure perfect effi- 
 ciency, in other words to make the joint as strong as the bar, and 
 when the bar is very long there is great economical advantage, 
 as the whole of the material is then utilized fully. In order to 
 do this the proportions of the eye must be carefully attended to. 
 These have been determined experimentally by Brunei, Sir Chas. 
 Fox, and Berkley in England, and Shaler Smith and others in 
 America, and their conclusions may be generally summed up as 
 follows, averaging the results when the authorities differ, as they 
 do, to a small extent. 
 
 (a) The internal diameter of the eye or diameter of the pin 
 
 must never be less than two-thirds of the width of 
 the bar, and if the bar has a thickness of more than 
 one-fifth its width this should be progressively 
 increased, till, when the thickness is half the width, 
 this diameter is 1*2, and when equal, the bar having 
 a square section, 1 -9 times the width. 
 
 (b) The sectional area of the metal on both sides of the eye 
 
 should be 1'33 that of the body of the bar for bars 
 whose thickness does not exceed one-fifth of the 
 width, increasing to 1-76 when the thickness equals 
 
31 
 
 the width and the bar becomes square. The outline 
 of the bar must consist of easy curves, and sharp 
 re-entering angles must be most carefully avoided, 
 (see Fig. 37). 
 
 (c) The pins must be designed as beams to endure the bend- 
 ing moment due to the pull of the eyebars, and if this 
 necessitates a larger diameter than the previous rule 
 (a) gives, the eyes must be correspondingly enlarged. 
 In America the eyebar construction in its most perfect form 
 is almost universal in the tension parts of the larger bridges, and 
 a very magnificent example of recent American practice is to be 
 seen in the great Hawkesbury Bridge, N.S.W. 
 
 In Europe, India, and Australia it is less usual, and where it 
 exists is often of very defective design, as the following examples 
 will show. 
 
 Fig 34 represents the wind bracing of the piers of the ill-fated 
 Tay Bridge, which was destroyed by a gale in 1879, involving the 
 destruction of a whole railway train and every person upon it. 
 Here no attempt has been made to form a proper eye, and only 
 about half of the strength of the bar is really utilized. 
 
 Fig. 35 represents a tension eyebar from the Taptee Viaduct, 
 Bombay, Baroda, and Central India Railway, of which the Gun- 
 dagai Bridge, N.S.W., appears to be a copy. It is also very 
 inefficient, utilizing less than half of the metal in the bar. 
 
 Fig. 36 represents the eyebar diagonals of the great Moora- 
 bool Viaduct on the Geelong and Ballarat Railway. The most 
 cursory inspection will reveal how far this departs from orthodox 
 proportions with its diminutive pin, its sharp internal angle at A 
 leading to great local intensification of stress and its two sides in 
 the aggregate barely equal to the body of the bar instead of being 
 33 per cent, greater. Experiments were made at the University 
 on models, first in lead, then in brass, and finally in iron on a 
 quarter full size scale, to determine the efficiency of this joint, 
 and the results varied from 64 to 70 per cent. Further experi- 
 ments by the Victorian Railway Department led to a practically 
 identical conclusion. Considering that there are several hundreds 
 of these bars in the structure it does seem strange that this 
 defective form was decided upon without experiment, and also 
 that the example of Brunei and others who had used fairly good 
 
32 
 
 eyebars in suspension bridges years earlier was disregarded. 
 After some years of discussion the Railway authorities yielded to 
 the writers representations, and condemned this viaduct as a 
 double line bridge. It now carries a single line only, though 
 containing abundant material if rightly disposed to make an 
 amply strong double line structure. 
 
 In the bottom chord of this viaduct eyebars are also used, 
 having the extraordinary peculiarity of the centre of the eye 
 being an inch above the centre line of the bar. As, however, 
 this chord is of excessive sectional area no real danger arises 
 from this singular departure from correct practice. 
 
 Structures having defective eyebars in them can be improved 
 only by reconstruction and replacement of the weak parts. If 
 this is impossible, the load carried should be reduced, by 
 narrowing the deck if a public road is carried or removing a 
 line of rails, placing the remaining line centrally as was done 
 at the Moorabool Viaduct. 
 
 Fig. 37 represents an eye from the Hawkesbury Bridge, and 
 may be regarded as an example of the best and latest practice. 
 
 The joints of compression parts are not often a source of 
 weakness. If they are solidly butted together, the only need for 
 rivetting is to prevent lateral displacement. The usual practice, 
 however, is to assume that the ends are not in contact, and 
 insert sufficient rivets to carry the whole stress as in tension 
 joints. In this case there is no need to have the single leading 
 rivet, and the arrangement shown in Fig. 33 is admissible. 
 Should the rivets of a compression joint be insufficient to take 
 the stress they will distort slightly and permit the ends of the 
 plates to come into contact, when further yielding will be 
 effectually prevented. The practice has been sometimes adopted, 
 and appears reasonable, of putting the girders together with but 
 a few loosely fitting "service bolts" in the rivet holes of the 
 compression joints, then loading them with a weight sufficient 
 to bring the ends of the parts into perfect contact, and then 
 rivetting up. If this method' be adopted the number of rivets 
 in compression joints may be made very small. 
 
 18. Local weakness at intersection of web members. In the 
 older form of lattice girders the web diagonals near the centre 
 of the span are usually made of angle bars, which give a suitable 
 
33 
 
 section in view of the circumstance that with varying conditions 
 of loading they may be called upon to endure either compression 
 or tension. When two of these angle bars intersect it is a usual 
 practice to cut away one limb of one of them, reducing it to a 
 simple flat bar, which is further reduced by the hole needed to 
 receive the connecting rivet. Thus the remaining or net 
 sectional area becomes about one- third of the gross area, and 
 as it further is subjected to the most injurious kind of stress, 
 that alternating from compression to tension, during the passage 
 of the load, a very serious but easily overlooked weakness ensues. 
 Fortunately the remedy is simple and cheap. It consists in 
 adding a second layer or reinforcing plate to the diagonal at the 
 weak point, extending about a foot on each side of the inter- 
 section, and connected with the unmutilated part of the angle 
 bar with a sufficient number of rivets. 
 
 19. Arrangements involving serious secondary stress are not 
 uncommon, especially in English types of girders. 
 
 The stress upon any bar of a framed structure with rigid joints 
 is of two kinds, primary and secondary. The primary stress is 
 that computed by the ordinary methods of analytical or graphic 
 statics ; in other words, by the successive application of the 
 proposition known as the parallogram or triangle of forces. 
 This investigation, provided the structure is not redundant, is 
 simple, and the result certain, admitting no possibility of dispute. 
 All such calculation, however, is based on the assumption that 
 each set of bars meeting at a point is connected by a perfectly 
 frictionless hinge joint. This assumption is by no means strictly 
 true, even in eyebar work, on account of friction, while in 
 structures having the joints made by complicated groups of 
 rivets it is manifestly highly erroneous. What then is the 
 nature and magnitude of the extra, or, as they are now called, 
 secondary stresses, due to the friction or rigidity of joints, 
 and how may they be minimised 1 
 
 This question was first discussed by the Austrian investigator, 
 Manderla, in 1878, but owing to the intricacy of the calculations, 
 and the delicate nature of the experiments needed, we have so 
 far arrived at but approximate determinations of its value. 
 
 The completest treatment that the writer has met with is that 
 of Professor W. Hitter, of the Polytechnic School of Zurich, and 
 was published in 1884. 
 
 3A 
 
34 
 
 Manderla's work is referred to in Bender's " Economy of Design 
 of Metallic Bridges," New York, 1885. Bender states that he 
 has applied Manderla's method to a number of examples, and 
 that he has found in a "100 foot Whipple truss, 20 feet deep, a 
 maximum secondary strain of 8 per cent." in the centre of the top 
 chord. He also says that he has found "Secondary strains of 
 172 per cent." of the primary stresses in a triangular pin-jointed 
 girder of 118 feet span and 12 -5 feet deep in South Germany. 
 Again he speaks of "secondary strains as high as 180 per cent." 
 over the middle piers of continuous bridges. Now, all this is 
 most unsatisfactory and alarming. Unsatisfactory, because 
 Bender gives no drawings or detailed dimensions of his bridges, 
 nor does he show how he arrives at his results. Alarming 
 because the only meaning that can be attached to his words is 
 that the secondary stresses in structures of ordinary type may be 
 greater than, in fact, nearly double of the primary stresses, 
 and if this be the case, the structures affected must be most 
 imminently dangerous, indeed it is difficult to understand why 
 they have not long since fallen. 
 
 Ritter's work, as quoted by Koechlin in his "Applications de 
 la Statique Graphique," Paris, 1889, is much fuller and more 
 satisfactory, and his results more intelligible and less alarming. 
 The maximum secondary stress that he arrives at in structures 
 of ordinary proportions, is less than 30 per cent of the primary 
 stress. Still, his method appears to the writer to be too general, 
 and to fail in indicating exactly at what points of a frame the 
 severest stress is to be expected. The writer has, after much 
 consideration, arrived at a method, which he submits as giving, 
 without inordinate labour, a fair approximation to the secondary 
 stress in, at any rate, the simpler types of structure. It consists 
 of the following operations : 
 
 (a) From the primary stress and sectional area of each bar, 
 
 and its known modulus of elasticity, its change in 
 length is computed. This will be an elongation or 
 shortening, according as the primary stress is tensile 
 or compressive. 
 
 (b) This change in length is exaggerated a convenient 
 
 number of times. The writer increases it one 
 hundred fold. 
 
35 
 
 (c) The frame is then re-plotted with the altered lengths of 
 
 the bars. One result of this is that the panel points 
 of the top and bottom chords, instead of lying in 
 straight lines, will lie in curves, which in most cases 
 are approximately circular, but in others that have 
 been tried, have a cusp at the centre, like a Gothic 
 arch inverted. This cusp indicates a point of intense 
 secondary stress. 
 
 (d) A smooth and regular curve (usually circular) is drawn 
 
 through all these panel points, and at each panel 
 point a tangent to this curve is drawn. This is most 
 conveniently done by taking a well-tempered piece of 
 spring steel and bending it so as to pass through all 
 the points. 
 
 (e) Lines are drawn, making the same angles with th< j se 
 
 tangents that the diagonals or web members made 
 with the chords, when the structure was free from 
 stress. If two such lines drawn from the two extre- 
 mities of a diagonal or web member coincide, forming 
 one straight line, that web member is free I'rom 
 secondary stress. But if, as is usually the case, they 
 do not coincide, then the diagonal, which, by virtue of 
 its rigid attachment to the chord is tangential to 
 these lines at its ends, must be bent into a curve, 
 usually of double curvature, or S curve as it is often 
 called. This curve will present a point of contra- 
 flexure and consequently of no bending moment at or 
 near the mid-length of the bar and each part of the 
 bar will be a cantilever, the deflection of the end of 
 which can be measured on the exaggerated scale 
 adopted, and from this, its width, and the modulus of 
 elasticity, the secondary stress can be computfd. 
 This secondary stress is usually least at the centre of 
 the bar, increasing to a maximum at the ends. To 
 find the exact curve assumed the piece of spring steel 
 mentioned before may be applied. 
 
 (/) The secondary stress of the chords is computed from the 
 radius of the curve d and in most cases is approxi- 
 mately uniform throughout. 
 
36 
 
 To carry out this method, diagrams of one of the simplest of 
 which Fig. 38 is a greatly reduced copy, have been made, and 
 from them the following results have been obtained : 
 
 The smallest secondary stress so far as he has gone, the writer 
 has found in the simple Warren girder, consisting of one series of 
 equilateral triangles. 
 
 In this girder, assuming that the transverse dimensions of the 
 chords and web members to be equal, and their sections symmet- 
 rical about the neutral axis, the secondary stress in the web 
 members is about four times that in the chords. 
 
 Taking a Warren girder of 8 panels as shown in Fig. 38, of 
 100 feet span, with all members 1 foot wide, stressed to 6 tons 
 per square inch with ordinary provision for partial loading, and 
 a modulus of elasticity of 26,000,000, the secondary stress in the 
 chords was 8 per cent, of the primary, and in the web members 
 30 per cent, of the primary. Any reduction in the width of any 
 bar (as measured in the plane of the frame) without altering its 
 sectional area, reduces the secondary stress in the same propor- 
 tion. Hence it is desirable to keep the web members of such 
 girders as narrow as other considerations will permit. 
 
 The usual trough or T section employed for chords is subject 
 to only about half of the increase of stress, that a rectangular or 
 other section symmetrical above and below experiences. This is 
 due to the fact that the neutral axis lies so much closer to the 
 side where the primary and secondary stresses are additive. 
 
 The N girder or that with alternate vertical and diagonal web 
 members is subject to considerably more secondary stress than 
 the Warren of equal dimensions and width of bars, especially 
 in the vertical members. It also shows an intensification of 
 secondary stress at the midspan if made with an even number 
 of panels. At each of these points the secondary stress is at 
 least 50 per cent, greater than at the corresponding points of 
 the Warren girder. 
 
 In the X girder, Fig. 23, the distribution of secondary stress 
 is peculiarly complicated. That in the chords is variable, 
 attaining maxima values at alternate panel points, and vanishing, 
 or nearly so, at the other alternate panel points, its maximum 
 value being about double what it is on the corresponding Warren 
 girder. That in the diagonals is about equal to what exists in 
 
37 
 
 the Warren girder if the diagonals are not connected at the 
 points of intersection. If they are it is increased about 50 per 
 cent. 
 
 At the root of a cantilever or over an intermediate support in 
 a continuous girder, the secondary stresses, both in chords and web 
 members, attain a value nearly twice as great as those in a girder 
 simply supported at the ends and designed to carry distributed 
 moving loads, such as ordinary road and railway bridges are 
 subjected to. This is due to the fact that both chords and web 
 members are stressed most heavily at the same time, which is not 
 the case at the centre of an ordinary discontinuous girder 
 the maximum stress comes on the chords under full load, and on 
 the web members under a load extending from one end to the 
 centre. 
 
 The foregoing results, while very far removed from the 
 alarming statements of Bender, nevertheless err on the side of 
 pessimism. The subjoined facts all indicate certain sources of 
 relief from secondary stress, which neither Bitter's nor the 
 author's methods of investigation take account of. 
 
 1. The full stress of 5 or 6 tons per square inch is not main- 
 
 tained throughout any structure. Many parts are, for 
 convenience, to obviate the use of too many differ- 
 ent sections of metal, or to facilitate jointing, made 
 10, 20, or even sometimes 50 per cent, more massive 
 than calculation requires. Hence the deformation 
 of the structure is reduced below what it would be 
 if more closely designed. This tends to reduce 
 secondary stress. 
 
 2. In both Ritter's and the author's methods it is assumed 
 
 that the chord sections are so much more massive 
 than those of the web members as to completely over- 
 power them, and compel them to accommodate their 
 direction to that of the chords. This is by no means 
 absolutely true. Assuming as a fair average that 
 the web members are one-fourth as stiff as the chords, 
 there will be a rotation of the joints, tending to 
 reduce the secondary stresses in the web members by 
 25 per cent, and increase those in the chords. As 
 the previously determined secondary stress in the 
 
38 
 
 web members was, other things being equal, about 
 four times that in the chords, this means a distinct 
 gain. 
 
 3. By virtue of resistance to secondary stress and entirely 
 
 apart from primary stress, a certain small portion of 
 the load is carried. 
 
 4. It is doubtful if ever the tightest rivetted joints are 
 
 absolutely rigid, and any microscopic yielding or 
 adaptation in them tends to reduce secondary stress. 
 In order to provide for secondary as well as primary stress, 
 with economy it is recommended in new designs. 
 
 (a) That other things being equal or nearly so, preference be 
 given to the Warren or equilateral type of girder, 
 with a single system of triangulation. 
 
 (/>) That chords of trough or T section be preferred to those 
 that are symmetrical about their horizontal neutral 
 axis. 
 
 (c) That all members be kept as narrow in the plane of the 
 
 girder as other conditions permit. 
 
 (d) That the unit stresses in the web system be made about 
 
 10 per cent, less than those adopted in the chords. 
 
 (e) That girders of ample depth, say not less than ^ of the 
 
 span, be preferred to shallower ones. 
 
 (_/") That those portions of continuous girders immediately 
 
 above non-terminal supports be made about 15 per 
 
 cent, more massive than the corresponding parts of 
 
 ordinary girders. This extra strength to taper away 
 
 till it disappears at the point of contraflexure. 
 
 Existing bridges should have their stresses determined by the 
 
 method previously described, and where the secondary stress and 
 
 primary stress together exceed the usually permitted primary 
 
 stress by more than 30 per cent., either the load should be reduced 
 
 or the weak part strengthened. This strengthening must be made 
 
 without increasing the breadth of the bar. 
 
 Girders of the N type with broad web members, such as that 
 shown in Fig. 17, where the diagonals have a width of one-eighth 
 of their length and are very firmly rivetted, should be looked 
 upon with the greatest suspicion and taken in hand first, also 
 continuous girders of all types. 
 
39 
 
 As some of the above remarks may appear condemnatory of 
 the American type of girder, of which the Hawkesbury Bridge is 
 so magnificent an example, it is well to point out that, owing to 
 the narrowness of the web members relatively to their length, 
 the secondary stress is here comparatively small, not exceeding, 
 according to the writer's method, 10 per cent., even on the 
 assumption that the joints are perfectly rigid, which, being eye- 
 bar and pin construction, they hardly can be, no matter how 
 tightly fitted and bolted up. 
 
 20. Arrangements involving severe temperature stresses. The 
 existence of heavy stresses due to variations of temperature has 
 been generally recognised in the case of metallic arches and 
 suspension bridges, but not in the case of ordinary girders. 
 There is, however, reason to believe that in a subtropical country 
 like Australia, and especially in those parts where the air is dry, 
 and so imposes but little resistance to the solar radiation, very 
 serious stresses, amounting possibly to tons per square inch, may 
 be produced by one of a series of parts that ought to act in 
 unison, being exposed to the direct rays of the sun, while the 
 others are in shade. In this way a difference of temperature of 
 30 deg. or 40 deg. may easily be produced, and the consequent 
 difference of expansion will give rise to temperature stresses 
 of 2 to 3 tons per square inch, which are cumulative upon the 
 ordinary stresses given by statical calculation. 
 
 That these temperature stresses really exist is abundantly 
 proved by recent experiences at the great Moorabool Viaduct 
 on the Geelong and Ballarat Railway. Here there are four 
 precisely similar continuous girders, each 1300 feet long. They 
 are completely sheltered from the sun by a broad overhanging 
 deck that surmounts them, with the exception of the lower chord 
 of the girder on the northern side. This chord consists of a 
 number of eyebars placed side by side, and it was observed by 
 the officers of the Railway Department that the outside bar 
 when highly heated by the sun actually buckled under the 
 compression, although at a part where the heaviest tension due 
 to the load existed. The result of this buckling was to increase 
 the stress on the adjoining bars by probably 30 per cent. To 
 remove this serious source of weakness, a wooden roof, the whole 
 length of the viaduct was erected over the chord so affected. 
 
40 
 
 This was undoubtedly the right thing to do, only, in the writer's 
 opinion, an iron roof would have been more permanent and more 
 in harmony with the monumental character and architectural 
 pretensions of the structure. 
 
 This question of temperature stress ought to be looked into in 
 the case of all girders that are partly or wholly exposed to direct 
 solar radiation, and where they are found to exist in any serious 
 degree, light screens or roofs of sheet iron should be introduced 
 so as to ensure vital and highly stressed parts of the structure 
 being always in the shade. As things are at present, it seems 
 impossible to resist the conclusion that structures designed in 
 the usual way for a working stress of 5 or 6 tons per square 
 inch are frequently, owing to the combined effect of secondary 
 and temperature stresses, subjected to actual stresses approaching 
 double their nominal amount. 
 
 Further, it is recommended that girders exposed to the direct 
 solar radiation be painted white, in order to keep them as cool 
 as possible. 
 
 21. Insufficient lateral bracing. While gravity is usually by 
 far the greatest force acting on bridges, there are other forces 
 that must not be overlooked operating in non-vertical directions, 
 and which may, and as a matter of history have wrecked 
 structures that gravity was powerless to injure. Of these forces 
 the most important are the horizontal pressure of wind or flood 
 against the structure, the lateral oscillation of badly balanced 
 locomotives, and the tendency of the compression chords of the 
 main girders to bend sideways as long columns. From this point 
 of view, a pair of columns such as shown in Fig. 2, form a verti- 
 cal cantilever, fixed at the foundation arid subjected to horizontal 
 forces from flood and wind. The columns form the chords of tho 
 cantilever, and must have sufficient sectional area to endure the 
 consequent compression and tension, as well as the compression 
 due to the load. In this way the bending moment is provided 
 for. The shear requires a suitably designed web system connect- 
 ing the columns, without which they cannot act together as one 
 efficient cantilever. Now, with regard to this web system, the 
 wildest inconsistency is found in existing bridges. In not a few 
 cases, as for example the Charing Cross Railway Bridge, London, 
 already referred to, it is entirely absent, although the rapid 
 
41 
 
 tidal current of the Thames and the prevalence of heavy barges 
 drifting therewith would appear to call for more than usual 
 provision against lateral shocks. In others, as for example the 
 railway bridge over the Murray, on the main line from Melbourne 
 to Adelaide, it consists of very light round rods. On the Vic- 
 torian Railways a fairly massive T iron bracing is usually 
 employed, while on the older New South Wales Railway Bridges 
 a still more massive and complex arrangement is used. The 
 N.S.W. Roads and Bridges Branch has adopted a practice 
 different from all the preceeding, and connects the two columns 
 by a continuous web of sheet iron, lightened by being pierced 
 with large oval openings. This arrangement, it is contended, gives 
 ample strength, and is not so likely to be injured by floating logs 
 as the others. It however involves the use of a large amount of 
 metal and comparatively complex workmanship. Now, various 
 and inconsistent as is the practice of Engineers in this respect, 
 the principles of design are few and simple, and are identical 
 with those applying to the design of framed girders. A non- 
 redundant system of triangles, free from eccentricity, with good 
 joints and bars massive enough to be safe from accidental blows, 
 is all that is required. The bracing of the Johnston Street Bridge, 
 as shown in Fig. 2, is open to serious criticism. It is in the first 
 place redundant. The horizontal pieces are costly and complex 
 rivetted girders, while the diagonals are angle irons of unduly 
 light section, so light, in fact, that they can be sprung some inches 
 by the pressure of the hand. Had the horizontal connections 
 been left out altogether, and a fourth of the money so saved 
 expended in making the diagonals twice as massive as at present, 
 the structure would have been strengthened and cheapened at the 
 same time, and the calculation of stress on its various parts made 
 easy and certain. In this and many other cases, the bracing 
 terminates above the summer level of the stream, leaving the 
 bottom part, when the shear is greatest, unbraced. This course 
 is usually excused on the ground of the difficulty of making 
 attachments under water, and if the lower part of the columns is 
 much more massive than the upper and well supported by the 
 firm ground around the excuse may be accepted. It is, however, 
 far more scientific and satisfactory to carry the bracing down to 
 the bottom, and this has been done in two of the most recent 
 bridges over the Yarra at Melbourne. 
 
42 
 
 The lateral bracing of the girders of existing bridges is just as 
 various and inconsistent as that of the piers in some cases being 
 entirely absent and in others overdone at unnecessary expense. 
 
 The older type of tubular bridges, such as the Footscray 
 Railway Bridge, Victoria, and those at Menangle and Penrith, 
 N.S.W., though presenting enormous surfaces to wind pressure, 
 are invariably absolutely devoid of lateral bracing. They resist the 
 wind simply by the resistance to bending of the main and cross 
 girders in their weakest direction, and must be subject to extra 
 stresses of serious amount in consequence. On the other hand, 
 one not unfrequently sees small open lattice girders offering but 
 insignificant surface to the wind, braced in the most costly and 
 elaborate manner. Now, both these extremes must be wrong,, 
 and a discussion of what is really needed will be of advantage. 
 A little consideration will show, as has been abundantly verified 
 by experiments on models at the University, that a girder may 
 be wrecked by lateral movement in one or more of the following 
 ways : 
 
 () It may fall over on its side, turning on its lower chord 
 as an axis. This may be caused by wind or other 
 lateral force acting on the top chord and web. The 
 tendency will be greatest with deep and narrow 
 girders, and becomes insignificant in the case of 
 those that are shallow and broad. If the traffic is 
 carried on the top of the girders this tendency may 
 be effectively met by inserting a diagonal of sufficient 
 section between the bottom of one girder and the top 
 of the other at each point of support. This, with the 
 cross girders, will keep all secure. Should, however, 
 the traffic pass between the girders, as is often the 
 case where headway is limited, such a diagonal is 
 inadmissible. We must, therefore, make the base of 
 the girder broad enough to secure stability, and 
 carry a pillar up, starting the full width of this 
 broad base, but tapering, if desired, toward the top, 
 as indicated in Fig. 12, or, as an alternative, cross 
 girders may be made continuous with stiff web 
 members, so that the vertically of the plane of the 
 latter is secured by the resistance to bending of the 
 
43 
 
 cross girder. Properly such cross girders should 
 carry no load, for if loaded their deflection will affect 
 the vertically of the main girder. This, however, 
 can hardly be insisted upon in practice. 
 
 (b) The chords may be bent sideways by the pressure of 
 wind upon the girder itself or upon objects supported 
 by it. This pressure will be great in the case of 
 plate web girders and of that chord of an open girder 
 that carries the deck. It is to be met by inserting 
 a proper system of diagonals forming with the 
 chords of the main girder, a complete horizontal 
 triangulation. It is certainly desirable that such a 
 triangulation, made of stout T or angle section, be 
 added to the older tubular girder bridges and others 
 that do not possess it. The smaller the width as 
 compared with the span the more important this 
 horizontal system is. There are some cases, however, 
 in which it is not needed. The first is when the 
 bridge is provided with a continuous metallic deck, 
 as is now often the case. Such deck forms a most 
 efficient horizontal web. The second is when the 
 bridge is built on a skew such that the cross 
 girders attached at or near the end of one main 
 girder meet the other main girder at a fourth to a 
 third of the span from one end. Here the cross 
 girders themselves form an efficient bracing. 
 
 (^r) The compressed chord may buckle or fail as a long 
 column. To prevent this, it must be rigidly held at 
 frequent intervals by some system of bars preventing 
 any small initial lateral bending from increasing. In 
 an ordinary discontinuous girder the top chord is 
 compressed, and if the deck is on the top, the same 
 bracing that resists the pressure of wind on the top 
 chord, deck, and load, will meet this requirement. 
 If, however, the deck is on the bottom, the top chords 
 may, if the girder be deep enough, be braced together 
 overhead, with a complete triangulation extending 
 from end to end. This is by far the most satisfactory 
 method, and is usually found in the larger American 
 
44 
 
 and European bridges of recent construction. If the 
 headway is insufficient to permit this overhead 
 bracing, then the top member must be kept straight 
 by some stiff construction continuous with the cross 
 girders, and extending from the ends of these 
 upward, and it is desirable that the cross girders be 
 very deep and stiff. This is well arranged in the 
 Toolamba Railway Bridge, Victoria, a section of 
 which is shown in Fig. 39, and in addition the 
 bottom chords must be kept from bending horizon- 
 tally by a stiff deck or complete horizontal system 
 of triangulation. 
 
 Very often the former of these requirements is met by 
 projecting the ends of the cross girders some distance outside the 
 main girders, and inserting an inclined strut from the end of the 
 cross girder to the top of the main girder. If this system be 
 used, these struts should be straight, of stiff section, capable of 
 bearing compression as well as tension, and making an angle of 
 about 30 deg. to the vertical. 
 
 The costly and complex arched connections extending overhead 
 from one main girder to the other at the Footscray Railway 
 Bridge, near Melbourne, and on most of the earlier railway 
 bridges in New South Wales, are of very little value. 
 
 Existing bridges should be carefully examined, and if found 
 insufficiently braced, have proper triangulated systems added, 
 capable of bearing a wind pressure on the loaded structure of 20 
 Ibs. per square foot, with a safety factor of at least 5, seeing the 
 wind may blow from either side, rendering the question one of 
 vibration strength. 
 
 Numerous errors occur in connection with the design and 
 arrangement of cross girders in many early road and railway 
 bridges, of these the following deserve notice : 
 
 22. Cross girders not placed in proper relation to the web 
 system of main girders. A most glaring instance is to be seen 
 in the bridge carrying the Heidelberg and Eltham Road across 
 the Plenty River, near Melbourne, shown in outline at Fig. 40. 
 Here the main girders are of the X type, and both triangulations 
 are equally strong. The cross girders, however, are so placed 
 as to discharge their load immediately upon the alternate panel 
 
r~ oo 
 i ~ 
 
 > O O 
 
 o o o 
 o o o 
 
 000 
 
 38. 
 
45 
 
 points, so that in theory, at least, one triangulation carries the 
 whole weight. Mr. J. A. L. Waddell, a leading American Bridge 
 Engineer, to whom photographs and particulars of this structure 
 were sent, expresses himself as follows : 
 
 " For unparalleled ignorance and stupidity the triangular truss 
 illustrated bears off the palm. It is almost incredible that 
 any man with common sense could put in a whole system of 
 triangulation where it is impossible for it to do any work 
 whatever." 
 
 While generally agreeing with Mr. Waddell's drastic condem- 
 nation of the absurdity of this design, I question whether his 
 closing words are strictly correct, for the following reason : If 
 all the load was carried on one triangulation only, the panel 
 points connected with it would deflect more than those connected 
 with the unloaded triangulation, and hence the top and bottom 
 chords instead of bending in an approximately circular curve 
 would bend in a sinous way, having numerous points of contra- 
 flexure. But such bending is impossible without evoking a 
 considerable beam action in the chords, which are several inches 
 in depth. Hence, some part of the load must be transferred to 
 the other triangulation. How much would be so transferred it 
 is difficult to compute, but certainly not sufficient to cause even 
 an approximate equalization in the stress on the two triangula- 
 tions. If we assume three-fourths of the total load to come on 
 one and one-fourth on the other triangulation, we shall probably 
 be taking a fairly favourable view. This bridge, undoubtedly, 
 might be largely strengthened by inserting cross girders at all 
 the panel points, and by replacing the thin flat diagonals near 
 midspan of the main girders by proper double acting (strut and 
 tie) sections capable of resisting the action of unsymmetrical 
 loading, and this should be done at once. 
 
 Another example of a similar fault is be seen in an important 
 bridge at Southampton, England, illustrated in "Engineering," 
 4th January, 1884, and criticised by the writer in "Engineering," 
 6th June, 1884. Here the cross girders are placed at intervals 
 having no direct relation to the panel points of the main girder. 
 At one point a cross girder comes exactly midway between panel 
 points, thus bringing an unnecessary and undesirable bending 
 moment of some magnitude upon the bottom chord. 
 
46 
 
 A. further instance of this fault was to be seen in the eastern 
 extension of the Victoria Street Bridge, Melbourne, erected in 
 1884, and represented in Fig. 41. This, however, was remedied 
 at the writer's recommendation. 
 
 23. Cross girders too numerous and individually too weak. 
 This fault is very commonly to be found in the earlier railway 
 bridges of Victoria and New South Wales that have come under 
 the author's notice. The heaviest local load to be provided for 
 is that of the driving wheel of a locomotive, and amounts to 
 slightly over 8 tons for one type of Victorian locomotive, and 
 between 7 or 8 tons in five other types. In New South Wales 
 the weights are practically the same, for, though the engines are 
 heavier, they are supported on a greater number of wheels. But 
 it must not be forgotten that this load is liable to be largely 
 increased, first by the downward resolved part of the thrust or 
 pull of the connecting rod, and second by the effect of imperfect 
 balancing, so that 10 tons is the very least amount it would be 
 safe to allow as the actual wheel load. Now, this load may come 
 upon every individual cross girder in succession, and therefore 
 every cross girder should be strong enough to resist it. At the 
 same time there is 110 advantage in placing them nearer together 
 than the minimum distance between the locomotive driving wheels, 
 which is about 5 feet. Cross girders then, at not less than 5 foot 
 intervals, each strong enough to carry the heaviest loaded pair of 
 engine wheels, constitute reasonable practice, and many good 
 recent structures correspond closely to this arrangement. On 
 some of the earlier Victorian bridges, however, the interval is 
 only 2 feet 6 inches, and in New South Wales, 3 feet. The 
 stresses in these girders are found by computation to be from 7 
 to 12 tons per square inch very alarming figures. Looking at 
 many of these earlier bridges it is difficult to understand why 
 their bottoms have not dropped out long ago. It is, however, 
 to be remembered that some of the worst have never been fully 
 loaded, double line bridges as at Penrith in New South Wales, 
 and Kororoit Creek, Victoria, carrying, hitherto, only single 
 lines of way, while in most cases heavy timber longitudinals or 
 stout continuous decks interposed between the track and the 
 cross girders tend to spread the load and prevent any individual 
 girder receiving its full punishment. Reliance upon these, how- 
 
47 
 
 ever, is not advisable, as bad workmanship, decay and imperfect 
 jointing may nullify their distributing action. The best thing 
 to do with these weak girders is to introduce longitudinal 
 connections of great stiffness between them. An arrangement 
 in iron or steel similar to what is known as " herring boning " 
 between the joists of a floor was recommended several years ago 
 by the author for Penrith Bridge, N.S.W., see Fig. 42. 
 
 24. Improperly designed cross girders. These occasionally 
 occur, especially in the earlier bridges, and seem to have arisen 
 from an ill-advised attempt to make the cross girders of similar 
 type to the main girders. Badly designed lattice cross girders 
 with vital junctions made by single rivets only, and heavy 
 compressions taken on thin flat bars of considerable length were 
 unfortunately to be found in some early Victorian bridges. 
 Many have now been removed, and their places taken by sub- 
 stantial plate girders. As an example of most improper design, 
 Fig. 43 may be quoted, which, not many years ago, was removed, 
 after a quarter of a century of service, from an important bridge 
 on a busy suburban railway near Melbourne. It will be seen 
 that the tension on bar AB is 10 tons per sq. inch, the shear on 
 the rivet A, 8 tons per sq. inch, and pressure on the bearing area 
 25 tons per sq. inch figures alarmingly high. The marvel is 
 that such girders failed to cause appalling disaster. 
 
 It is fully illustrated here as a warning to bridge designers, 
 and also as an encouragment ; for the fact of these frightfully 
 over-stressed constructions having carried a busy suburban traffic 
 for a number of years without giving way, is a conclusive proof 
 of the extraordinary endurance of the material, which was only 
 iron, and an evidence of the wide margin of strength against 
 unforeseen contingencies possessed by structures designed in a 
 scientific way under usual limitations as to permissible stress. 
 
 25. Unscientific forms of footpath brackets. Many railway 
 and road bridges are provided with overhung footways outside 
 the main girders. The brackets supporting these should be 
 rationally designed cantilevers continuous with the cross girders, 
 and consisting of a proper top and bottom chord, and suitable 
 web, either of continuous plate, or triangulated series of bars. 
 Unfortunately, however, an unhealthy desire for ornament, over- 
 looking the fact that the really beautiful must be based upon 
 
48 
 
 and grow out of that which is scientific and useful, has led many 
 designers into extravagancies and absurdities. For example the 
 old Church Street Bridge, Richmond, near Melbourne, originally 
 had footpath brackets made of thin round rods bent into the 
 curves of a ram's horn, an absurd and excessively weak form, 
 while the recently constructed Swing Bridge at Footscray has 
 the webs of its footpath cantilevers made of circular rings of L 
 iron, a costly and unscientific arrangement, the exact strength 
 of which it is impossible to compute. It is suggested that such 
 brackets be carefully examined, tested, and if showing any signs 
 of weakness strengthened, and that in future structures, scientific 
 and rational forms be adopted instead of these unsatisfactory 
 pseudo-ornamental abortions. 
 
 26. Parapets too low^ too weak, or too open. These are of not 
 uncommon occurrence, and as sources of danger to the public 
 are frequently of serious import. An examination of such 
 parapets on bridges in or near Melbourne has revealed the fact, 
 that some are less than 3 feet in height, while others approach 
 5 feet. The former are certainly dangerously low, the latter 
 needlessly high. It is recommended that no bridge parapet 
 should be less than 3 feet 6 inches, which is the height of the 
 elbow of a man of medium size, while 4 feet may be taken as a 
 maximum beyond which it is unnecessary to go. The same rule 
 should, in the writer's opinion, be applied to the balustrades of 
 staircases, landings, and balconies in buildings. These are 
 usually too low, and have repeatedly been the cause of serious 
 accidents. 
 
 No rule has been to the writer's knowledge generally accepted 
 for the strength of parapets. He therefore proposes that to 
 provide for the pressure of a dense crowd, they be made strong 
 enough to endure a horizontal pressure of 100 Ibs. per foot in 
 length, applied at the top with a safety factor of not less than 
 3 for metal and 5 for timber. 
 
 This strength may be provided by the resistance to bending of 
 the uprights or standards of the parapets. But if this be found 
 to involve an undesirable amount of material, lighter standards 
 may be employed, with sloping struts outside. These struts 
 should be straight, inclined at an angle of not less than 20 deg. 
 to the vertical, and extend from the projecting end of the foot- 
 
Fig. 
 
 9 2. 
 
49 
 
 path cantilever to a point about three-fourths of the height of the 
 parapet. They may be made of angle, T, channel, or any other 
 stiff section of metal and securely rivetted or bolted top and 
 bottom. In some recent and otherwise excellent bridges near 
 Melbourne, small triangular plates of thin metal rivetted along 
 the bottom and the vertical side have been used. These are 
 not to be commended, as the maximum compression comes on the 
 thin edge of the plate that is least able to endure it, and the 
 majority of the rivets are placed where they endure but little 
 stress and are of proportionately little service. The same amount 
 of material and labour put in a substantial sloping strut would 
 give far greater strength. 
 
 A parapet may be high enough and strong enough, and yet a 
 source of danger by having openings in it large enough for 
 children to pass through. An examination of a considerable 
 number of such parapets leads the writer to recommend that if 
 formed of paralled horizontal bars, these bars should not be more 
 than 9 inches apart vertically, or if as is often the case formed 
 of lattice work showing square openings, such openings should 
 never be more than 1 foot square. It is recommended that all 
 parapets accessible to the public be altered when necessary to 
 comply with the above requirements. 
 
 In concluding this necessarily very inadequate treatment of 
 a vast and complicated subject of extreme public importance, 
 the writer desires to apologise for its brevity and other defects, 
 and to express his hope that it may be the means of rendering 
 a most important section of engineering work in some small 
 measure more consistent, economical, and secure against accidents 
 than it has been hitherto. 
 
 4A 
 
PRINTED BT 
 
 KORD AND SON, CARLTON, 
 MELBOURNE. 
 
F ou ro 
 
 
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