Opened in October 1886, the Luis I Bridge is a shaped Fe trussed arch p which ps the Douro River between Porto and Vila Nova de Gaia in Portugal. Designed by the Belgian applied scientist Th ophile Seyrig, in coaction with L opold Valentin ; it was, at the clip of its building, the longest arch p in the World, at 172m [ 1 ] , and remains the longest pning Fe arch to this twenty-four hours. It represents the swan vocal of wrought Fe Bridgess as at the start of the twentieth century stronger steel of more consistent quality would about wholly replace the usage of wrought Fe in p building.
The new p was commissioned in 1881 to replace an ailing suspension p at the same location ; Seyrig designed a double-deck arch p with one deck at the top of the arch resting on wharfs and the 2nd deck at the degree of the abutments, hanging from sinews ( Fig. 1 ) . The two decks have seen a assortment of lading over their life ; originally both decks were designed to transport route traffic, the lower deck briefly carried trolley coachs but is now a individual carriageway route, the upper deck was converted in 1905 to transport ropewaies and widened in 1931 to add a 2nd path.
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The aesthetic analysis of a p is mostly subjective, Fritz Leonhardt attempted to rationalize the aesthetic design of Bridgess in 1982 with the publication of his book, Br cken, which sets out ten cardinal points that should be considered during design.
2.1 Fulfilment of Function
This relates to how good the p divulges the manner it works ; in the Luis I bridge the arch is the chief structural component through which forces are carried. This is evident from looking at the p as the arch is the most significant member. Truss structures in general are peculiarly indicative about the manner they carry tonss, and the Luis I bridge is no exclusion.
The structural honestness of the p is called into inquiry where the arch meets the masonry abutments ; it appears as though the top member of the arch passes directly into the abutments but the abutments are non able to defy the high minute this would bring forth, so the top member of the arch must be lightly stressed at its utmost terminals. On closer review it can be seen that the concluding diagonal members on both sides of the arch are of more significant cross-section ( Fig. 2 ) in order that they are able to transport all of the force in the top rim of the arch down to the pinned connexion at the terminal of the bottom rim.
Figure 2: Forces transferred to bottom rim
Sometimes, one facet of a p s aesthetics must be sacrificed in favor of another ; in the Luis I bridge the truss which forms the upper deck is of uninterrupted deepness along its length, but the attack ps are notably longer than the subdivisions which make up the chief p. Functionally, the applied scientist could hold designed the attack ps to be deeper than the chief p but this break to the horizontal line of the deck would hold been to the hurt of the aesthetics of the construction as a whole.
As discussed above, the upper deck is deeper than it needs to be ; proportionately this contrasts aggressively with the lower deck which is significantly more slight despite crossing an equal distance. This difference is non adequately explained by the grounds already discussed. The upper deck may good hold been designed to get by with a higher burden than the lower deck ; surveies have shown that, prior to the transition of the upper deck to light rail, the upper deck carried about double the traffic of the lower deck [ 2 ] . Furthermore, at the clip that Seyrig was planing the Luis I bridge he had merely finished the building of the Maria Pia Bridge ( 1877 ) , designed in concurrence with Gustave Eiffel, which was to transport a train line over the same river. It is possible that the upper deck of the Luis I bridge was designed to transport develop tonss should it be converted to that intent in the hereafter, as so it was. The structural systems for the upper and lower decks differ greatly which may lend to the disparity in their deepness ; the lower deck is a lattice through truss with traffic running within the truss itself whilst the upper deck is a brown deck truss where the deck is placed on top of the truss girder. The province of emphasis within the two decks besides differs as the bottom deck is used to bind the arch and therefore is capable to a high initial tensile burden ; the advantage of shaped Fe as a building stuff was its affinity for tensile tonss and it may be that this excessively contributes to the reduced deck deepness.
The rise to cross ratio of the arch is 1:4 ; this is chiefly dictated by the dimensions of the gorge in which the p sits, but the consequence is an arch of typical masonry proportions [ 3 ] which offers the feeling of stableness.
2.3 Order within the Structure
A sense of order is given to the p by the repeat of the truss elements throughout the lift. Although the lower deck uses a somewhat different type of truss, the crossed elements are still present to keep the order within the p.
When viewed closer up, the members are seen to be composed themselves of multiple elements, and from oblique angles the criss-crossing of these members can look disordered ( Fig. 3 ) .
The wharfs and tenseness roads which support the two decks line up to cut down the figure of perpendicular lines and divide the p into equal parts. They are sufficiently near together so as non to do the arch appear otiose, but no so near as to herd the p with perpendicular lines.
2.4 Polishs of Design
Polishs refer to the subtle inside informations within the p which can hold a momentous consequence on the overall entreaty of the construction. In the Luis I bridge the wharfs taper towards the top ( Fig. 4 ) which adds position by doing the towers appear less compact and prevents the optical fast one of the wharfs looking to be wider at the top than they are at the underside.
In the attack ps where the perpendicular infinite beneath the upper deck is greatest, the deck ps a greater distance in order to keep the aspect ratio of the infinites under the deck.
The aspect ratio of the crossed brace in the arch is besides maintained ; where the divergent parabolic curves, which make up the top and bottom rims of the arch, dispersed apart the distance between verticals is increased to maintain the crosses make fulling a approximately square form. Equally good as being aesthetically delighting, this serves the structural intent of maintaining the members inclined at an angle where they can execute at maximal efficiency.
As antecedently mentioned, the single members which make up the trusses are themselves tied box subdivisions ( see Fig. 2 ) , this gives the construction elation, both in footings of its overall weight and besides aesthetically by cut downing the ratio of solid to nothingnesss and doing the members seem more slender. However, this elation comes at the disbursal of order.
Figure 3: Disorder Figure 4: Tapering wharfs
2.5 Integration into the Environment
Pivotal to the aesthetic success of a p is how good is tantrums into its environment ; the arch signifier used for the Luis I bridge is peculiarly good suited to utilize in the deep gorge, and fills the infinite good. Despite the size of the construction, it looks comfy in its environment.
The girder which forms the upper deck has no obvious terminal but alternatively gives the feeling of unifying into the hillside ; this makes the p seem like an built-in portion of the gorge.
2.6 Colour of Components
Though originally unpainted ( Fig. 5 ) the p now has as gray-blue coating which allows the p to intermix good into the sky, this has the consequence of doing the muss of the truss less obvious and contributes to the members looking more slender.
The broadening of the upper deck in 1931has led to the creative activity of a dark line of shadow which serves to pull the oculus off from the deep truss underneath.
Figure 5: Original design without pigment
2.7 Aesthetic Decisions
The Luis I bridge is a construction of great beauty and much consideration has obviously been given to aesthetics in its design. Despite this, as no point has structural efficiency been forfeited for strictly aesthetic grounds. The structural public presentation of the p will organize the following subdivision of this paper.
3 Structural Behaviour
In 1881 the Lusitanian authorities invited the stamp for a new p over the Douro River ; the chief challenge of the strategy was that there could be no intermediate wharfs placed in the river. This was due to high H2O deepnesss of more than 12m, insecure land conditions and a high tidal scope in the river [ 4 ] which would hold made building exceptionally hard. A figure of strategies were proposed and the winning strategy, designed by Th ophile Seyrig, consisted of a tied parabolic arch of shaped Fe building, 172m in p, back uping two truss girder decks ( Fig. 6 ) . Seyrig was familiar with the usage of wrought Fe holding worked closely with Gustave Eiffel in the design of other shaped Fe Bridgess such as the Maria Pia p ( 1877 ) . In this new venture he sought to bring forth a design which would take full advantage of the mechanical belongingss provided by shaped Fe.
Figure 6: Elevation
The arch is connected to the upper and lower decks, by wharfs and sinews severally, in merely four topographic points ; as a consequence of this the arch is capable to flexing minutes even when the decks are uniformly loaded. Wrought Fe is a stuff which performs good in tenseness and it is apparent the interior decorator expected the stuff in the lower rim of the arch to be in tenseness at all times.
A polish of the Maria Pia design was the usage of the lower deck to bind the arch and so cut down horizontal burden of the hapless quality land at the abutments. A farther going from case in point was the usage of divergent parabolic curves to make an arch more slender at the vertex, where it is 7m in deepness, than at the supports ( 17m ) . The alteration was made because of jobs encountered during the building of the Maria Pia p, which has a semilunar arch ; whilst the first subdivisions of the arch were being built out from the abutments it had proved troublesome to supply equal support for them utilizing overseas telegrams and presenting had had to be employed [ 4 ] . In the Luis I bridge the arch is much deeper at the supports hence leting the first subdivisions to be erected more firmly and at less cost, it was a technique which would be used about 40 old ages subsequently during the building of the Sydney Harbour Bridge ( 1923 ) .
The long deep gorge through which the Douro flows is characterised by high air currents ; the unfastened truss system used for the Luis I bridge reduces the lading consequence of the air current by restricting the country on which the air current can move. Eiffel frequently used cannular subdivisions where possible in his Bridgess to increase the aerodynamic public presentation of his designs [ 5 ] , but Seyrig chose non to make so in the design of the Luis I bridge, presumptively to do the connexions more straightforward.
The connexions are riveted together, in pattern this mean that the articulations have some minute capacity but as the elements will still move preponderantly axially, the connexions in the truss can be modelled as pins without presenting excessively much mistake into the analysis. At the clip of the p s building, there was much argument over the comparative virtues of pinned or riveted connexions in p building [ 6 ] ; whilst the riveted truss was of superior efficiency, pinned trusses could be assembled faster and cheaper utilizing simple tools and techniques.
The connexion to the abutments is by manner of a rotational articulation at the utmost terminals of the lower rim of the arch ( Fig. 7 ) . This means that the arch can be considered a two-pin arch and will be analysed consequently.
Figure 7: Foundation connexion
In 2004 a survey was undertaken to measure the current province of the p [ 1 ] and some samples were removed and tested. It is usual to use measured stuff belongingss, where available, in p appraisal instead than conservative characteristic values ; tensile trials on removed subdivisions of shaped Fe from the p yielded a tensile strength of 397Mpa. Testing to happen compressive strength was non performed so a value of 270MPa will be assumed.
Seyrig was a innovator in the hard-on of Fe Bridgess, to the point that he wrote a paper on the topic which was presented at the Institution of Civil Engineers ( ICE ) in 1881 [ 6 ] . In it, Seyrig inside informations his strong belief that the building methods employed in the hard-on of Fe Bridgess has the largest impact on their overall economic system, safety and lastingness.
For the Luis I bridge, as with the Maria Pia p, Seyrig chose to use a method of building which least required the usage of immaterial contraptions, viz. hard-on by overhang. In this technique the lasting construction of the p itself is used to back up the building of more distant subdivisions. The paradigm for this method of p building was the Requejo Bridge designed by Jos Ribera ( Fig. 8 ) .
Figure 8: Requejo Bridge, Spain
In the Luis I bridge the attack ps were foremost constructed on both sides of the river until the upper deck girder protruded about 30m beyond the chief wharfs which mark the start of the arch. The girders were pushed out on a set of four rollers which sat on top of each wharf ( Fig. 9 ) .
Figure 9: Peal setup
The arch was so built out as a series of premade subdivisions which were tied back with steel-wire ropes to a point on the upper deck girder. The whole arch was constructed utilizing merely two ropes on each side of the arch, so it was necessary to be able to rapidly travel a overseas telegram once it has been superseded by a overseas telegram farther along the arch ; for this intent the overseas telegrams were connected merely to the top rim of the arch utilizing a rounded shoe ( Fig. 10 ) under which the uninterrupted rope was fed.
Whilst most of the subdivisions were erected with all of their constituents in topographic point, the last few panels were put up with the top rim and some of the diagonal brace removed in order that they should be every bit light as possible. Once the two halves of the arch had met and the cardinal linking piece inserted, the losing constituents were so added to the lightened subdivisions.
Figure 10: Cable to curve connexion
The work was performed to such truth that in program the two halves of the arch met precisely, but in lift both sides were about 350mm excessively high. This was done intentionally as it was decided that there was possible for the two halves to be excessively low in which instance it would hold been really hard to raise them. Provision was made for take downing the arches to their right place by the remotion of a certain figure of dramatis personae Fe cuneuss which had been placed beneath the overseas telegram connexions.
Once the two halves of the arch had been connected it was of import to slow off the steel overseas telegrams instantly as a bead in temperature could hold caused the overseas telegrams to shorten and bring on emphasiss into the arch.
With the arch in topographic point the midget wharfs could so be erected and the upper deck girder placed on top. Precisely the same procedure was used for the building of the Maria Pia p and is shown schematically in Fig. 11. The lower deck would hold been added last, merely by crossing between the wrought Fe sinews, impermanent intermediate overseas telegrams may hold been added to cut down the hogging minutes caused by cantilevering out.
Figure 11: Erection by overhanging
The Luis I p was built before design standardization had to the full emerged ; accordingly it was likely designed to whatever lading the applied scientist deemed to be sensible. It was besides built at a clip when the Equus caballus drawn passenger car was the prevailing agencies of conveyance ; Karl Benz built the first true car in 1885. For the intents of this study the p will be analysed under its current loading conditions in conformity with BS-5400 [ 7 ] .
Partial burden factors, as detailed in Table 1, will be applied to nominal tonss so combined to give the worst possible burden conditions.
Table 1: Partial burden factors [ 8 ]
Load Type Partial Load Factor ( ? Florida )
Dead 1.05 1.0
Super-imposed Dead 1.75 0
Live Traffic 1.5 0
Wind 1.1 0
5.1 Dead Tonss
The structural elements of the p are of shaped Fe building with a denseness of? = 7700kg/m2. The entire weight of the p is equal to 29841kN [ 9 ] which is about distributed as shown in Table 2.
Table 2: Unfactored dead tonss
Upper Deck 31kN/m
Lower Deck 23kN/m
5.2 Super-Imposed Dead Loads ( SID )
Super-imposed dead tonss are the non-structural inactive tonss on the p such as route coatings, illuming and street furniture. They have a high burden factor ( 1.75 ) to reflect the strong likeliness of them altering over the life-time of the p ; they may besides be removed wholly should the p be capable to major plants, though were this the instance, traffic tonss would about surely be reduced. Suggested tonss given in Table 3 correspond to a 200mm bed of asphalt route surface.
Table 3: Unfactored SID
Upper Deck 38kN/m
Lower Deck 28kN/m
The values are different because the two decks are of different breadth ; the upper deck is 8m broad and the lower deck is 6m.
5.3 Live Traffic Loads
The lower deck carries route traffic ; at 6m broad it can be considered to hold two fanciful lanes. Eq. ( 1 ) gives the unrecorded traffic lading per metre per lane ( HA ) :
w=151 ( 1/L ) ^0.475 ( 1 )
L is the laden length which in this instance is 172m so the end point unfactored burden over two lanes is 26.2kN/m. A knife border burden ( KEL ) of 120kN should besides be added, placed to bring forth maximal extra emphasis.
In this case HB burden has non been considered as the entree routes to the lower deck would be unpassable by really big vehicles and the newer, high-ranking p near by, which is crossed by a double carriageway, would be the more suited path.
The upper deck carries light rail traffic, each train has an unfactored weight of 2000kN [ 2 ] and a length of 70m. The trains move really easy on the p such that dynamic effects can be discounted.
5.6 Worst Case Loads
For the arch, worst instance flexing minutes occur when the arch is non-uniformly loaded ; this corresponds to to the full factored dead, SID, and unrecorded tonss on one half and unfactored dead loads merely on the other side ( Fig. 12 ) . For the upper deck, two trains go throughing at one-fourth p have been considered.
Worst instance shear tonss would be caused by to the full factored dead, SID and unrecorded tonss at all points on the p.
Figure 12: Worst instance lading agreement
In this subdivision, the worst instance burdens calculated antecedently will be applied to the construction to determine whether the end point emphasiss are within the tolerances of the stuffs.
The chief structural constituent of the p is the tied arch. For the intents of this study it will be modelled as a two pin arch, with the lading agreement in Fig. 12 simplified to four point tonss ( Fig. 13 ) .
Figure 13: Simplified arch tonss
By taking minutes about the point A, the perpendicular reactions are found to be: VA = 21691.2kN and VB = 14644.8kN.
6.1.1 Flexibility Analysis
To happen the horizontal push produced by the arch a flexibleness analysis was performed by let go ofing the horizontal reaction at B and using the unit burden method to happen the attendant supplanting at B ( ? B, H ) and the flexibleness coefficient ( a11 ) . Eq. ( 2 ) can so be used to happen the value of horizontal push:
_ ( B, H ) +a_11 H=0 ( 2 )
B, H and a11 are found by incorporating the minute in the arch with regard to the discharge length which is rather complex, but the job can be simplified by presuming that the I value of the arch changes around its profile such that I = I0sec ( ? ) , where I0 is the 2nd minute of country at the vertex of the arch [ 10 ] . Ultimately it can be shown that the value of horizontal push is given by Eq. ( 3 ) , where a is the horizontal distance from A to the point at which the force is moving, H is the tallness of the arch, L is the p and W is the magnitude of the force. Multiple forces can be superposed together to acquire a concluding value of push of 21946.9kN.
H_1= ( 5W_1 a ) / ( 8hL^3 ) ( L^3+a^3-2La^2 ) ( 3 )
6.1.2 Line of Thrust
The deliberate information for tonss and reactions were used to plot a thrust line for the arch under worst instance lading conditions ( Fig. 14 ) .
Figure 14: Thrust line
From this secret plan, the minute at any point in the arch can be calculated as the eccentricity of the thrust line multiplied by the horizontal force. The minutes in the arch are shown in Fig. 16 ; maximal drooping minute is 148.8MNm and occurs at 36m from A, maximal hogging minute is 125.9MNm and occurs at 131m from A.
For the intents of this study, it will be assumed that flexing forces in the arch are resisted by the top and bottom rims, whilst the diagonal brace resists shear forces ; any axial forces are shared amongst all the members. The force in the rim required to defy the maximal minute detailed in Fig. 15 is equal to the minute divided by the deepness of the truss which yields a force of 14.2MN.
Figure 15: Moment in arch
This burden consequences in emphasiss of 133.2Mpa in each of the four arch girders ; tenseness in the lower girders and compaction in the upper girders, which is good under the stuff capacity.
Axial compaction due to the arch form must besides be considered ; by declaration of the reactant forces in the supports, it can be shown that an axial compaction of 30MN is carried in the arch. Split amongst the entire country of wrought Fe available in the subdivision, this consequences in an extra compressive emphasis of 74.7Mpa.
In the tenseness rim this acts as a relieving emphasis which reduces the overall emphasis to 58.5Mpa ( tenseness ) . In the compaction flange the emphasiss sum up to give a entire emphasis of 207.9Mpa, which is nearing but still below the stuff compressive strength of 270Mpa.
Metallic members are frequently susceptible to clasping under high compressive tonss. Eq. ( 4 ) was used to happen the burden required for the arch members to clasp.
F_e= ( p^2 EI ) / ? L_eff? ^2 ( 4 )
The effectual length was taken to be the p between diagonal brace elements as it was assumed that the cross brace would supply sufficient parturiency to forestall buckling over a longer length. The burden at which clasping would happen was found to be 136MN which corresponds to a emphasis good above the compressive strength of the stuff, so failure would ne'er happen through buckling.
f3 values were non considered in the burden computations for the arch as the analysis methods used will ensue in rather high mistake, the excess capacity within the stuff, as shown above, histories for the deficiency of truth in the analysis techniques.
6.1.3 Shear in Arch
Equally good as flexing minutes, the tonss on the arch besides induce shear forces which are carried in the diagonal brace members. Worst instance shear theoretically occurs under maximal burden possible which would be 13488kN applied at the four point burden locations on the arch. Moments under this burden scenario were calculated utilizing the thrust line method and so shear forces were found by distinction of the minutes. The consequence, shown in Fig. 16, predicts a maximal shear force of 7242.8kN located at 35m from point A.
The shear force is resisted by the diagonal brace elements which act together, one in tenseness and one in compaction. The force in each brace member must be 5121.4kN which corresponds to tensile or compressive emphasiss of 194.7MPa.
Figure 16: Maximal shear in arch
6.2 Temperature Effectss
Particularly in excess constructions like two pin arches, little strains caused by temperature alterations can bring on important emphasiss into the construction as the constructions tend to be less flexible. As the Luis I bridge is a tied construction there should non be a high temperature difference between its elements, but overall temperature alterations should be considered.
In the arch, a rise in temperature would ensue in the arch seeking to spread out ; confined by the wharfs, this would do minute in the arch which would be carried as tenseness in the top rim and compaction in the bottom rim. This would move as a alleviating action from the dead and unrecorded burden so should non do a job. A bead in temperature, on the other manus, would ensue in extra compressive emphasiss in the top rim which is already extremely compressed.
The upper deck is exposed to the most direct sunshine, and the solid route surface puts the underside into shadiness so there may be a high temperature gradient which would ensue in emphasiss. The fluctuation in temperature throughout the subdivision in the forenoon period is shown in Fig. 17 where 0 C corresponds to ambient temperature.
Figure 17: Temperature difference in upper deck
The thermic enlargement coefficient ( a ) for wrought Fe is 12 strain/ C, utilizing e=a? T the strain due to the temperature gradient is shown in Fig. 18. Generation of these values by the Young s modulus of 185GPa gives the emphasiss besides detailed in Fig. 19.
Figure 18: Strains ( left ) and emphasiss ( right )
The rollers on top of the chief wharfs, as discussed in subdivision 4, now act as roller bearings which allow the deck girder to lengthen and so relive some of these emphasiss. The emphasiss cut down by the mean emphasis value which in this instance is 6.6MPa ; this now produces the emphasis profile shown in Fig. 19.
Figure 19: Extra temperature emphasiss
The emphasiss in Fig. 19 correspond to a changeless minute over the length of the upper deck. As the deck is uninterrupted over the wharfs there is no demand to see an extra minute to guarantee the minute at the supports remains equal to zero.
6.3 Wind Effectss
Porto lies on the Atlantic seashore of Portugal and so it can be assumed that it is capable to rather high air currents, the p itself besides sits in a gorge which will hold a funnelling consequence on the air current. The arch itself is trussed so as to catch small air current, but the decks, when high sided vehicles base on balls over them, will hold a big jutting country and so may be capable to high air current burden. This is peculiarly true of the lower deck because it is a through truss so the unfastened construction offers no advantage. Suspended as it is by tenseness rods, the lower deck may be extremely susceptible to weave induced effects.
Assuming a average hourly air current velocity of 34m/s, akin to the velocities found on the Atlantic seashore of the UK, the maximal air current blast ( vC ) on the p can be found from Eq. ( 5 ) to be 52m/s, where K1 and S2 are factors harmonizing to BS-5400 and S1 is a funnelling factor taken to be 1.1.
v_C=vK_1 S_1 S_2 ( 5 )
Horizontal air current burden can now be found utilizing Eq. ( 6 ) , A1 is taken as the jutting country presuming high-sided trucks are traversing the p. When the deck is to the full loaded the truss is obscured so the retarding force coefficient can merely be calculated utilizing the b/d ratio. The consequence is a sidelong force of 1.6MN which must be resisted by the deck.
P_t=0.613? v_C? ^2 A_1 C_D ( 6 )
Without cognizing the under-structure of the lower deck it is hard to measure how this burden is carried, but it is assumed that a cross braced truss tallies underneath the deck and prevents the deck from flexing laterally.
The air current can besides ensue in dynamic effects such as galloping and waver ; these effects tend to most affect suspension Bridgess because of their built-in flexibleness. The lower deck of the Luis I bridge, which is suspended by sinews, would be the most likely to endure from these effects but some facets of its design provide stiffness against them. The sinews are able to transport compaction every bit good as tenseness, and are cross braced to supply torsional stiffness ; coupled with the truss moving longitudinally this gives the p stiffness in all of the planes in which the effects of aerodynamic instability might move. There are besides huge sums of riveted connexions within the p to supply muffling against quivers.
The Luis I bridge is over 100 old ages old and has hence been capable to a high sum of lading rhythms, it seems prudent hence to give some consideration to its fatigue public presentation. The p is located near to the sea and so is considered to be in a marine environment ; wrought Fe is regarded as holding a lower opposition to corrosion than other common building stuffs of the clip like dramatis personae Fe [ 11 ] , corrosion is worst around possible wet traps like connexions where hapless care can take to interfacial corrosion ( Fig. 20 ) . The riveted connexions are besides prone to tire failure because clefts can organize during fiction and the pluging action can ensue in local work indurating around the studs.
Figure 20: Interfacial corrosion
In a survey performed by Fernandes et Al, samples of stuff, including a riveted connexion, were removed from the p and analysed to happen their mechanical belongingss [ 2 ] , besides performed were ace growing surveies, notch stamina proving and an analysis of metallurgical content. This information was used to happen the figure of lading rhythms the assorted constituents of the p would be able to defy.
By presuming that merely trucks cause fatigue burden and that one truck represents one rhythm of lading it was calculated that the p had exhausted merely 10 % of its fatigue life and that staying fatigue life was greater than 100 old ages. The survey besides considered the usage of the upper deck for light rail and concluded that one train was the equivalent of four burden rhythms and that residuary life was less than 10 old ages. Consequently the p was retrofitted and reinforced before the new tube line was allowed to go through over it.
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