Structural Analysis of Historical Constructions - Modena, Lourenço & Roca (eds) © 2005 Taylor & Francis Group, London, ISBN 04 15363799

Long-term creep in wooden-iron bridges: a comparative study of different truss types

F. Lanza & A. Mattarucco University J. UA. V ofVenice, Dept. ofArchitectural Construclion, Venice, [taly

F. da Porto University of Padua, Dept. of Slruclural and Transporlation Engineering, Padua. [Ialy

ABSTRACT: Since mid-nineteenth century iron was widely introduced into wooden bridge truss types. A long-term creep evaluation, based on linear elastic model , is here presented in order to compare the effects of dead load in six different kinds of trusses in which iron is used in different truss members. The structural efficiency of the different truss forms has been evaluated in terms of initial elastic deflection and time needed to viscous deformation induced by creep so as to double the initial elastic deflection.

fNTRODUCTION

The advantages of using metal ties to build bridge members working in tension were recognized in Europe since the late XVI century (Verantio 1595). Tron ties in wooden bridge construction were used by Hans Hulrich Grubenrnann when he built in 1757 the Schaffausen bridge (Fig. I).

However, iron production methods were so expen­sive that an extensive use of this material in bridge construction was practically impossible. During the industrial revolution, the development of new tech­niques resulted in strong reductions of iron costs, which induced in Europe the substitution of many wooden bridges with iron bridges since the beginning of the second part of lhe 19th century. In the United States, the large availability of timber kept lumber price very low; hence lumber use was economically convenient also after the industrialization of the iron production methods. This condition induced the devel­opment of many hybrid structural types in which iron was lIsed for tensioned members and wood for those sllbject to compression (Fletcher & Snow 1976).

The use of iron elements, besides eliminating some wood tensile connections, carried other significam improvements to the structural efficiency ofthe differ­ent truss forms. First, il ma de it easier and more effec­tive to apply and maintain pre-stressing (Gasparini & da Porto 2003), that was first introduced in ordinary St. Andrew's cross type all-wood trusses by Stephen Har­riman Long (Long 1830). Second, iron, if compared to wood, does not show to be subjected to creep: hence

Figure I. lron counterbraces in lhe end panels of the Schaffausen bridge built by Hans Ulrich Grubenrnann in 1757.

its introduction is effective in counteracting the effect of creep due to the dead load of the bridges.

In the present contribution, six kinds oftrusses, built with wooden and iron elements, are compared. Each of them differs from the others in terms of overall geome­try and of distribution ofthe iron members. The effect of long-term creep is studied in a simplified manner, by means oflinear elastic analyses. The structural effi­ciency of the different trllSS fomls is thus analyzed taking into account the effect ofthe iron elements.

2 ANALYZED TRUSS TYPES

Table I summarizes the six analyzed bridges, built with a combination of wood and iron elements. Figure I

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Table I. Analyzed bridges.

Num. Bridge name Truss type Source

** Burr Trautwine (1895)

2 Connecticut River Howe Trautwine Bridge* ( 1895)

3 ** Pratt Trautwine (1 895)

4 Standard bridge of Whipple Whipple the NY Canal Dept* ( 1899)

5 *** Child Child (1846)

6 Newburgh RR Post Davies Bridge* (1 908)

* built bridge. ** standard Burr & Pratt trusses described in Trautwine 's book. *** standard Child truss as described in Horace Chi ld 's Patent

Figure 2. Burr truss according to Trautwine (1895).

Figure 3. Detail of a pier of the Connecticut River Bridge at Springfield, bui lt by William Howe in 1842.

shows a detail of the fi rst wooden bridge built with iron elements in Switzerlad by Grubenmann, in 1757. Following, a short description of the seven analyzed structures is given.

2.1 Burr truss

The Burr truss is a compounded structure - an arch plus a truss - patented byTheodore Burr in 1817. In its most advanced version - the one reported by Trautwine - it has arch suspension rods and counterbrace ties.

Figure 4. Scheme of Pratt truss.

Figure 5. Whipple 's truss widely used in the NewYork State canais for common road bri dges.

Figure 6. Child truss scheme.

Figure 7. Post truss scheme.

2.2 Howe truss

Will iam Howe deposited the patent of a truss bridge with wooden diagonaIs and iron posts in 1840. The first bridge built according to this structural scheme was on the Western Railroad, spanning over the Connecticut River at Springf ield. Timber Howe trusses, as those described byTrautwine in his manual (1895), were still used for railroad purpose till the end of 19th Century.

2.3 Pratt truss

Thomas and Caleb Pratt patented their truss in 1844; it consists basically in a Long truss in which braces and counterbraces are substituted by iron ties.

Trautwine gives in his handbook (1895) a descrip­tion of the dimensions of a standard Pratt truss.

2.4 Whipple s truss

This truss invented by Squire Whipple is described in the second edition of his book (1899). It consists in the superposition of three trusses based on triangular

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scheme and in a series ofvertical ties to which the deck beams are suspended.

2.5 Child truss

Horace Child patented his truss in 1846. The geometry of the truss is very similar to a Long truss: the differ­ence is that counterbraces are substituted by iron ties.

2.6 Post truss

Simeon Post introduced this type of truss in 1865. It was made completely of iron or of iron in combina­tion with wood. This second version had timber upper chorei, timber inclined post, iron diagonais and iron lower chord. The here analyzed Post truss bridge was on the Connecticut Railway at Newburgh, Dutchess.

The relative description appears in Davies (1908).

3 TRUSS ANALYSIS

3.1 Finite element analysis ofthe bridge

The structural behaviour of the six bridges was pre­dicted by computer analysis oftwo-dimensional , linear elastic frame models. The geometry of the models is shown in Figure 8.

Dimensions and member cross sections were obtained from the sources quoted in Table I. For the analysis, it was assumed that the bridges had been built with Eastern White Pine (pinus strobus), which was considered a suitable material for bridge con­struction (Long 1830) and was the most common timber used during ali the first part of 19th century (Fletcher & Snow 1976). The following assumptions were made about the mechanical properties ofEastern White Pine. The modulus of elasticity was taken equal to 8550N/mm2 and the Poisson's ratio to 0.33.

W rought iron used for the rods was assumed to have a modulus of elasticity equal to 186 kN/mm2, Poisson 's ratio equal to 0.3 and yield stress equal to 207 N/mm2 .

The models were used to predict the effects of dead load, in terms of initial elastic deflection at midspan (Table 2), and lhe effect of creep.

Creep is a time-dependent phenomena related to the behaviour ofwood under loael, and consists in increase of strain under a constant stress . Actually, if a wooden element is restraineel, creep is hindered and the ele­ment is subjected to effective axial forces from creep. The corresponding behaviour of the truss under creep can be evaluated by computing the axial forces from nodal displacements in the truss elements when ali the creep nodal loads are applieel, and by superposing the effect of the fixed end forces . A predictive creep model, described more in detail in §3 .2, which does not take into account the effects of cyclical variations of

1

1

3

4 /lZlZKrs:r-...,. ..d... À

5

6

Figure 8. Models of the six analyzed slructures.

Table 2. Bridge span, defleelion aI mid-span due lo dead loacl, ralio between defleelion aI midspan and bridge span and time needed to ereep so as 10 double the inilial elaslie defleetion.

Span 1]midspan 1Jmidspan l 1*

Truss type [m) [em) Span [x 10- 4 ) [years)

Burr 54.43 0.79 1.45 33.4 Howe 29.94 0.63 2.1 30.7 Pratt 29.94 0.55 1.84 51.6 Whipple's 24.19 0.76 3.14 37.3 Child 27.21 0.43 1.58 55.7 Posl 29.63 0.80 2.7 43.9

temperature and of moisture content within the ana­Iyzed perioel, was assumed to estimate the value of creep strains. The effective nodal loads, C; , due to the creep deformation for loading parallel to the grain were therefore calculated for each element by using eq. (I):

(I)

where ê;(t) is the creep strain, E the modulus of elasticity ofwood and A; the area ofthe i-element.

The effect of creep was thus evaluated in terms of time needed to viscous deformation to increase of a certain rate the initial elastic deflection due to dead load at midspan. Besides the effect of envi­ronrnental conditions, also the effect of prestressing,

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13.34 kN

.----- 13.34 kN

Figure 9. Kingpost geometrica l scheme with applied loads.

0.9

I ! 0.7 ~ ·s -; c " "" ~ 0.5

~

0.3

(bl

10 15 20 25 30 35 40 45 50 55 60 Time (yeanl

Figure 10. Comparison between defl ecti ons at mid-span of the ki ngpost ca lculated by Tissaoui [a] and according to eq. (2) [b].

achieved in some of the analyzed structures by tight­ening nuts or using similar devices, was neglected in these simplified analyses.

3.2 The proposed creep model

A long-term, five parameter model was used to esti­mate the value of creep strains at different times t, tak ing into account the constant actual state of stress ai of the elements before creep starts. The model was based on the following equation, proposed by Dinwoodie (1984):

(2)

where a i is the compressive stress parallel to the grain in the i-element before the creep starts and f3 are the model parameters that depend on the wood species, temperature and moisture content.

Being not known to the authors the values of the five parameters of eq. (2) from experimental tests on wood samples of Eastern White Pine, they were set on the bases of different long-term creep analyses proposed by Tissaoui (1 996). Tissaoui analyzed three structures: a kingpost truss, shown in Figure 9, a space

E I~ 39.84m j

Figure I I . Varax Dome of the Church of the Nazarene.

" = ~ " '"

Ib)

i lal Q

-"'l - r r - .. ··_·r · .... ·--,_······"'··-r-'- r- ---·r····--r ---l 1- ····r ·-5 10 15 20 25 30 35 40 45 50 55 60

Time fyear_1

Figure 12. Comparison between vertica l displacements aI the apex of the Varax dome calculated by Tissaoui [a] and accordi ng to eq. (2) [b].

structure found in the Varax dome ofthe Church of the Nazarene, shown in Figure 11, and a three-hinged arch, shown in Figure 13. The creep analyses performed by Tissaoui on the kingpost truss and the Varax dome follow Gamalath's model (199 1):

(3)

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/Hinge

~m D},m 1o-1.----30.48m----+I~1 -J l.-

(a) (b) 17. 15 em

Figure 13 . Three-hinged arch .

10 J e 8 ~ -; I ~ l :li! 6 -e ;;

Ib)

10 15 20 25 30 35 40 45 50 55 60 Time [yea .. )

Figure 14. Comparison between deflections at mid-span of the arch calcu[ated byTissaoui [a] and according to eq. (2) [b].

where Der is the creep compliance, Do the instan­taneous compliance, P I = 0.0749 - 2.291 X 10- 8 E and P2 = 0.3358 are constants from regression analy­sis and average on experimental data. The results ofthe analyses are given in terms of deflection at midspan under constant load, corresponding to three point loads applied at the nodes in the case of the kingpost truss, and to dead load and a uniform distributed load in the case of the Varax dome.

Equivalent geometrical models were defined and analyzed under long term loading, by applying eq. (2), in order to set the five parameters. Elements dimension and mechanical properties of wood and loading condi­tions were taken equal to those described by Tissaoui (1996). First, the value of the parameter f31 in eq. (2) was set on the kingpost truss, by imposing the con­dition that the initial (t = O) deflection of the truss at midspan is equal to the initial elastic deflection.

Subsequently, the parameters f32, f33, f34, f3s were set in order to fit the curve describing the displacement at middle ofbottom chord that had been calculated by Tissaoui. This latter curve is reported in Figure 10 [a], together with the curve based on eq.(2), Figure 10 [b]. The said values are: f32 = 0.3; f33 = 0.31; f34 = 0.142; f3s = 0.48.

After calibrating the values of the f3 parameters on the bases ofthe kingpost truss, eq. (2) was used to cal­culate the vertical displacement due to wood creep at the apex ofthe Varax dome. The results ofthe analysis

were compared to those obtained by Tissaoui (1996), in order to check the applicability and reliability of eq. (2). Despite the differences between the structure on which eq. (2) was calibrated, the kingpost truss, and the structure ofthe dome - different wood species, different dimensions and kind oftrusses - the two anal­yses on the Varax dome gave consistent results. The average differences between the vertical displacement at the apex ofthe dome evaluated according to Tissaoui (curve [a] in Fig. 12) and according to eq. (2) (curve [b] in Fig. 12) were equal to 4%, and were considered to be acceptable.

Finally, Tissaoui (1996) applied a different creep model, the power law proposed by Nielsen (1992), to calculate the creep deflection at the apex of a three­hinged arch (Fig. 13), under dead load and a uniform distributed load. The same structure was analyzed by applying eq. (2), and the results were again compared to those obtained by Tissaoui. In this case, the results obtained by applying eq. (2) seems to overestimate the creep deflection, therefore the two deflection curves diverges, as can be seen in Figure 14. However, the maximum divergence in the long term, at 50 years, is equal to about 13% that can be still considered an acceptable variation. The broader difference depends on the fact that the law used to calculate the deflec­tion ofthe three hinged arch, compared to eq. (3) on which the proposed creep model (eq. 2) was calibrated, introduces other phenomena, i.e. considers wood as a damaged viscoelastic material.

In conclusion, it was considered acceptable to use the five parameter eq. (2), as calibrated on the bases of Galamath's long-term creep model, and it was applied to study the effects of creep in the described bridge trusses. The procedure followed to study the effect of creep has been already illustrated in §3.1.

4 EFFICIENCY OF DIFFERENT TRUSS TYPES

4.1 EJTectofdeadload

The instantaneous elastic deflection at midspan due to the effect of dead-Ioad, as calculated by means oflinear elastic analysis of two-dimensional frame models, is given Table 2. The ratio obtained dividing such deflec­tion by the truss span was calculated so as to evaluate the initial efficiency of different structural types. The length of the spans and the ratios between the initial elastic deflection at midspan and the span length are also reported in Table 2.

4.2 Elfect of creep

The midspan deflection due to creep induced by dead­load was evaluated by applying equation (2) at differ­ent times t, taking into account the actual state of stress O'i of the elements before creep starts, and assuming

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6 5

\///;;/ c o

'.p u

'" c;:: '" 1.0 't:I u

'.p '" '" 0.75 ril c o

0.5 '.p u , , '"

, , c;:: '" 0.25 't:I p.. , , '" '" I-

O U , ,

O 20 40 60 80 100

Time [years]

Figure 15. Creep defleetion as a ratio of initial elastie defleetion versus time: I Burr truss; 2 Howe truss; 3 Pratt truss; 4 Whipple's truss; 5 Child truss; 6 Post truss.

the five parameters found in the analysis of the king­post truss. Curves representing the ratio between the creep detlection and the initial elastic detlection ver­sus time, for the various analyzed trusses, are reported in Figure 15 . The period of time t*, afier which the vertical detlection at midspan results twice as the ini­tial elastic detlection due to dead load, is reported in Table 2.

Creep detlections afier two years were calculated for each truss according also to the exponential creep law proposed by Le Govic for the use in building codes, and reported in Tissaoui (1996):

(4)

Table 3 reports the values of detlection due to creep afier two years, calculated according to eq. (2) and eq. (4).

4.3 Comparison of dijJerent trusses

As it may be easily seen in Table 2, the response ofthe analyzed bridges to dead load varies considerably with the different truss forrns, with values of ratio between initial elastic detlection and bridge span ranging from about 1.5 x 10-4 to about 3 x 10- 4 . The same can be said about the creep behaviour, with time needed to viscous deformation induced by dead load so as to double the initial elastic detlection varying from about 30 to about 55 years.

As for the long-terrn creep (Fig. 15, Tab. 2), similar behaviour and values of time needed to double the initial elastic detlection, around 50 years, may be found on the Child and the Pratt truss, both having iron ties used for diagonal elements. These two trusses are also characterized by low values of ratio between initial

Table 3. Comparison between defleetions at midspan due to dead load and ereep after two years, ealeulated aeeording to eq. (2) and eq. (4) for the various analyzed bridges.

1Jmidspan 17midspan Truss type eq. (I) [em] eq. (2) [em] Diff. [%]

Burr 1.045 1.036 0.8 Howe 0.8 15 0.849 -1.3 Pratt 0.696 0.6 13 13.6 Whipple 's 0.995 0.957 3.9 Child 0.546 0.47 16.2 Post 1.04 0.95 8.6

elastic detlection and bridge span, respectively equal to 1.58 x 10- 4 and 1.84 x 10- 4 (Tab. 2), thus revealing a good behaviour both under instantaneous and long­term loading.

Similar analogies may be seen in Howe and Whip­pie truss, both built with iron vertical posts, for which the time needed to double the initial elastic detlec­tion is around 30 years. These two trusses are also characterized by high values of ratio between initial elastic deflection and bridge span, respectively equal to 2.1 x 10- 4 and 3.14 x 10- 4 (Tab. 2). Conversely, the Burr truss, that presents similar values of time needed to double the initial elastic detlection, shows the lowest value of ratio between initial elastic deflec­tion and bridge span (1.45 x 10-4) . In this case, the efficiency of the arch plus truss structure in increas­ing the stiffness of the bridge is revealed, but this does not correspond to a similar efficiency in the long-term behaviour ofthe bridge. Finally, the Post truss revealed an interrnediate behaviour both regarding the initial and the long-term response to dead load.

Considering that, according to Trautwine proposed design, Pratt and Howe trusses have the same span, chord section and truss form, but the latter has vertical post iron elements, while the first has iron diago­nais, one might infer that trusses with diagonal iron elements prove themselves to be more efficient.

The comparison ofthe results obtained in the creep analyses afier two years with eq. (2) and eq. (4), shows that the calculated values do not vary considerably (less than 10% difference in most of the cases, max­imum difference of 16.2%). In general, the values of creep detlection found by applying the exponen­tial, four parameter law given by eq. (4), are higher than those found by applying eq. (2), but the equation proposed for the codes allows to carry out only a short­term creep analysis, as the value of creep obtained by means of eq. (4) stabilizes afier two years.

5 CONCLUSIONS

In this paper, a comparison of different trusses, in terms oftruss response to dead load and oftime needed

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to creep so as to double the initial elastic deflection, is shown. The presented results may be not consid­ered of general validity as they are influenced by the geometry - aspect ratio of the panels and member cross sections - and lhe overall characteristics of the analyzed bridges.

In order to determine the influence ofthe iron mem­bers in the truss response and to evaluate the effect of the design proportions, it would be significant to analyze the same truss forms built with ali wooden members, or to vary the ratio between length and height ofpanels within each truss formo

Ifmore detailed information about the bridges were available - e.g. the condition ofwood used during con­struction, the occurrence of periodical retightening of the nuts on iron rods, etc. - it would be significant to analyze the trusses more in detail, introducing also the effects of shrinkage and pre-stress.

Finally, it has to be highlighted that for more reliable creep study, viscoelastic analyses where stress redis­tributions under constant loads are taken into account, with creep laws formulated and applied for variable stresses, should be carried out instead of simple linear elastic analyses.

ACKNOWLEDGEMENTS

F. Lanza is grateful to the US-ICOMOS for the oppor­tunity he had to study directly American wooden bridges and for the support received by the HAER team, in particular by Eric de Lony and John Ochsendorf.

REFERENCES

Bodig,1. & Jayne, B.A. 1982. Mechanics ofWood and Wood Composites, NewYork: Van Nostrand Reinhold Company.

Chi ld, Horace. 1846. Patent No. 4, 693 August 12, 1846. Davies, M. W. 1908. The Iheo/)I and praclice of bridge

conslruclion in timber iron and steel, London: MacMillan & Co.

Duggan, G. 1850. Specimens of lhe SlOne iran and wood bridges viaducts ILmnels culver/s &c. ofthe Unites S/ates rail roads, New York: D. Appleton & Co.; John Wiley, George, G. Putnam.

Fletcher, R. & Snow, 1.P. 1976. A History ofthe development ofwooden bridges. In A merican Wooden Bridges: 29- 123. New York: ASCE.

Gamalath, S. 1991. Long-Ierm creep Modeling of Wood Using Time- Temperarure Superposition PrincipIe, Ph.D. dissertation , Wood Science and Forest Products, Virginia Polytechnic Institute & State Un iversity.

Gasparini, D.A. & da Porto, E 2003 . Prestressing of 19th century wood and iron truss bridges in the U.S., In Santi­ago Huerta, Proc. Ofthe Firsl IlIIernational Congress on Construction histo/y, Madrid 20-24 Jan . 2003 , Madrid.

Gasparini, D.A. & Simmons, D. I 997.American Truss Bridge Connections in the 19th Cenlllly. ASCE Journal ofthe Per­formance ofConstructed Facilities, Vol. li , No 3, August 119- 129.

Killer, 1. 1941. Die werke der baumeister Grubenmann, Zurich: Leenman.

Long, S.H. 1830. Description oftheJackson Bridge togelher with directions to bridge builders of wooden OI' ji'{Jllle bridges, Baltimore: Sand & Neilson.

Morlier, P. 1994. Creep in timber structures, Report of RILEM Technical Committee 112-TSC, London: E&FN Spon.

Nielsen, L.F. 1992. Lifetime of Wood as Related to Strength distribution, Reliabiliry-Based Design of Engi­neered Wood Slructures, Bodig, 1. (ed.), Kluwe Academic Publishers.

Parsons, W.B. 1939. Engineers and engineering in lhe reinas­sance, Baltimore: The Williams & Wilkins Company.

Peters, T.E 1979. The development of long-span bridge building, Zurich: ETH.

Prevost, L.M. 1842. Description of Howe 's Patent Truss Bridge carrying the Western Railroad over the Connecticut River at Springfield, Massachusetts. Journal of the Franklin [nstitute 3(5): 289- 292.

Tissaoui , 1. 1996. EffecIs of Long-Term Creep on the Integrity of Modern Wood S/ructures, Ph.D. dissertation, Virginia Polytechnic Institute and State University

Trautwine, 1.C. 1895. The Civil Engineer's Pocket-book, New York: John Wiley & Sons.

Veranzio, E (ca.) 1595. Machinae nova e Fa vsti Verantii siceni Cvm dec/ara/ione latina ilalica hispanica gallica el germanica. Venetiis.

Whipple, S. 1899. An elementary and praclical trealise on bridge building an enlarged and improved edilion, New York: D. Van Nostrand Company.

Wood, D.V 1878. Treatise on lhe IheO/y oflhe conslm ction ofbridges and roofs, New York: John Wiley & Sons.

Zago, E 1993. I1legno di conifera la deformazione difJerila, Edolo: Habitat Legno.

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