1. INTRODUCTION
The arch bridge is one of the oldest types t ypes of brides and has been in existence in the world since more than 2000 years. The Romans were the first to take the advantages of the arch in building bridges. Applying arch into bridges bridges and buildings has a long history also in the East. Arch is sometimes defined as a curved structural member spanning an opening and serving as a support for the loads above the opening. This definition omits a description of what type of structural element; a bending and/or an axial force element makes up the arch. A true or perfect arch, theoretically, is one in which only a compressive force acts at the centroid of each element of the arch. The shape of the true arch can be thought of as the inverse of a hanging chain between abutments. It is practically impossible to have a true arch bridge, except for one loading condition. However, an arch is usually subjected to multiple loadings, which will produce bending stresses in the arch rib that are generally small compared with the axial compressive stress. 1.1 History The history of the tied or bowstring arch in America can be traced back to King's truss. Originally tied arch bridges were designed with deep ribs, to carry the majority of the live load moment. In 1941, J. M. Garrelts revolutionized the design of tied arch bridges in America. Virtually all tied arch spans constructed today utilize the stiff tie and slender rib concept. By using an orthotropic deck, the dead load of a bridge can be greatly reduced. In some cases the entire deck is being used to act as the tie. For increased stability inclined tied arches are being tried. These are all topics which would be of interest for further research. Today, arch bridges are generally constructed of concrete or steel. However, there is still a great deal of research on stone arches directed toward determining their ultimate load capacit y, their remaining life, their stability, their maintenance requirements, and also to determine the best methods to retrofit the structures. The The reason for this great interest is, of course, that there are thousands of these stone arch bridges all over the world that are still carrying traffic and it would be an enormous cost to replace them all, especially since many of them are national monuments. 1.2 Comparison of Arch Bridge with Other Bridge Types The arch bridge is very competitive with truss bridges in spans up to about 275 m. If the cost is the same or only slightly higher for the arch bridge, then from aesthetic considerations the arch bridge would be selected instead of the truss bridge. Tied arch bridge provides stable foundation and evenness in tension and compression. Anchorages only hold vertical compression allowing more weight to be put on bridge. For longer spans, usually over water, the cable-stayed bridge has been able to be more economical than tied arch spans. The arch bridge has a big disadvantage in that the t he tie girder has to be constructed before the arch ribs can function. The cable-stayed bridge does not have this disadvantage, because deck elements and cables are erected simultaneously during the construction process. The true arch bridge will continue to be built of long spans over deep valleys where appropriate. 1.3 Classifications of arch bridges An arch bridge has many variations according to structural arrangements, structural behaviors, and materials. Based on the arrangements of the main arch and the deck system, arch bridges are usually classified as (1) deck arch arc h bridge, (2) half-through arch bridge, and (3) through arch bridge. As shown in figure 1, a deck arch bridge is one where the bridge deck locates completely above the crown of arch; a through arch bridge is one where the deck locates at the 1
springing line of the arch; and half through arch bridge is one where the deck locates at an elevation between a deck arch and a through arch. When choosing a t ype of arch bridge among these three arrangements, the deck elevation is the primary control factor. Horizontal outward thrust at abutments distinguishes an arch bridge from other t ypes of bridge. The counterbalance of such outward thrust from the abutments, which reduces the bending effects in the arch, however, requires foundations capable of resisting huge horizontal thrust. Situations where foundations are not permissive, the arch can be tied horizontally by the deck or external tendons. When tied, the horizontal outward thrust is balanced internally, instead of externally by foundations. In this regard, arch bridges can be classified as (1) thrusting arch bridge and (2) non thrusting arch bridge. A non thrusting arch bridge, which is often called a tied-arch bridge, is widely used as there is no additional horizontal thrust requirement in the foundation. Traditionally, a deck-through arch bridge is tied as the tie at the deck level connecting two ends of the arch. It is the most effective way to balance the outward thrust. A half-through arch bridge can also be tied at the deck level, in which tying forces are transfer red to the main arch from side arches in two side spans.
Figure 1 Deck arch bridge
Figure 2 Half-through arch bridge 2
Figure 3 Through arch bridge When an arch bridge is tied, externally, the whole structure will behave as a single span of a simply supported girder bridge. The moment distributed to the arch and tie is related to the stiffness ratio of the arch to tie. A tied arch bridge can further be classified as (1) stiffened arch with flexible tie, (2) stiffened arch with stiffened ti e, and (3) flexible arch with stiffened tie. As local moments due to live loads are inevitable, a flexible tie girder will distribute more live loads to arch and the arch requires a higher bending stiffness to resist moments; a stiffened tie girder will distribute less live loads to arch and the arch does not need a higher bending stiffness. Stiffnesses of the arch and the tie girder are dependent on each other; it is possible to optimize the size of each according to the goal established for aesthetics and/or cost. An arch bridge can be so designed and built to release live load moments at crown and/or springing. As shown in Figure 4, an arch bridge can be classified as (1) non-hinge arch, (2) one-hinged arch, (3) two-hinged arch, and (4) three-hinged arch.
Figure 4 Illustration of (a) fixed and (b) hinged arch bridges. 3
1.4 Working of tied arch bridge Thrust arches rely on horizontal restraint from the foundations, as shown right. The vertical and horizontal reactions resolve into a force along the arch members – the horizontal component is of significant magnitude. This will be the most satisfactory solution when the arch bears onto good foundation material such as competent rock. The ends of the arches are normally pinned. However, rock is not always available and so a thrust arch will not be the most economical solution at these locations, as the horizontal reactions lead to heavy uneconomic foundations.
Figure 5 Reactions for a thrust arch bridge Tied arch bridges are distinguished from other forms of arch bridges by the presence of a tie chord. The tied-arch offers a solution when it can be arranged that the deck is at such a level that it can carry the horizontal force as a tie member, as shown on right side. The tied-arch is sometimes referred to as a bowstring arch. By taking the arch thrust through the tie member, the primary requirement for the substructure reduces to only carrying vertical loads. It can be seen that one end will still require a longitudinal restraint to carry wind, braking, acceleration and skidding forces, and that the other end is permitted t o move longitudinally.
Figure 6 Reactions for Tied arch
Figure 7 Typical profile of a tied arch bridge and gives the nomenclatur e of the parts of the structure 4
A tied-arch bridge is an arch bridge in which the outward-directed horizontal forces of the ar ch, or top chord, are borne as tension by the bottom chord (either t ie-rods or the deck itself), rather than by the ground or the bridge foundations. Hence, tied arches are ideally suited for sites where ,foundation conditions will not permit an economical substructure, which could carry the thrust of a conventional arch. Tied arches are also used where moderate span lengths are required with a maximum clearance. Thrusts downward on such a bridge's deck are translated, as tension, by vertical ties of the deck to the curved top chord, tending to flatten it and thereby to push its tips outward into the abutments, like other arch bridges. However, in a tied-arch or bowstring bridge, these movements are restrained not by the abutments but by the bottom chord, which ties these tips together, taking the thrusts as tension, rather like the string of a bow that is being flattened. Therefore, the design is often called a bowstring-a rch or bowstring-girder bridge. The elimination of horizontal forces at the abutments allows tied-arch bridges to be constructed with less robust foundations; thus they can be situated atop elevated piers or in areas of unstable soil. In addition, since they do not depend on horizontal compression forces for their integrity, tied-arch bridges can be prefabricated offsite, and subsequently floated, hauled or lifted into place. A tied arch uses a strong tension element connected longitudinally between the arch springing points to balance the large horizontal thrusts. The foundation design is much simpler for a tied arch than it is for an ordinary arch because the horizontal thrust is balanced internally by the tension tie. The roadway is supported by the arch rib through high-strength steel ropes, called hangers. Bridges of this type are often aesthetically pleasing, and give the motorist a feeling of openness and an unobstructed view of the river. As with the parallel chord truss, lateral bracing is required to integrate the trusses and provide a load path for horizontal loads If a load is placed on the deck, it is transferred to the arch via the hangers, as the global stiffness of the arch is greater than the bending stiffness of the deck. This creates thrust in the arch, which is balanced by tension in the tie beam.
Figure 8 Structural behaviour of tied arch
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1.5 Design Considerations for an Arch Bridge 1.5.1 Arch Bridge Design Adequate literature have information concerning the design of decks that also apply to the design of decks of arches. By deck is meant the roadway concrete slab or orthotropic steel plate and its structural supports. The rise-to-span ratio for arches may vary widely because an arch can be very shallow or, at the other extreme, could be a half-circle. Most arches would have rise-to-span ratios within the range of 1:4.5 to 1:6. After the moments and axial forces become available from the three-dimensional finite-element nonlinear analysis the arch elements, such as the deck, ribs, ties, hangers, and columns can be proportioned. Steel arch ribs are usually made up of plates in the shape of a rectangular box. The ties are usually either welded steel box girders or plate girders. In the 1970s there were problems in several arch bridges in that cracks appeared in welded tie girders. Repairs were made, some at great cost. However, there were no complete failures of any of the tie girders. Nevertheless, it caused the engineering community to take a new look at the need for redundancy. One proposal for arch bridges is not to weld the plates of the steel tie girders together but rather to use angles to connect them secured by bolts. Another proposal is to prestress the tie girder with post-tensioning cables. Another is to have the deck participate with the tie girder. 1.5.2 Vortex Shedding Every now and then an arch is identified that is having problems with hanger vibrations especially those with I-section hangers. The vibrations are a result of vortex shedding. The usual retrofit is to connect the hangers as shown in figure 9, which effectively reduces the length of the hangers and changes the natural frequency of the hangers. Another method is to add spoiler devices on the hangers. In addition to the hangers, there have also been vortex shedding problems on very long steel columns that carry loads from the ar ch deck down to the arch rib.
Figure 9 Horizontal cable connecting hangers. 1.5.3 Buckling of Arch Rib Since the curved rib of the arch bridge is subject to a high axial force, the chance of a failure due to buckling of the rib cannot be ignored and must be accounted for. It is necessary to optimise the main dimensions, especially to find the optimal ratio of arc rise to its le ngth. Then, the configuration of upper longitudinal bracings is varied from common truss systems to frame ones. After the preliminary design and optimisation process, more complex static analysis, analysis of stability and dynamic analysis could be performed. The usual in-plane buckling deflection is in the form of a reverse curve with part of the arch rib going down and the other part going up. This buckling tendency should be taken into account in the allowable axial stress, just as it is in other compression members.
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2 LITERATURE REVIEW
A paper on Preliminary analysis and hanger adjustment of tied arch bridges by William Edward Beyer was reviewed and a summary of the study is illustrated. 2.1 Effects of various parameters upon tied arch behavior 2.1.1 Discussion of parameters Preliminary analysis of a tied arch is complex due to the many possible geometric and member parameters for a structure. The effects of some of the various parameters on the behavior of a tied arch were investigated. The parameters considered in this discussion are: 1) Rise to span ratio. 2) Ratio of moments of inertia of rib and tie. 3) Ratio of areas of rib and tie. 4) Hanger spacing.
Other important design parameters which must be considered include: 1) Type of rib, tie, and deck. 2) Type of joint at connection of rib and tie. 3) Tie depth to span ratio. 4) Rib depth to span ratio. 5) Curved rib versus segmental rib. Following are some values of the typical parameters used for various bridges 1. Arch rise to span ratio typically lies within 1/5 and 1/6.5. 2. For arches with deep ties and shallow ribs, tie depth to span ratio typically lies within 1/50 and 1/70. 3. Ratio of moments of inertia of rib to tie for solid rib and tie bridges typicall y lies within 1/20 and 25/1. 4. Ratio of span to hanger spacing typically lies within 10 and 20. 5. Ratio of areas of rib to tie for solid rib and tie bridges typically lies within 0.6 and 1.5. Increasing the stiffness of the deck main girders may affect the bending moment in the arch ribs, while inclining the arch ribs may provide a better resistance to lateral loads but may also change the in-plane and out-of-plane bending moments in the ribs under gravitational loads. Varying the rise-to-span ratio will affect the internal forces in the arch ribs. There is an optimum rise-to-span ratio at which the thrust line is close to the neutral axis of the arch, resulting in low bending moments in the arch ribs. 2.1.2 Rise to span ratio The rise-to-span ratio for arches varies widely. A range from 0.12 to 0.3 would include almost all bridge arches. Most are in the range from 0.16 to 0.2. An increase of rise decreases arch thrust inversely with the rise-to-span ratio, reducing the axial stress from dead and live load and the bending stress from temperature change. The axial tension in a tie, if used, is also decreased in the same way. Offsetting these effects from the standpoint of economy is the increased length of the arch rib. This greater length increases the quantity of steel and the dead load. It also increases the buckling length in the plane of the arch and the moment magnification factor. The lengths of the suspenders are increased. The total length of lateral bracing between the ribs is increased, and the wind overturning and stresses are increased. Many existing tied arches have a rise to span ratio of about 0.2. 7
2.1.3 Hanger spacing The compression forces in the arch increases with the number of hangers. It was observed that with increasing number of hangers, compression increases in the arches, while the hanger’s axial efforts decreases. Bending moment decreases with the increas ing number of hangers, and this difference is remarkable when the number of hangers is lower and the bending moments in the arch grow rapidly. The tie beam axial efforts variations do not appear in the system with vertical hangers, but the hanger number variation significantly influences the bending moment in the beam b ecause the hangers play the role of elastic supports for tie beam. As a consequence, in the arch with vertical hangers, bending is a decisive factor when it comes to the choice of the cross-section of the chords.
To study the effects that the other parameters have upon tied arch behavior, the Mobile Arch Bridge, designed by the consulting firm of Howard Needles Tammen & Bergendoff was selected for anaIysis. The geometry for the Mobile Arch Bridge is given in figure 10. The cases considered for study are given in Table 1.
Figure 10 Mobile Arch Bridge geometry
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Table 1 Cases considered for parametric study of tied arch behavior. Where: Ir/It = Ratio of moments of inertia of rib to tie at centerspan Ar/At= Ratio of areas of rib to tie at centerspan s = Number of panels It was decided to keep the cross sectional area of the arch at centerspan constant at 600 in2 . Similarly the total moment of inertia of the rib plus tie was held constant at 1.5 x 10^6 in4 . The rib and tie areas and moments of inertia were held constant across the span. The hanger area remained constant at 8.3 in2 . All of the cases were run for a rise to span ratio (H/L) of 1/5.9. The analysis was carried out by computer using matrix structural analysis. The member element used in the analysis allowed axial and flexural deformations, and gave a linear first order solution. Therefore axial-flexural interaction was not accounted for. The size effects of the connection at the rib and tie were also neglected. The results were analyzed in terms of: 1. Rib and tie moment influence lines. 2. Hanger forces. 3. Rib and tie deflection. 2.1.3 Rib and tie moment influence lines
Figures 11 through 16 show the graphs of the rib and tie moment influence lines for three of the 16 panel cases. The H/L ratio for all cases is 1/5.9. a) In all cases the rib moment influence lines tend to be more rounded near the peaks. This indicates distribution of moment to adjacent panels, as the rib deforms. b) The tie moment influence lines show much sharper peaks, especially when Ir/It becomes large. This indicates more localized bending at the point of load application. All curves indicate the same shape of moment envelopes, although the amplitudes vary. Figures 17 through 22 show the graphs of the rib and tie moment influence lines for three of the Ir/It = 1/10 cases, for different hanger spacings. The H/L ratio for all cas es is 1/5.9. c) The results indicate that the live load moment envelope does not change significantly for different hanger spacings. By using Figures 11 through 22 the loading cases for maximum rib and tie live load moment can be determined.
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Graph of rib moment influence lines for 16 panels
Figure 11 Ar/At = 0.6 , Ir/It = 1/20 , 16 panels
Figure 12 Ar/At = 1.0 , Ir/It = 1.0 , 16 panels
Figure 13 Ar/At = 1.5 , Ir/It = 20 , 16 panels 10
Graph of tie moment influence lines for 16 panels
Figure 14 Ar/At = 0.6 , Ir/It = 1/20 , 16 panels
Figure 15 Ar/At = 1.0 , Ir/It = 1.0 , 16 panels
Figure 16 Ar/At = 1.5 , Ir/It = 20 , 16 panels 11
Graph of rib moment influence lines for different hanger spacing
Figure 17 Ar/At = 1.0 , Ir/It = 1.0 , 10 panels
Figure 18 Ar/At = 1.0 , Ir/It = 1.0 , 20 panels
Figure 19 Ar/At = 1.0 , Ir/It = 1.0 , 24 panels 12
Graph of tie moment influence lines for different hanger spacing
Figure 20 Ar/At = 1.0 , Ir/It = 1.0 , 10 panels
Figure 21 Ar/At = 1.0 , Ir/It = 1.0 , 20 panels
Figure 22 Ar/At = 1.0 , Ir/It = 1.0 , 24 panels 13
3. CONCLUSION
A tied arch behaves similarly to a self-anchored suspension bridge. In the self-anchored suspension bridge the cables carry tensile force and no moment. In a tied arch by designing a stiff tie to carry the live load, the rib carries compressive force with little moment. By using high strength steels the size of the rib can be reduced to a minimum siz e based upon slenderness effects. One of the major advantages in using any arch is being able to carry the dead load of the structure primarily by axial forces. This produces a more efficient use of the materials. By shaping the axis of the arch correctly, and eliminating axial deformations, the dead load moments in a tied arch can be substantially reduced. Since the predominant dead load of a tied arch bridge is the floor system, and is nearly uniform, the rib should be nearly parabolic. It is easiest to design the tie as a parabola, and make any adjustments for non-uniform loading to the rib geometry. a) The axial forces carried by the rib and the tie are approximatel y proportional to the rise to span ratio. A flatter arch will have larger axial forces. Although the axial forces decrease with larger rise to span ratios, the slenderness ratios increase. Thus there is a trade off in economy. b) The Ir/It ratio primarily determines how much live load moment is being car ried by the rib and by the tie. c) The hanger spacing does not appreciably affect the live load moment envelope. This is because the live load moment envelope is primarily a function of the span length and the rise to span ratio. The primary effects of hanger spacing on tied arch design is in the dead load and aesthetics. Hangers spaced further apart will cause increased dead load due to the longer panel lengths. d) The Ar/At ratio does not affect the overall behavior of a tied arch substantially. The Ar/At ratio is governed by allowable stresses, and therefore depends greatly upon what types of steel are being used. The Ar/At ratio does affect the maximum live load deflection more than the Ir/It ratio, but not greatl y.
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4. REFERENCES
a) Chandrangsu; Sirilakn; and Sparkes; Stanley R. "A Study of the Bowstring Arch having Extensible Suspension Rods and Different Ratios of Tie-Beam to Arch-Rib Stiffness" Proceedings, Institution of Civil Engineers (Great Britain) Vol. 4, Part 3, August, 1954, pp.515-563. b) Godden, William G., and Thompson, J.C. "Experimental Study of Model Tied-Arch Bridge" Proceedings, Institution of Civil Engineers (Great Britain) Vol. 14, Paper No. 6391, December, 1959, pp.383-394. c) Kishida; Nakai; Ichiba; Kojima; and Naruoka "Loading Test on Trussed Langer Girder" Journal of the Japan Society of Civil Engineers vol. 50, No. 11, November, 1965, pp.27-32. d) Lightfoot, E., and. Hutchinson, G.L. "Optimum Design Considerations for Arch Bridges" Proceedings, Institution of Civil Engineers (Great Britain) Vol. 67, Part 2, 1979, pp.1015-1033 e) Richardson, George S. "Arch Bridges" In Structural Steel Designers' Handbook, Section 13, Frederick S. Merritt. New York: McGraw-Hill, 1970. f) "Thick Girders Tie Span's Thin Arch" Engineering News Record, August 12, 1965, p .119. g) “Preliminary analysis and hanger adjustment of tied arch bridges” by William Edward Beyer .
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