report on arch bridge

8/18/2019 Report on arch bridge

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1. INTRODUCTION

The arch bridge is one of the oldest types 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 and buildings has a long history also in the East.

Arch is sometimes defined as a curved structural member spanning an opening and serving asa 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 capacity,

their remaining life, their stability, their maintenance requirements, and also to determine the

best methods to retrofit the structures. 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 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 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


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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 type 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 types 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 transferred to the main arch

from side arches in two side spans.

Figure 1 Deck arch bridge

Figure 2 Half-through arch bridge


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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 tie, 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.


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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 to move longitudinally.

Figure 6 Reactions for Tied arch

Figure 7 Typical profile of a tied arch bridge and gives the nomenclature of the parts of thestructure


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A tied-arch bridge is an arch bridge in which the outward-directed horizontal forces of the arch,

or top chord, are borne as tension by the bottom chord (either tie-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-arch 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 DesignAdequate 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 archcan 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 isto prestress the tie girder with post-tensioning cables. Another is to have the deck participate

with the tie girder.

1.5.2 Vortex SheddingEvery 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 arch 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 failuredue 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 length. 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 parametersPreliminary 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 typically 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 ratioThe 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 stressesare increased. Many existing tied arches have a rise to span ratio of about 0.2.


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2.1.3 Hanger spacingThe 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 increasing 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 because 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 centerspanAr/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 cases 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


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Graph of tie moment influence lines for 16 panels

Figure 14 Ar/At = 0.6 , Ir/It = 1/20 , 16 panels


Figure 16 Ar/At = 1.5 , Ir/It = 20 , 16 panels


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Graph of rib moment influence lines for different hanger spacing





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Graph of tie moment influence lines for different hanger spacing





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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 size based upon slendernesseffects.

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 approximately 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 atrade off in economy.

b) The Ir/It ratio primarily determines how much live load moment is being carried 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 greatly.


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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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