Preface

This book provides the reader with a comprehensive overview of the state of the art in vibration control and safety of structures, in the form of an easy-to-follow, article-based presentation that focuses on selected major developments in this critically important area.

Safety, reliability and long life of structures are the key points in engineering industries. Although many criteria for structural reliability exist, resistance to various types of dynamic loading is perhaps decisive among them. Thanks to progress in basic research in theoretical and experimental disciplines as well as in industrial development, protection against external dynamic influences need not only be passive, but can be applied through many active control systems. Consequently, the vibration control of structures is a crucial aspect of protection against sudden dynamic forces. Although the widespread introduction of digital control has meant phasing out of passive vibration diminution devices, both remain suitable and have a part to play in specific situations.

Structural vibration control is designed to suppress and control any unfavorable vibration due to dynamic forces that could alter the performance of the structure. Although many vibration control schemes have been investigated so far, questions involving their practical application, such as the use of advanced optimization techniques to control the vibration of structures, require further study. At the same time, it is necessary to realize that external environmental excitation processes are not only of a deterministic type, but are characterized by strong random processes. The two types of phenomena usually combine to form a complicated dynamic system, especially when the structure has to be considered in a nonlinear state. Such assignments require an analysis of the dynamic stability of the structure interacting with excitation sources.

In order to cover as much of the discipline as possible, the chapters of this book range from an enumeration of typical dynamic processes encountered in engineering practice to various styles of control in particular cases, highlighting the specific response processes of individual dynamic systems.

The field of vibration control of structures is, of course, much broader than the scope of presentation allowed for in this book. However, its contents represent a selection of typical topics discussed in this domain at the level of the basis of rational dynamics itself and applications in engineering practice, typified by the interaction of civil and mechanical engineering, with a possible overlap into theoretical and experimental physics.

In order to be successful in control and general management of the dynamic effects endangering civil engineering structures, it is necessary to evaluate statistics of the most serious events either of natural or operating origin. The first chapter, therefore, presents a balanced overview of structures and the causes of their failure due to disasters caused by the dynamic effects of wind, traffic, or earthquakes, due to insufficient knowledge of the dynamic behavior of structures, their complicated

long-term interaction with environmental processes or material reliability, and, last but not least, due to inadequacy of standards and codes. As a consequence of these incidents, there have been significant changes in the codes and design philosophy of bridge construction in recent decades. The chapter illustrates progress in bridge engineering due to scientific and technological advances concerning the influence of wind, seismicity and heavy traffic. As the author points out, further research is still needed to mitigate the long-term effects of vibration and material degradation on the performance and integrity of bridge structures.

Chapter 2 studies a fractional distributed optimal (or sub-optimal) control for a class of infinite-dimensional parabolic bilinear systems evolving in a spatial domain Ω by distributed controls depending on the control operator. The main efficiency of the operator follows from a fractional spatial derivative of the Riemann‒Liouville type. Using Fréchet differentiability, the existence of an optimal control depending on both time and space is emphasized. In principle, a quadratic function is minimized, which accounts for the deviation between the desired and the achieved state. Then, the characterizations of optimally distributed control for different admissible control sets are given. The chapter shows the importance of a strong theoretical background in dynamic models, particularly in the optimizing process, provided it is used in practice for reliable control. The authors developed and tested an algorithm materializing the above theoretical derivation. Subsequent simulations illustrate that the previous theoretical results are meaningful and can provide stable and practically applicable results.

A very interesting device that can serve to reduce structural vibrations due to various external shocks is based on the dry sliding phenomenon. Generally in physics and engineering, sliding represents both positive and negative effects with respect to the reliability and dynamic character of the system. For instance, bowed musical instruments are based on a complicated sliding force at the bow‒string contact, which decreases with the velocity of the bow. In engineering, on the other hand, it can be understood as a very effective principle of energy absorption over a very large range of frequencies and amplitudes of relevant oscillations. This makes it an excellent candidate for various damping devices applicable in environments where excitations are extremely unpredictable in the frequency spectrum and amplitude content, e.g., anti-seismic facilities. These factors led to the invention in the mid-20th century of the sliding mode controller as an effective nonlinear controller for structures in seismic engineering, piping vibration damping, etc. However, practical implementation revealed that the sliding-based controller suffers from low sensitivity to uncertainties and other system variations due to chattering effects. Chattering is a harmful phenomenon because it leads to low control accuracy, high wear of moving mechanical parts, and high thermal losses in power circuits. In the first phase of the development of sliding mode control theory, the chattering was the main obstacle to its implementation. Thanks to the law of adaptation, this shortcoming was overcome by dynamically adapting the controller parameters depending on the system changes. Chapter 3 describes relevant research, numerical simulations and experimental measurements.

Another area that has seen intensive testing of dynamic effects is the suspension systems of softly sprung vehicles. In Chapter 4, a low-cost, customized, and effective damper dynamometer is constructed using computer-aided design and finite element analysis to measure the properties of suspension dampers used in a racing car. The chapter presents an excellent example of the advanced engineering process in the field, from construction design to race-track testing. Particularly inspiring is the description of the development of special equipment that had to meet strict requirements given the conditions in which it operates. The authors carefully follow the entire path of balanced design, manufacturing, testing and interpretation. Chapter 5 provides a typical example of complex nonlinear dynamic processes occurring in a non-conventional spherical absorber. Although passive absorbers have been investigated theoretically and experimentally many times and are commonly installed in practice, there are still many gaps in the information about new and progressive types. It is important to note that inappropriate configuration of a vibration absorber can not only reduce its efficiency but can even result in its negative influence. This is quite often the case, for example, with a passive or semi-active pendulum absorber when its spatial character is neglected. The system is strongly nonlinear and the interaction of the horizontal response components gives rise to complicated effects that can lead to various forms of stability loss.

A more sophisticated system, presented in the final chapter, is a ball-shaped absorber moving in a spherical cavity. This arrangement allows for many modifications. For instance, the cavity may be elliptical in shape, allowing the absorber to possess different eigen-frequencies in the principal directions, which is the usual disposition when the vibrations of a building require reduction. Another variant is a cylindrical absorber, as required for damping the horizontal vibration of a bridge deck. The spherical ball absorber is even more sensitive to dynamic nonlinear effects that cannot be avoided in the theoretical modeling of this system. Particularly interesting may also be the demonstration of Gibbs' principle of constructing the governing dynamic differential system, which in certain configurations leads to a more efficient system than that resulting from the direct application of the Hamiltonian principle to obtain a Lagrangian system.

> **Jiří Náprstek and Cyril Fischer** Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, Prague, Czechia

## **Chapter 1** Vibration Control in Bridges

*Kenneth C. Crawford*

### **Abstract**

The purpose of this chapter is to examine methods to control induced vibrations in steel and reinforced concrete (RC) highway bridges caused by three primary vibration forces, specifically wind, heavy traffic, and seismic events. These forces manifest their effects in bridge structural elements to different degrees, from small vibrations to large forces causing destruction of the bridge. This chapter examines bridge failures caused by induced vibrations, from wind loading, traffic loading, and seismic vibration loading and presents solutions developed to compensate for these vibrations. Bridge failures from seismic vibrations are the most destructive and are described in two major earthquakes in California. A major bridge failure from induced wind vibrations is considered, and two bridge failures caused by vibrations from heavy traffic loading are described. With lessons learned from these and other bridge failures, new design criteria and methods have been established to reduce and mitigate the destructive forces of induced vibrations. Significant changes in bridge structural engineering codes and design philosophy were made. While bridge structural design improvements have reduced the effects of wind, seismic, and heavy traffic vibrations, further research is needed to mitigate the long-term effects of vibrations on bridge performance and structural integrity.

**Keywords:** bridges, wind, heavy traffic, seismic events, vibrations, failures

#### **1. Introduction**

A national highway system is a large and extensive infrastructure made up of roads, tunnels, bridges, interchanges, ramps, and embankments in a complex combination of designs and configurations. The continuous and uninterrupted flow of traffic in a highway system is vital to a nation's economy and flow of goods and services. The efficient operation of a highway transportation system is dependent on its original construction and maintained condition of its key elements, in particular bridges. Steel and RC bridges are a critical component in a national highway system requiring sound design and high quality construction with an effective long-term inspection and maintenance program. The performance and survivability of bridges, under wind and heavy traffic loading, and in a natural disaster, such as a seismic event, is critical in a nation's transportation network. The performance of RC highway and steel bridges under these induced forces is a function of their ability to withstand damaging forces and induced vibrations in critical structural members. Many bridges constructed before the 1970s, both in Europe and the USA, do not meet current seismic design standards and are potentially subject to possible

failure in the event of a major earthquake. Concrete and steel bridges constructed today are designed to perform to high standards under wind, heavy traffic, and seismic vibration loading.

#### **1.1 Objective of chapter**

Considering the impact of vibrational forces on bridge structures the objective of this chapter is to examine the nature of induced vibrations in bridges from natural and man-made forces and to gain an understanding on how these vibrations influence a bridge's structural performance. Induced vibrations from wind, heavy traffic and seismic events can significantly degrade the structural integrity of a bridge and its ability to sustain its designed load performance. To consider and understand the effects of induced vibrations in bridges this chapter examines several cases of bridge failures that have resulted from wind and heavy traffic loading, and from seismic events that destroyed a large number of bridges in a highway interstate system. The goal is to learn from these bridge failures and what role the induced vibrations played in their failure. The lessons learned in studying bridge failures provide an opportunity to better understand the forces of nature and the types of vibrations they induce in bridge structures and to be better able to develop improved bridge design codes, criteria, methods, materials, and construction process. A bridge today should not fail from wind, heavy traffic, or seismic induced vibrations.

#### **2. Bridge failures from induced vibrations**

While bridge failures occur for a number of reasons, normally through the deterioration of materials in structural members, the study of vibrations in a bridge's structural integrity provides an insight on how a bridge will perform under the stress of severe vibration loading. The effects of wind vibration are examined in two cases in which bridges failed from inadequate design. Two bridges are considered that failed from vibrations induced by heavy traffic loading. The third category of bridge failures is the result of destructive forces induced by the vibrations from seismic events. Earthquakes, depending on the magnitude of vibrations, are a major factor in the disruption and destruction, of highway bridge networks. The point in studying bridge failure mechanisms from induced vibrations is to learn and to establish better designs to improve long-term bridge performance to mitigate destructive vibrations forces.

#### **2.1 Bridge failures from wind vibrations**

Since the early 1800s when the first suspension bridges were being designed and built in England and the United States little was understood about wind induced vibrations. Vibrations from seismic events and heavy and traffic loading were not an issue at the time. After a number of wind induced suspension bridge failures in the first half of the 1800s, **Figure 1**, it was not until 1840 and 1849 serious consideration was given by bridge designer John Roebling (1806–1869) to design for wind loading in suspension bridges.

In the mid-1800s a number of the early suspension bridges collapsed for various reasons, some with loss of life. Poor-quality iron, and shortfalls in design and constructions were identified as contributory causes. In the aftermath of the collapses it was recommended structures should be periodically inspected and chains should be load-tested. Unfortunately these actions were not mandatory. Various

*Vibration Control in Bridges DOI: http://dx.doi.org/10.5772/intechopen.107501*

## **Figure 1.**

*Bridge failures from wind vibration loading in 1800s.*

#### **Figure 2.**

*Tacoma narrows bridge failure from a 40 mph wind.*

design schemes were adopted to limit vibrations but the single most important was to stiffen decks by the addition of truss-parapets [1].

One of the classic examples of the effect of wind induced vibrations on a suspension bridge is the failure of the new Tacoma Narrows Bridge in Nov 1940, as the result of a 40-mile an hour wind, **Figure 2**.

Based on Austrian civil engineering deflection theory the engineer firm Moisseiff and Lienhard, New York City, who produced the original design for the bridge, stated the main cables were stiff enough to absorb wind pressure and stablilize the bridge, and assumed the wind forces would only push the bridge sideways. From the beginning the bridge had large vertical deflections even from moderate winds.

The primary explanation of the bridge failure was described as "torsional flutter." "Torsional flutter" is a complex mechanism. "Flutter" is a self-induced harmonic vibration pattern which can grow to very large vibrations. The external force of the wind alone was not sufficient to cause the severe twisting that led the Narrows Bridge to fail. It is noted the bridge deck's twisting motion caused torsional oscillation which became self-generating causing the bridge to absorbed more wind energy in a condition called "self-excited" motion [2].

While vortex shedding may occur in low wind speeds around 25–35 mph, and torsional flutter occurs at higher wind speeds of 80–100 mph, the instability in the Tacoma Narrows bridge caused by vortex shedding and torsional flutter occurred at

#### *Vibration Control of Structures*

relatively low wind speeds, less than 25 mph. Because 0f the type of bridge design, and relatively weak resistance to torsional forces from the vortex shedding instability the bridge went into self-amplifying "torsional flutter", which is what destroyed the bridge [2].

#### **2.2 Bridge failures from traffic load vibrations**

It is rare that a bridge fails from the vibrations of heavy traffic loading but two cases stand out as examples of failure under heavy load vibrations. In each case the vibration loading exceeded the designed loading capacity of the bridge with the failures compounded by other factors, such as design flaws, construction deficiencies, inspection errors, and maintenance short falls.

#### *2.2.1 I-35 W bridge collapse Minneapolis, MN*

The 8-lane I-35 W bridge, known as bridge 9340, was constructed in 1967 and served over 140,000 vehicles per day. The bridge consisted of fourteen spans: nine spans were of steel multi-girder construction, two were of concrete slab construction, and the main three were of deck truss construction. The Minnesota Department of Transportation (MnDOT) was tasked with taking over annual bridge inspection beginning in 1993. Prior to this, it was federally inspected every other year. Inspection reports by MnDOT often indicated significant corrosion, rusting, warped plates, and other structural issues with the bridge. It was noted that the lack of redundancy in the main truss design meant that the bridge was vulnerable to a collapse if a single critical piece in the truss were to fail. Subsequent inspection reports expressed concern about the bridge's structural integrity, but no motion to close or drastically reinforce it was ever made [3].

In 1 August 2007, at 6 pm, the I-35 W Mississippi river bridge collapsed suddenly taking with it 111 vehicles, killing 13 people, and injuring 145. The bridge, **Figure 3**, was non-redundant and fracture critical, meaning if one member failed the entire bridge would collapse. Although the iron frame bridge with riveted gusset plates had supported heavy traffic volume for over 40 years it was a single half inch gusset plate, in a badly corroded condition, that failed along a line of rivets that caused the entire 250 foot bridge to fail. It was the additional weight of construction equipment plus the vibrations of rush hour traffic at the time that actually triggered the failure of the gusset plate [3].

**Figure 3.** *I-35 W Mississippi River Bridge collapse August 2007.*

#### *Vibration Control in Bridges DOI: http://dx.doi.org/10.5772/intechopen.107501*

The deterioration of the gusset plates in periodic annual inspections was not labeled as potentially critical. While the gussets were identified as the root cause of this devastating collapse, the investigation found a combination of separate factors coming together led to the disaster: design flaws, inadequate inspection, MnDot policies not being followed, poor information flow, the organizational structure not addressing bridge conditions and safety. All these factors combined caused the bridge to collapse [3].

#### *2.2.2 Hyatt Regency Hotel, Kansas City, MO Skywalk Collapse*

In 1981 the Hyatt Regency Hotel in Kansas City, Missouri, suffered a structural failure of two of its three skywalks above the hotel atrium (**Figure 4**). At 7:05, July 17, with approximately 1600 people gathered in the hotel atrium for a tea dance, the fourth level walkway, suspended directly over the second-floor walkway, gave way and fell on the walkway below taking both walkways to the ground floor, killing 114 and injuring 216. The primary cause of the failure was the induced vibrations from a large number of people on the skywalks (overloaded) dancing to the rhythm of the music on the ground floor. It was the worst civil engineering failure in US history, since the collapse of Pemberton Mill over 120 years earlier. Many lessons and reforms for this structural failure contributed to engineering ethics and safety and to emergency management.

The root cause of the structural collapse was the failure of a hangar bolt bracket in fourth floor skywalk. Contributing factors: failure in engineer review of shop drawings of a field change in the skywalk hangar bolts, inadequate design of skywalks, and lack of oversight responsibility. Kansas City society was affected for years, with the collapse resulting in billions of dollars of insurance claims, legal investigations and city government reforms.

#### **2.3 Bridge failures from seismic vibrations**

Vibrations from seismic events have devastating effects on bridges and structures. Earthquakes in California and the bridge failures that resulted from large seismic vibrations are examined. The highway system in southern California is a complex network of Interstates, bridges, and flyovers, and is subject to significant deteriorating impacts from earthquakes and seismic induced vibrations.

The Interstate 5 (I-5) is the main Interstate highway on the West coast of the United States running largely parallel to the Pacific coast of the continental U.S. and

**Figure 4.** *Collapsed skywalk bridge in Hyatt Regency Hotel.*

**Figure 5.** *Interstate I-5 and State Road 14 interchange over the Newhall Pass.*

Route 99 from Mexico to Canada. The Golden State Freeway on I-5 begins one mile east of downtown Los Angeles and extends north through San Fernando Valley, across the Newhall Pass into the Santa Clarita Valley. I-5 then goes north from the Newhall Pass over the Grapevine Pass to eventually reach its second-highest point at Tejon Pass with an elevation of 1275 m, into the San Joaquin Valley, and further to Sacramento.

The Newhall Pass Interchange, **Figure 5**, is a major highway interchange north of Sylmar in Southern California, connecting Interstate 5 (Golden State Freeway) with State Route 14 (Antelope Valley Freeway) (SR 14). The interchange is extremely large, and consists of numerous flyover ramps and two tunnels. Portions of Interstate 5 in the pass reach up to 21 lanes wide. The complex interchange structure combines a directional T-interchange with a collector-distributor bypass.

#### **2.4 Impact of seismic vibrations on California highway bridges**

The failure of the Interstate 5 and SR14 at Newhall Pass interchange in southern California, along with other freeway overpasses, in the 1971 earthquake, and again in the Northridge earthquake in 1994, provide examples of the devastating impact seismic vibrations can have on the local economy and a critical state highway network in an urban area. The failure of highway bridges in these two earthquakes occurred because they did not meet the updated Caltrans bridge seismic design criteria and had not been retrofitted before the earthquakes occurred.

#### *2.4.1 Sylmar earthquake bridge failures*

The Sylmar earthquake (also known as San Fernando earthquake) took place near the San Fernando Valley in southern California on February 9, 1971. This earthquake was of magnitude 6.6 on the Richter scale and had an epicenter with coordinates of 34.41°N 118.40°W. The earthquake lasted 12 s and had a depth of 13 km (8.1 miles). Thrust faulting ruptured a segment of the San Fernando fault zone with a total surface rupture of 19 km with a maximum slip of 2 m. 65 persons died, 49 in the collapse of a Veterans Administration Hospital. 200 people were injured. An estimated \$505–553 million occurred in structural damage.

In the Sylmar earthquake twelve overpass bridges failed and fell onto the freeways below. Major bridge failures occurred at the Interstate 5 and State Road (SR) 14 interchange, **Figure 6**. A total collapse of the southbound I-5 to northbound

**Figure 6.** *1971 Sylmar Bridge Failures on I-5—State Road 14 interchange.*

SR14 overpass occurred as a result of the earthquake. This collapse resulted in the additional collapse of the intersecting southbound SR 14 to southbound I-5 overpass (as this connector bridge was directly beneath the I5—SR 4 overpass) [4].

Both bridges fell directly onto the southbound I-5 truck bypass. There was damage to all bridge structures involved, varying from minor cracking and splaying, to the loss of complete sections of bridges. Most of the bridge damage in the Sylmar earthquake occurred on the I-5—SR14 interchange, **Figure 6**. Vibrations from this 6.6 magnitude earthquake caused the structure between two columns to separate from the actual supporting column which caused the highest overpass road (Newhall Pass) to collapse on top of the overpass below it, which then all collapsed onto the freeway below it. The rebuilt interchange was completed in 1973.

On the I-5—SR 14 interchange, it was noted the column that collapsed experienced damage at the ends, while the middle part of the column received little damage. Jennings noted, the small length of seating at the end of the fallen section, the lack of effective ties(steel reinforcing) to neighboring sections, and the general configuration of the inverted-pendulum structure were indicative of inadequate attention to the effects of strong earthquake motion. There are a variety of possible ways that the bridge structure might have failed, but two points are clear. First, the evidence strongly indicated a vibration failure. Permanent ground displacements (none were noted) were not thought to have played a significant role in the collapse [5].

#### *2.4.2 1994 Northridge Earthquake Bridge Failures*

The 1994 Earthquake (known as Northridge Earthquake) occurred on January 17, 1994 near Reseda, California, a neighborhood in the north-central San Fernando Valley region of Los Angeles. The epicenter was 34.213°N 118.537°W. The magnitude of the earthquake was 6.7 Mw (moment magnitude) and caused over \$50 billion in damage. 57 people died and over 8700 were injured. 40,000 buildings were damaged and 20,000 were left homeless. While about \$2 billion occurred in damaged transportation infrastructure (roads and bridges), over \$50 billion in damages occurred with severe impacts on the local economy over the following 3 years. The lesson learned is that small damage to a transportation network can have a devastating impact on the local economy for years after [4].

The Northridge earthquake was the first earthquake since the 1933 Long Beach earthquake to strike beneath an urban area and occurred on a blind thrust fault producing the strongest ground motions ever recorded in urban areas in North America. Damage to freeways, office and apartment buildings, and parking structures was extensive. Structures were lifted of their foundations by high levels of

**Figure 7.** *Two bridge failures on I-5—State Road 14 interchange.*

**Figure 8.** *I-5 Newhall bridge failure near SR14.*

vertical and horizontal accelerations. Bridge damage was substantial. Over 4000 km2 of the earth's crust deformed, forcing the land surface upward in the shape of an asymmetric dome [6].

The Northridge earthquake appears to be the result of a truncated fault that broke in the 1971 San Fernando earthquake at a depth of 8 km, resulting in a reverse skip of more than three meters along a 15-km long south-dipping thrust fault line. This fault raised the Santa Susana mountains by more than 70 cm. Because the fault was directly under the city the Northridge earthquake caused many time more damage. Of all the damage the biggest surprise was the fracture of welds in steelframe buildings. Concealed thrust faults remain the greatest potential for strong ground shaking for Los Angeles, even in moderate quakes [7].

The Northridge earthquake collapsed seven freeway overpass bridges and caused the disruption of a large portion of the northwest Los Angeles freeway system, **Figures 7** and **8**. The Northridge earthquake caused the southbound SR14 to southbound I-5 connector to collapse, **Figure 6**, and a bridge crossing on the San Fernando Freeway.

#### *2.4.2.1 Causes of Northridge seismic vibration structural failures*

Over 350 square miles (900 square kilometers) received extensive damage to residential, commercial building, and regional lifelines from the main shock and aftershocks. Although the earthquake magnitude of 6.7 was moderate by earthquake standards, the neighboring communities of Sylmar, Burbank, Van Nuys,

**Figure 9.** *Failure of I-210 overpass to I-5 south.*

Glendale, Santa Monica, Newhall, and San Fernando sustained damages. In looking at other earthquakes the 1971 San Fernando had a magnitude of 6.4, 1964 Alaska had 8.1, 1989 Loma Prieta 7.1, 1987 Whittier Narrows 5.9, and the 1991 Sierra Madre had a magnitude of 5.8.

There was also major bridge damage to the Golden State Freeway (I-5) and Foothill Freeway (I-210) Interchange, **Figure 9**. The westbound I-210 to southbound I-5, under construction and complete except for paving at the ramp section, collapsed over the I-5. Possible cause of failure was vibration that moved the overpass off its supports due to an inadequate column seat. Unlike the situation at the I-5—SR 14 Interchange, permanent ground movement (defined as several inches of left-lateral displacement with possibly an element of thrusting) was observed in the area.

Examination of the earthquake magnitude and epicenter and resulting bridge failure was made with consideration for the specific modes of bridge failure. Of the seven major freeway bridges that failed, two bridges on the SR 118 had flexure/ shear failure of short and stiff columns and a low transverse reinforcement ratio. The I-5 bridge failure was from skewed geometry and unseating of expansion joints. The I-10 bridge failures were caused by flexure/shear failure of short stiff columns and brittle shear failure of stiff columns. The I-5—SR 14 bridge failures were caused by short column brittle shear failure. Five of the failed bridges were scheduled for retrofit which had not been accomplished before the earthquake. The two other failed bridges had been identified as not requiring retrofit [6, 8].

**Figure 10.** *Failed highway bridge columns on Santa Monica Freeway.*

**Figure 11.** *Failed bridge columns on Santa Monica Freeway and I-5.*

**Figure 12.** *Column failure of I-210 overpass to I-5 south.*

#### *2.4.2.2 Northridge bridge column failures*

The Northridge earthquake caused extensive damage to bridge columns, particularly on the Santa Monica Freeway (I-10) from the I-5 to Santa Monica on the ocean and SR 118 further north, **Figures 10**–**12**. The column failures were caused by flexure and shear failures of short stiff columns and by the brittle shear failure of stiff columns, **Figures 10** and **11**.

The Northridge earthquake's high vertical acceleration was the primary force causing the bridge column failures. The rate of vertical acceleration was the highest ever recorded in North America. In studying the ground wave motion there was evidence of surface wave amplification which increased structural damage. The resulting seismic induced vibrations were devastating to the bridge columns not designed for the magnitude of the vibrations, resulting in widespread column destruction.

#### **3. Lessons in controlling bridge wind vibrations**

The construction of a suspension bridge consists of main towers, main suspension cables, anchorages for the cables, trusses, and stiffening girders. After the main cables are suspended between the towers and connected to their anchorages,


#### **Figure 13.** *Bridges designed and built by John Roebling.*

vertical suspenders are connected to the deck which carries the traffic load. The main cables, made of high-strength steel, are the primary load carrying members of the bridge and are efficient in reducing and mitigating wind vibrations. Because the bridge structure deadweight is reduced longer suspension bridge spans are possible.

In the early to mid-1800s suspension bridges were most often light spans with flexible decks and were vulnerable to the aerodynamic forces of cross winds. To counter these wind forces bridge engineers began moving to heavier and stiffer suspension bridges. An example is the Brooklyn Bridge designed in 1883 by John Roebling to which he added mass and stiffness to resist the strong winds on the East River (**Figure 13**). However by the early 20th century bridge engineers failed to learn from past bridge failures. David Billington, Gordon Y.S. Wu Professor of Civil Engineering at Princeton University, stated "Roebling's historical perspective seemed to have been replaced by a visual preference unrelated to structural engineering, as seen in the failure of the Tacoma Narrows bridge" [2].

John Roebling recognized the problem of wind loading on suspension bridges and designed a number of features in the bridge to reduce the effects of wind vibrations. This involved adding stays and trusses to counteract wind loading.

**Figure 14.** *822 ft Niagara railroad suspension bridge.*

**Figure 15.** *John A. Roebling Bridge Cincinnati OH.*

These features were added to the 1849 Niagara railroad bridge and the 1855 Niagara suspension bridge.

The Niagara railroad bridge, **Figure 14**, opened in 1849, had a top deck for streetcars and a lower deck for pedestrians and wagons. Two tracks for streetcars were laid. Diagonal stays were added to increase load capacity, strengthen the floor, and check train and wind vibrations. Wrought iron trusses were added, running the length of the bridge.

With the design and construction of the Cincinnati river bridge, **Figure 15**, opened in 1867, additional features were added to mitigate the effects of wind. Roebling made further improvements for wind vibration stability by adding additional stays and trusses and increasing the mass of the bridge. These features were then used for the design of the Brooklyn Bridge in which stiffening girders and additional mass were added to provide a stable bridge deck for the high winds on the East River. With the design of the Brooklyn Bridge Roebling had a good understanding of the relationship of suspension bridge span length and the forces of induced wind vibrations. This understanding would not extend to the suspension bridges designed and built in the next century.

After a series of suspension bridge failures in the 1800s and following the Tacoma Narrows Bridge failure, professor J.K. Finch, Columbia University, civil engineering, in an Engineering New-Record article, stated: **"**These long-forgotten difficulties with early suspension bridges clearly show that while to modern engineers, the gyrations of the Tacoma bridge constituted something entirely new and strange, they were not new — they had simply been forgotten**.** An entire generation of suspension-bridge designer-engineers forgot the lessons of the 19th century." Prior to the Tacoma Narrows bridge failure the last major suspension bridge failure was the Niagara-Clifton Bridge, constructed in 1847, which collapsed in a storm in 1889. Well into the 1930s, aerodynamic forces on bridges were not well understood and researched, resulting in insufficient wind loading designs for suspension bridges [2].

#### **4. Lessons controlling heavy load bridge vibrations**

The bridge failure cases in Section 2.2 illustrate what the impact of uncontrolled vibrations can have on bridge structural integrity. Through extensive research new methods and devices have been developed to dampen and significantly reduce vehicle (truck, train) induced vibrations in bridges. One such device is the tuned mass damper (TMD), also known as a seismic damper of harmonic absorber.

#### *Vibration Control in Bridges DOI: http://dx.doi.org/10.5772/intechopen.107501*

Consisting of a mass mounted on damping springs the TMD is mounted on bridges and buildings to reduce mechanical vibrations. The TMD's oscillation frequency is tuned to synchronize with the resonant frequency of the object to which it is mounted.

Tuned mass dampers stabilize against violent motion caused by harmonic vibration. They use a comparatively lightweight component to reduce the vibration of a system so that its worst-case vibrations are less intense. TMDs can prevent damage and structural failure and are frequently used on highway and rail bridges to reduce harmonic vibrations [9].

Using the modal properties of a bridge structure in bridge engineering the TMD is designed to reduced vibrations in bridges. Depending on the design methodology of the TMD, bridge vibrations in certain frequencies are reduced while other frequencies are amplified.

One application of the TMD is on railroad bridges. A moving mass model is used to consider the dynamic response of the bridge to the moving train load. Zhaowei Chen et al., introduce the design methodology of bridge-based designed TMD (BBD-TMD) in which a detailed train-track-bridge coupled dynamic model with attached BBD-TMD is established based on the multi-body dynamics theory and the finite element method. To evaluate the running performance of a train, three indicators are selected, namely wheel-axle lateral force (Fw), derailment coefficient (DC), and wheel unloading rate (WUR). The authors note the indicator WUR is aggravated in some cases by the BBD-TMD, indicating that the performance of a running train at different speeds should be seriously considered in designing TMDs based on the bridge modal property [10].

Using the train wheel and body for a 2-degree of freedom (DOF) system a high-speed train such as the TGV can be modeled. For a three-span bridge using the midpoint vertical displacements and the fast Fourier transform and comparing the results before and after installation, the efficiency of the TMD can be shown. The TMD has a variety of merits in that it has permanent service time, and only requires easy management and maintenance efforts and no external power supplying sources [10].

#### **5. Lessons learned for controlling seismic vibrations in structures**

No single earthquake like the 1994 Northridge earthquake had such an impact on the art and practice of structural engineering, causing an overall and widespread reevaluation of engineering practices so deeply rooted in structural engineering. Following 1994 the most significant changes by the Seismic Advisory Board (SAB) in the philosophy and design practice of structural engineering were in the following areas:


f. Development and application of performance based design methodologies.

g.Significant changes and additions to building codes and standards.

Prior to the 1994 Northridge earthquake welded steel moment resistant frames (WSMRF) in steel-frame buildings were considered the most reliable and sought after structural systems for earthquake-resistant construction. The poor performance of WSMRFs in the Northridge earthquake, with failures in steel frame welds because of the ductility of steel with ground movement forces, revealed the limitations on the valid bounds of experimental research on which the use of WSMFR was based [1]. The failures were in extrapolations of limited steel frame seismic tests on which designs were based and in the failure of the processes and quality of steel welding [8].

The lesson learned in the Northridge earthquake provided key lessons learned for earthquakes that occur beneath cities, indicating the concealed faults under Los Angeles are far more complex than previously thought. The one primary lesson learned shows urban areas can be subjected to ground motions with peak accelerations approaching the force of gravity, exceeding the levels of shaking anticipated by building codes. It is essential building codes address the forces expected on buildings subject to earthquakes.

The US Geological Survey (USGS) has established national and regional maps of probabilistic earthquake ground shaking through the USGS (US Geological Survey). The National Seismic Hazard Mapping Project (NSHMP) integrates the results of research in historical seismicity, paleo-seismology, strong motion seismology, and site response taking into account all the possible locations and magnitudes that are likely to happen in future hypothetical earthquakes. By the year 2000, all US model building codes incorporate ground motion hazard maps derived from the USGS studies to insure structures are engineered to have the appropriate level of resistance to earthquake ground motion [8, 9].

#### **5.1 Improvements in highway bridge seismic design**

The development of seismic design criteria and guidelines in the US, and particularly in California, has evolved in response to substantial earthquake damages to bridges and structures. Following the 1971 Sylmar earthquake near Los Angeles a major bridge retrofit program was started by the California Department of Transportation Caltrans). Following the devastating 1989 Loma Prieta earthquake in Oakland, CA, the Governor of California created, in 1990, the Seismic Advisory Board (SAB) under Caltrans. The SAB is an independent body whose role is to advise Caltrans on seismic policy and technical practices to enhance the seismic safety and functionality of California's transportation structures. The SAB initiated significant changes in bridge and structural design philosophy and criteria, moving from established prescriptive criteria to developing performance-based seismic engineering (PBSE) concepts and methodologies. FEMA-273 guidelines (1997) made PBSE a reality for structural engineers by defining performance of components and systems in terms of a spectrum varying from continuous operation to collapse prevention [11].

#### **5.2 Bridge seismic vibration response**

The response of RC highway bridges under conditions of a natural disaster such as an earthquake is a function of its design and construction and its ability to withstand the vibrations and energy of local ground shaking without collapse. In

#### *Vibration Control in Bridges DOI: http://dx.doi.org/10.5772/intechopen.107501*

analyzing the ground motion of the 1994 Northridge earthquake, the strength of ground shaking was measured in the velocity of ground motion, the acceleration of ground motion, the frequency content of the shaking and duration of the shaking. When assessing the potential shaking hazard at a site where frequent strong motion is expected to re-occur, consideration is made of the characteristics of waves produced by an earthquake rupture, also strongly influenced by the fault rupture orientation, its depth, and the details of how the slip spread across the ruptured fault patch. In the Northridge earthquake the rupture of a concealed fault beneath an urban area caused widespread and extensive damage to bridges and buildings [12].

#### **5.3 Bridge seismic vibration design for critical components**

The ability of a RC highway bridge to withstand damaging vibrations from an earthquake depends on seismic design guides available at the time of the bridge design and construction. Bridges designed and constructed before the 1971 Sylmar earthquake did not comply with the latest seismic design guides. Following three relatively moderate earthquakes between 1971 and 1994, two in southern California and one in Oakland, California, which resulted in significant infrastructure damage, Caltrans, led by the Seismic Advisory Board, made a substantial effort to redefine and improve their seismic structural codes.

In their Seismic Design Criteria, Caltrans defines a ductile member in an RC bridge as any member that is intentionally designed to deform in elastically for several cycles without significant degradation of strength or stiffness under the demands generated by the Design Seismic Hazards. The Design Criteria states seismic-critical members may sustain damage during a seismic event without leading to structural collapse or loss of structural integrity. Bridge components are designated as seismic-critical if they will experience any seismic damage as determined by the project engineer and approved during type selection. Ductile and seismic-critical members are defined as columns, Type I shafts, pile/shaft groups and Type II shafts in soft or liquefiable soils, pier walls, and pile/pile-extensions in slab bridges (designed and detailed to behave in a ductile manner). Other bridge components such as dropped bent cap beams, outrigger bent cap beams, "C" bent cap beams, and abutment diaphragm walls are to be designed as seismic critical. All other components not seismic-critical shall be designed to remain elastic in a seismic event [13, 14].

#### **5.4 Seismic vibration control in buildings and bridges**

Seismic vibration control consists of technologies to reduce the seismic effects in structures (building and bridges), and thus minimize earthquake damage. When the seismic waves travel upwards through the base of buildings and bridges, reflections considerably reduce the wave energy.

To control residual energy in seismic waves, which are the source of major damage in earthquakes, seismic vibration control technologies are used with dampers, which absorb energy over a wide range seismic wave frequencies. Seismic energy flow into buildings is also controlled by isolating the building with pads mounted in the base load carrying elements decoupling the building superstructure from the foundation substructure.

An excellent example of bridge engineering to control seismic and wind vibrations is provided by the Rio Antirrio bridge, **Figure 16**, over the Gulf of Cornith in Greece.

To absorb the energy from earthquakes it was necessary to develop new design and construction techniques for the piers and pier footings. The pier footings were

#### **Figure 16.**

*2380 m Rio Antirrio fanned cable-stay bridge.*

#### **Figure 17.** *Rio Antirrio bridge with four pylons and five spans.*

not buried in the sea bed but mounted on top of a gravel bed allowing the piers to move laterally while the gavel bed absorbs the earthquake energy. To absorb movement in the bridge deck jacks and dampers were connected to the bridge pylons. Protection from the effect of high winds on the decking is provided by the use of aerodynamic spoiler-like fairing and on the cables by the use of spiral Scruton strakes.

The design of the pylon footings, not anchored in the seabed, but simply placed on a level bed of rock is unique in structural engineering for controlling seismic vibration (**Figure 17**). The bed of rock absorbs the energy of seismic vibrations without transmitting the energy through the pylons to the bridge structure. The bridge is designed to withstand an earthquake up to a 7.4 magnitude.

#### **6. Role of FRP systems for bridge stability in seismic vibrations**

Since the mid-1990s advanced composites were first used In the United States for seismic retrofit of buildings and bridges which have also seen a significant increase worldwide in the use of advanced composite materials for bridge rehabilitation to repair damaged structures, to strengthen structures for increased demand (vehicle loading), and to retrofit structures to control seismic vibrations. Referred to as fiber reinforced polymers (FRPs), these advanced composite materials consist of glass, carbon, or aramid fibers embedded in a polymer matrix. These FRP overlays successfully used to strengthen columns and girders for shear, reinforced concrete slabs in flexure, and on joints for external cap and column connections. During the Caltrans Phase I and Phase II Bridge Column Retrofit Program, early applications of

#### *Vibration Control in Bridges DOI: http://dx.doi.org/10.5772/intechopen.107501*

FRPs were developed and implemented demonstrating significant benefits over the more conventional steel jacketing.

Other key benefits of FRPs are their high mechanical characteristics and their light weight (up to 5 times stronger and 5 times lighter than mild steel). Other issues the Seismic Advisory Board believes need to be better addressed for broad based FRP applications concern fire resistance and quality control/inspection measures during and after the retrofit installation. For FRP applications to be used on California bridges and to meet life safety codes Caltrans requires testing for proof of concept and performance validation testing of FRP technology for bridge retrofit. Although the retrofit concept was tested on scaled bridge components, final proof testing was done on full scale bridge elements [8].

#### **6.1 Example of FRP bridge retrofitting**

To accomplish stability in bridge structures from seismic vibrations it is necessary to strengthen and stabilize bridge bents and foundations for seismic loading. Analysis considers types of retrofitting applications on bridge bents and the advantages of FRP systems to increase structural member axial capacity and ductility in columns and beams. Retrofitting RC bridges by encasing and strengthening bridge bents with CFRP (carbon fiber-reinforced polymers) systems provides an effective method of mitigating the impacts of seismic vibration loading. The carbon fiber and epoxy resin composite for carbon-fiber reinforced polymer material (CFRP) has 28,000 unidirectional carbo fibers per tow with 6.5 tons per 25.4 mm, a modulus of elasticity of 65 GPa, a tensile strength of 628 MPa, ultimate axial strain of 10 mm/m, and a layer thickness of 1.32 mm.

For CFRP retrofitting of bridge bents, **Figure 18**, it is necessary to develop a higher base shear and moment capacity than the existing foundation and pile cap system. Performance-based design determines column CFRP jacket thickness for plastic hinge confinement, shear strengthening, and lap splice clamping. The design increases displacement ductility of the bridge bent developing a higher base shear and moment capacity. The RC beam connecting the pole cap completes the tension and compression load path, increasing shear and flexural capacity of the foundation [15, 16].

Many studies on the use of FRP jackets 0n reinforced concrete (RC) columns have shown the jackets are effective in increasing shear capacity and flexural durability in the columns. However the contribution of FRP jackets for flexural strength for small axial loads is minimal. While applying FRP sheets in the direction of a column is difficult because difficulties with base anchorage, a research project

**Figure 18.** *CFRP strengthening of bridge bents and columns.*

#### *Vibration Control of Structures*

to upgrade the flexural capacity of RC piers used near-surface mounted (NSM) FRP rods. Flexural strengthening was achieved using NSM carbon FRP rods anchored into the footings. The piers were tested under static push/pull load cycles [17].

Another test was performed on RC piers in which three of the four piers were configured with different combinations of FRP rods and jackets. Using an analytical model with given load levels the net forces acting on the bridge pier were determined with strengthening techniques and modes of failure and confirming the effectiveness of the technology to strengthen RC piers [17].

The performance of highway bridges in earthquakes over the past several decades has been less than satisfactory because of poorly designed details and outdated design principles. In an effort to improve bridge performance in seismic events tests were conducted on the South Temple Bridge, built in 1963, during the I-15 reconstruction project in Salt Lake City. Five reinforced concrete bridge bents were tested, with three bents in as-is condition, two bents after a carbon fiber reinforced polymer (FRP) composite seismic retrofit, and one bent after a carbon FRP composite repair. The lessons learned from these tests were used in developing improved recommendations for the seismic retrofit design of bridge T-joints using FRP jackets. Using a nonlinear pushover static analysis of the as-is bent the performance-based design procedure includes determination of the column FRP jacket thickness for plastic hinge confinement, shear strengthening, and lap splice clamping. Using three elements the FRP jacket in the T-joints consists of diagonal FRP composite sheets for resisting diagonal tension, FRP composite sheets in the direction of the beam cap axis for shear strengthening and increased flexural capacity, and U-straps clamped at the column faces that go over the beam cap. The in-situ tests demonstrated that application of an external FRP composite seismic retrofit to concrete bridges with inferior seismic design details provides adequate ductility and seismic performance [17].

In a 2001 project in the Republic of Macedonia 19 slab and girder highway bridges were strengthened with CFRP plates to strengthen the bridges to NATO military load class 100 to compensate for induced vibrations from heavy military transports. The CFRP strengthening increased the bending moment and load capacity of the bridges by 60%. In 2019, non-destructive testing (NDT) was conducted on 12 of the 19 bridges to determine the condition of the CFRP plateconcrete bond. The results of the NDT field survey indicated 100% of the CFRP plates remain bonded to the bridge structural members 18 years after application. The use of CFRP material is a proven technology to reduce heavy traffic vibrations on RC highway bridges [18, 19].

#### **7. Conclusion**

The purpose of this chapter on vibration control is to examine the effects of wind, heavy traffic, and seismic vibrations on steel and RC highway bridges by providing an overview of bridge performance and failure under different types of induced vibration loading. Cases of bridge performance are presented for wind, heavy traffic, and seismic vibration loading. Bridge failures from induced vibrations are presented with analysis of why bridges failed. The effects of seismic vibrations on RC highway bridges, in particular from earthquakes in California, with extensive destruction of highway bridge networks, led to changes in bridge design. The lessons learned following extensive bridge damages from the 1971 Sylmar, 1989 Loma Prieta, and 1994 Northridge earthquakes, causing major damage and disruptions in the economy and highway systems in southern California, drove the California Seismic Advisory Board (SAB) to make significant changes in design

#### *Vibration Control in Bridges DOI: http://dx.doi.org/10.5772/intechopen.107501*

philosophy in structural engineering and the approach Caltrans uses in designing and constructing bridges. The major change was moving from established prescriptive criteria to developing performance-based seismic engineering (PBSE) concepts and methodologies. These changes have become standard in national structural engineering practices. Lessons learned from bridge failures from wind and heavy traffic loading vibrations have led to improved design codes and criteria, better construction methods, and improved materials and processes. While modern bridge design addresses vibrations for heavy traffic loading, the natural forces of wind and seismic events will always be a challenge for bridge engineers. The study and analysis of past bridge failures from induced vibrations provides lessons on how a bridge's structural configuration responds to the destructive forces of vibrations. Bridge engineers have made significant progress in designing for these forces. Today's highway and rail bridges meet high structural standards. The challenge going forward is to continue to improve bridge designs and construction to meet ever changing vibrational forces.

## **Conflict of interest**

The author declares he has no conflict of interest.

## **Author details**

Kenneth C. Crawford Institute for Bridge Reinforcement and Rehabilitation (IBRR), Bloomington, IN, USA

\*Address all correspondence to: ken.crawford@ibrr.org

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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#### **Chapter 2**
