FIGURE 1.43Howrah Bridge, Calcutta, India [Virola, 1969].The Quebec Bridge in Canada (Fig. 1.25) and the Firth of Forth Bridge in Scotland (Fig. 1.26) are two of the longest and most famous cantilever bridges. An unusual variation on this type of bridgea five-span continuous bridgewas built in 1901-1909 for the railroad at Queensboro over the East River, New York. This bridge consists of two unequal main spans (1182 and 984 ft), a middle 630-ft anchor span, and two shore spans (469 and 459 ft) [Tyrrell, 1911; Virola, 1969]. Designed by Gustav Lindenthal, its unusual feature is that each main span consists of two cantilever arms joined at their extremities without any suspended span, creating a suspension bridge-like appearance (Fig. 1.42) [Tyrrell, 191 l;Steinman and Watson, 1957;Smith, 1953; Virola, 1969].The worlds longest highway cantilever bridge is the Greater New Orleans Bridge, a 1575- ft span over the Mississippi at New Orleans, Louisiana, built in 1955-1958 [Virola, 1969]. Another great cantilever bridge is the 1500-ft span Howrah Bridge in Calcutta, India (Fig. 1.43), opened to traffic in February, 1943. It has an unusual featurethe roadway is suspended below the bottom chords rather than supported above by them, as is usually the case [Virola, 1969].1.3.3.7 Cable-stayed bridgesCable-stayed bridges represent the most innovative and dramatic development of the post-World War II period. These bridges are very competitive economically for medium and long spans. They can be built with girders of either steel or prestressed concrete. Cable-stayed bridges are unique in that the superstructure is supported (or hung) at several intermediate points by inclined cables, or stays, radiating from and continuous over the towers, instead of being supported from underneath by conventional piers or bents. Cable-stayed bridges are classified by the form of the cable arrangement, as shown in Fig. 1.44.As a structural system, cable-stayed bridges fill a gap between the deck type bridges, with the supporting girders installed underneath the bridge deck, and the suspension bridges. Similar in scheme to suspension bridges, cable-stayed bridges consist of three spanstwo side spans and the central main span. Two towers, or pylons, separate the side spans from the main span. The side spans may be flanked by one or more approach spans. However, in contrast with this general arrangement, cable-stayed bridges with only two spans and a central tower have also been built.Unlike suspension bridges, in which the superstructure loads are transmitted to the cables through vertical hangers, the loads in a cable-stayed bridge are transmittedFIGURE 1.44Classification of cable-stayed bridges by form [Fiege, 1966].FIGURE 1.45Shapes of towers used for cable-stayed bridges [Fiege, 1966].directly by the inclined stays, which connect the deck to the towers. Fig. 1.45 shows various shapes of towers used for cable-stayed bridges.Several cable-stayed bridges have been built around the world in the last forty years, mostly in Europe. Many cable-stayed bridges have been built in Germany, particularly over the Rhine and Elbe Rivers; most of these replace the many bridges destroyed in World War II and improve the highway transportation system. Development of cable- stayed bridges in various countries has been reported by several authors [Fiege, 1966; Thul, 1966; Taylor, 1969; Leonhardt and Zellner, 1970; Narouka, 1973], Podolny and Flemming [1972] and Kavanagh [19731 examine the historical development of cable- stayed bridges. A chronological history of the construction of cable-stayed bridges and the aesthetics of some of these bridges are presented by Billington and Nazmy [1990].FIGURE 1.46The Maracaibo Bridge, Venezuela [Smith, 1953],FIGURE 1.47Combination of simply supported and cantilever arrangements for the Maracaibo Bridge [Salvadori and Heller. 1975].The first modern cable-stayed bridge was built in 1955 at Stroemsund, Sweden (243, 600, and 243 ft74, 183, and 74 m), followed in 1957 by the 853-ft (260-m) main span North Bridge in Dsseldorf, Germany [Fiege, 1966; Leonhardt and Zell- ner, 1970; Podolny, 1974; Podolny and Scalzi, 1986]. Later, several other cable-stayed bridges were built in Europe. One of the most noteworthy examples of a cable-stayed bridge is the 135-span 5.4-mile Lake Maracaibo Bridge in Venezuela (Fig. 1.46), completed in 1962. It includes five 771-ft (235-m) prestressed-concrete cable-stayed girders with suspended spans, providing navigation openings. These main spans feature cantilevered stayed sections with intermediate beams simply supported at their tips (Fig. 1.47) [Morandi. 1961; Bridge, 1963; 1CJ, 1963: Podolny and Scalzi, 1986].Several cable-stayed bridges were built in the United States during the past 25 years. The first is a 36I-ft-long (72, 217, and 72 ft) pedestrian bridge located in Menomonee Falls, Wisconsin. Built about 1971, this 10-ft-wide bridge is supported on two W33 X 130 main steel girders [Woods, 1973], The first cable-stayed highway bridge in the United States, the Sitka Harbor Bridge (150, 450, and 150 ft), was built in 1972 in Alaska. Its total length is 1255 ft, including several 125-ft approach spans [ENR, 1972a; Gute 1973a,b]. It was followed by the construction of the Pasco- Kcnnewick Bridge (main span 981 ft) in the state of Washington, in 1978 [Grant, 1977], The Sunshine Skyway Bridge (main span 1200 ft) was built in Tampa, Florida, in 1986 [Garcia and Robison, 1986]. The Hale Boggs Memorial Bridge (main span 1222 ft) in Luling, Louisiana, was completed in 1983. The East Huntington Bridge (main span 900 ft) in East Huntington, West Virginia, was completed in 1985 [Grant, 1987],Several cable-stayed bridges with record-breaking spans were built around the world, mostly in the 1980s and later. See Appendix C (Table C.l) [Podolny, 1997]. Billington and Nazmy [1990] have provided schematic elevations of 84 of the worlds leading cable-stayed bridges constructed before 1987. Shanghais Yang Pu Bridge, a 1975-ft main span cable-stayed bridge, Chinas longest, was completed in 1993. Presently, the longest cable-stayed bridge is Frances 2808-ft (856-m) Pont de Normandie (the Normandy Bridge), with a main span of 2047 ft (624 m). It opened to traffic in January 1995. Except for the main span, which consists of orthotropic steel box girders, this entire bridge is built with 8700 psi high-performance concrete [PCA, 1995]. This innovative construction is referred to as longitudinally composite. Two other bridges of this type are Mexicos Tampico Bridge and Japans Ikuchi Bridge IRobinson, 1993], The Baytown cable-stayed bridge, in Texas (482, 1250, and 482 ft), completed in 1994, also has composite construction. With its 426-ft-high towers and two 78-ft-wide decks, this bridge has a record-setting 350,000 ft2 of deck area [Lovett and Warren, 1992], The longest cable-stayed bridgeunder construction and due to be completed in 1999is the Tatara Bridge in Ehime, Japan, having a 2920-ft main span. Figure 1.48 shows Indias longest cable-stayed bridge (597, 1499, and 597 ft), over Hoogly River, Calcutta, completed in 1993 [ENR, 1972b, 1975b, 1978b].The various arrangements of radiating cables (Fig. 1.44) and the imaginative forms and shapes of towers (Fig. 1.45) have made cable-stayed bridges one of the most aesthetically pleasing structures. Figure 1.49 shows the magnificent view of the stay ropes of the Friedrich Ebert Bridge, a 919-ft-main span cable-stayed bridge (394, 919, and 394 ft120,280, and 120 m) over the Rhine at Bonn, Germany [Leonhardt andZellner, 1970],Most cable-stayed bridges are stationary; however a movable 360-ft-span swing cable-stayed bridge with a swing radius of 180 ftperhaps the only one of its kind in the worldhas been built over the Sacramento River at Meridian, California.Several variations of cable-stayed bridge principles have been adopted for construction of other bridges. A bridge type similar in appearance to the cable-stayed bridge is the bridle chord type. This type of bridge is actually intermediate between the cable- stayed and the cable-suspended (suspension) bridges. Unlike the curved cables of aFIGURE 1.48Indias longest cable-stayed bridge, over Hoogly River, Calcutta.FIGURE 1.49llnef i?70]rPeS ^ FredrCh ^ Brid8e VCr the Rh"le' aI B(,nn- Germany [Leonhardt and74 DESIGN OF MODERN HIGHWAY BRIDGESsuspension bridge, in a bridle chord bridge the main cables are not continuous between the towers, but are anchored to the longitudinal girder in the main span. However, like a suspension bridge, it does have hangers along the length of the cables, which provide additional support for the deck. An example of such a bridge is the Ruhrort-Homberg Bridge over the Rhine, in Germany, as shown in Fig. 1.50 fKavanagh, 1972}.Another variation on the cable-stayed bridge is the bi-stayed bridge, in which the cable stays consist of both self-anchored and earth-anchored cables, and the entire midspan is supported by the stays. Figure 1.51(a) schematically compares the cable- stayed bridge to its bi-stayed variation. In the bi-stayed bridge system, the self-anchoredFIGURE 1.50Bridle chord bridge over the Rhine at Ruhrort-Homberg, Germany fKavanagh, 1972],FIGURE 1.51(a) Schematic comparison of cable-stayed and bi-stayed bridges [Muller and Lockwood, 1992];stays (hi) are located in the side spans of the bridge and also in the main span, where they are distributed over nearly the same distance from the pylon as they are in the side spans (al). The earth-anchored stays (h2) are longer and anchor into the deck over the remainder of the main span (a2). These earth-anchored stays bend over the pylon tops and anchor into a separate anchor block away from the extremity of the bridge; hence, they cause no further compression in the bridge deck. It is suggested that a bi-stayed bridge could feasibly support clear spans extending 10,000 feet [Muller and Lockwood, 1992]. The hybrid cable-stayed suspension bridge (Fig. 1.51 (ft)), the hybrid doublecantilever suspension bridge (Fig. 1.51(c)), and the spread-pylon cable-stayed bridge (Fig. 1.51 (c/)) are other variations of cable-stayed systems proposed for longer spans (see Sec. 1.3.3.8).Analysis and design of cable-stayed bridges is an advanced topic and is not covered in this text. Design guidelines for cable-stayed bridges are reported in Highway Focus [1973] and in ASCE [1977a, 1991], and a bibliography and data areFIGURE 1.51 (continued)(b) hybrid cable-stayed suspension bridge [Lin and Chow, 1991]; (c) hybrid double-cantilever suspension bridge [Lin and Chow, 1991]; (d) spread-pylon cable-stayed bridge [Starossek, 19961.presented in ASCE [1977b], Design and construction of cable-stayed bridges is presented by OConnor [1971], Kavanagh [1972], Podolny and Scalzi [1986|, and Heins and Firmage [1979], Methods of analyzing cable-stayed bridges are discussed by many researchers, such as Smith [1967], Tang [1971a, 1971b], Lazer [1972], and Lazeret al., [1972], Design, construction, and interesting features of a few cable-stayed bridges are presented by many authors, such as Simpson [1970], Thul [1966, 1972], Demers and Simonsen 11971], OConnor [1971], Narouka [1973], Podolny [1974], and Stahl and Christopher [1992], Prestressed concrete cable-stayed bridges are discussed by Leon- hardt 11987],1.3.3.8 Suspension bridgesSuspension bridges are recognized for spanning the longest distances and for their superior aesthetics. A cable could span the largest possible distance if it could carry just its own weight, but it would break under the smallest additional load. Assuming an optimal sag-to-span ratio of one-third to minimize the weight of the cable, it can be shown that a 200-ksi cable could span a distance of 17 miles [Salvadori and Heller, 1975], Since the actual cable spans must carry heavy imposed loads in addition to their own weights, the span limitation of cables is reduced to only a few thousand feet.The principle of a suspension bridge is very simple. It consists of four essential parts: the towers, the anchorages, the cables, and the deck. The deck, usually supported on stiffening trusses, is hung from the suspension cables. It consists of a central main span and is flanked on each side by a side span that is separated from the main span by towers. The ends of the suspension cables are secured at the anchorages, which are usually built of masonry or concrete.The roadway and the stiffening construction have local importance, but both may be wholly or partially destroyed without causing the collapse of the bridge. In all other types of bridge construction, the failure or buckling of a single truss member will precipitate the collapse of the entire structure. A suspension bridge is the safest type of construction in that local overloading or structural deficiency will not jeopardize the safety of the structure as a whole [Steinman and Watson, 1957, p. 331J.The theory and design of suspension bridges is discussed by many builders and researchers [Navier, 1823; Roebling, 1841, 1846, 1855; Barlow, 1858, 1860; Statics,1863a,b; Bender, 1872;DuBois, 1882;Melan, 1888, 1913; Mehrtens, 1900, 1908; Suspension, 1909; Johnson et al., 1910; Steinman, 1913, 1929, 1935; Martin, 1927; Hardesty and Wessman, 1938; Gronquist, 1941; Modjeski and Masters, 1941; Steinman and Watson, 1957; Selberg, 1954; Peery, 1954; Parcel and Moorman, 1955; Pugsley, 1968; OConnor, 1971; Kavanagh, 1972; Gimsing, 1983]. A very complete history of suspension bridges (up to 1940) in bibliographical form is provided by Jakkula [1941 ]. A brief description of the theory and history of suspension bridge design from 1823 to 1940 is presented by Buonopane and Billington [1993],Suspension bridges can be classified by the type of cable anchorage as either external or internal. When the cables are anchored to massive external anchorages, the suspension bridges are externally anchored (Fig. 1.52). They may, however, be self- anchored (internally anchored), suitable for short to moderate spans (400 to 1000 ft) where foundation conditions do not permit external anchorages [Kavanagh, 1972]. In this case, the cables are attached to the stiffening trusses at the outer ends of the sideFIGURE 1.52Externally anchored suspension bridge and terminology.FIGURE 1.53Self-anchored suspension bridge.spans that rest over the supports (Fig. 1.53). The vertical component of tension in the side span cable helps reduce the dead load reaction at the end support; the horizontal component of tension creates compression in the stiffening truss. The decks are usually supported by stiffening trusses made of steel, although variations have been used. In the Hudson Hope Bridge (192, 680, and 207 ft) over Peace River in British Columbia, Canada, the stiffening girder consists of 34 precast, prestressed concrete box girder units; each unit is 29 ft 6 in. wide and 4 ft 1 in. deep [Osipov, 1969],In some of the early suspension bridges built for the railroads, excessive deflection was a serious problem. To reduce these deflections, the German engineer Prof. F. Dischinger suggested adding inclined stays to the suspension cable [Dischinger, I949a,bj, but it was soon discovered that they were not very effective in reducing deflections of suspension bridges [Leonhardt and Zellner, 19701. In some suspension bridges, inclined stays (or secondary cable systems), in addition to the conventional vertical hangers, were incorporated to increase the torsional rigidity. Some examples of this approach are Roeblings Brooklyn Bridge in New York, Deer Isle Bridge in Maine, and the Cincinnati Bridge across the Ohio River ISteinman and Watson, 1957; Hopkins, 1970; Kavanagh, 1972; Buonopane and Billington. 1993J. For the same reason, inclined stays were added to the Rllets suspension bridge at Wheeling, West Virginia, when, after its collapse in 1854, it was rebuilt by Roebling [Hopkins, 1970]. In modern suspension bridges, additional inclined stays are generally not used, however. Figure 1.55 shows the San Marcos Bridge in El Salvador, which employs multiple inclined cables in the form of a grid or a network, known as a cable-truss concept [Kavanagh, 1972],The longest suspension bridge in the United States is the Verrazano Narrows Bridge in New York (1215,4260, and 1215 ft), completed in 1964, which outspans the Golden Gate Bridge (1125,4200, and 1125 ft), completed in 1937. The San Francisco-Oakland Bay Bridge (Fig. 1.56), completed in 1936, is a 1.95-mile-long double-deck twinFIGURE 1.54Salazar Bridge at Lisbon. Portugal, an example of a suspension and cable-stayed system: (a) Typical initial construction, for highway traffic only. (Only left half of the elevation is shown.) (b) Typical final construction, with cable stays, for highway and railroad traffic. (Only right half of the elevation is shown.) This bridge carries only highway traffic now. [Kavanagh, 1972],FIGURE 1.55San Marcos cable truss bridge, El Salvador [Kavanagh, 1972].FIGURE 1.56San Francisco-Oakland Bay Bridge, a twin suspension bridge [EERI, I990J.suspension bridge (1171,2310, and 1160ft; and 1160, 2310, and 1160 ft) [OConnor, 1971; Kavanagh, 1972; Virola, 1968]. The upper and lower decks each carry five lanes of traffic to the west and east, respectively. The lower deck was originally designed for trains. This bridge actually encompasses, in addition to the twin suspension structure, four shallow simple-span trusses on Yerba Buena Island, a long cantilever truss bridge, five deep simple-span trusses, fourteen shallow simple-span trusses, and a number of simple-span deck systems, covering a distance of 4.35 miles between San Francisco and Oakland, California.The present recordholder for the longest suspension bridge is the Akashi-Kaikyo Bridge (main span 6529 ft, total length 12,828 ft or 3910 m) linking Akashi City in Hyogo Prefecture to Awaji Island, Japan [CE, 1975; Stahl and Christopher, 1992; CE. 1992; Brown, 1993; Podolny, 1994]. It has been designed for such engineering challenges as 80-mph wind loads and a seismic design factor of 8.5 on the Richter scale [CE, 1992]. This bridge outspans the Humber River Suspension Bridge (920, 4626, and 1739 ft) on the Humber River estuary, 160 miles north of London. |ENR, 1975b, 1976, 1978c]. Completed in 1981 after 8 years, the Humber Bridge, unlike the most modern suspension bridges, has hangers that are inclined in a zigzag patterna unique feature similar to that of the Severn Bridge (1000, 3240, 1000 ft) completed in 1966, also in England [Brown, 1993].Conventional suspension bridges consist of two parallel cables as the main loadcarrying element. A recent development is a suspension bridge with a single cable as the main load-carrying element. An example of this is the Hokko Bridge in Japan, a single-cable, self-anchored suspension bridge. With a main span of 984 ft (300 m) and side spans of 394 ft (120 m), it carries a four-lane highway from the Hokko Wharves to the Northern District island of Osakas north port. Loads from the bridge superstructure are transferred to the main cable through a continuous pattern of diagonal suspenders [Billington, 1990].In summary, both cable-stayed and suspension bridges can be characterized as cable (or cable-supported) bridges; the cable profile marks the distinction between the two types. In cable-suspended bridges, commonly referred to as suspension bridges, the main cables are curved and continuous between the towers. The deck and other vertical loading is suspended from these cables at relatively short intervals. Being relatively flexible, the main cables develop funicular shape, which is a function of the magnitude and the position of loading. On the other hand, in cable-stayed bridges, the cables are straight and extend from one tower, and they are connected directly to the deck at discrete points. Being taut, they furnish relatively inflexible supports along the span at several points, and they provide the bridge with relatively greater stiffness than that achievable in suspension bridges. Both types rely on very-high-strength steel cables or tendons. Recent research has led to the development of carbon-fiber-reinforced plastic (CFRP composite) cables that compete with steel in strength and provide excellent corrosion resistance, very high specific strength, and an equivalent elastic modulus. Such cables were proposed for use in a cable-stayed bridge under construction in 1996 in Winterthur, Switzerland [Meier and Meier, 1996],Bridging increasingly longer spans continues to be a challenge for bridge builders, and it remains in the domain of cable bridges. This is possible because high-strength tensile elements (cables) are used. Accordingly, both cable-stayed and suspension bridges provide the solutions needed for long-span bridges. Since modern cable-stayed bridges evolved much later than suspension bridges did, suspension bridges were historically preferred over cable-stayed types because their performance had been proven and because builders had gained significantly greater knowledge and experience with their use. However, this has now begun to change, and cable-stayed bridges are considered feasible for long spans traditionally considered the domain of suspension bridges [Leonhardt and Zellner, 1972], Also, it is believed that the greater stiffness provided by cable-stayed systems makes their limit span less susceptible to wind-induced vibrations, compared to the limit span of suspension bridges. Research continues to find new forms of towers (for suspension bridges) and pylons (for cable-stayed bridges), and more efficient cable arrangements to span yet longer spans. Some examples of these new approaches are the hybrid cable-stayed suspension bridge system (Fig. 1.51(6)), the hybrid double-cantilever suspension bridge system (Fig. 1.51(c)) [Lin and Chow, 1991], and the spread-pylon cable-stayed bridge system (Fig. 1.51(r/)) [Starossek, 1996], These systems promise to be economical for very large spans (in the 16,000-ft range). Discussion on the challenges posed by long-span bridge construction can be found in the literature [Mallick, 1983; Gimsing, 1988; Lin and Chow, 1991; Starossek, 19961.Deciding on the feasibility of a particular bridge type for long spans is difficult, and there are no rules or criteria that provide a quick answer. While the cost is a major factor that may dictate the choice between a suspension bridge and a cable-stayed bridge, there are many other factors that may influence the selection process. These include aesthetics, traffic capacity and the need for future widening, structural stability, foundation conditions, erection procedures, underclearance requirements, and general civic requirements with respect to location, financing, and community values [Kavanagh, 1972],Table C.2 (see Appendix C) gives a chronology of the worlds major suspension bridges [Podolny, 1997J.1.3.4 Classification by Span TypesBridges can be classified by the type of span used with respect to the support conditions, namely, simple or continuous. Short-span bridges are built as single spans having simple supports. In medium- or long-span bridges, depending on the site conditions, multiple simple spans can be built to span the distance. Such a bridge would consist of two end abutments and several piers as intermediate supports. As discussed earlier, distances beyond the short-span range can always be spanned by arch, cable-stayed, or suspension bridges. However, the site or the economic conditions may dictate building a multispan bridge instead.Figure 1.40 shows schematically the behavior of a continuous beam under loads. In a simple beam, the moment is positive and maximum at the midspan (under gravity loads). In a continuous beam, the positive moments are considerably reduced in the midspan portion of the beam, but negative moments are created at the supports. These negative moments are much higher than the positive moments at the midspan, although they are still considerably smaller than the positive moment in a simple beam. Because of these larger negative moments, theoretically a larger girder cross section is required at the supports than at the midspan. Although this can be accomplished by providing a haunch at the supports (i.e., a deeper section than at the midspan), this alternative is not always economical. For spans under about 175 ft, prismatic girders may be more economical than haunched girders. This is because the cost of fabricating the haunches and the required splices to effect savings in the weight of steel may exceed the cost of additional steel required for a prismatic girder for the entire continuous span. The ends of a continuous beam are usually simply supported.Advantages of continuous spans over simple spans include reduced weight because smaller beam cross sections are required, and greater stiffness, smaller deflections, and fewer bearings and expansion joints are needed. Continuous spans also offer redundancy and greater overload capacity than simple spans.Continuity in bridges is obtained in a variety of ways. As Fig. 1.37 shows, the general practice is to provide a suspended span to be supported by cantilever spans, which are simply the overhangs of simple spans called anchor spans. This scheme can be achieved in many kinds of bridges, such as plate girder bridges, truss bridges, box girder bridges, cantilever bridges, and cable-stayed bridges. Figures 1.46 and 1.47 show the scheme of suspended spans in the cable-stayed bridge over Lake Maracaibo, Venezuela.1.3.5 Classification by Load Path CharacteristicsFrom the perspective of load path (or load distribution) in the bridge superstructure, bridges can be classified as one-dimensional or two-dimensional systems. A one- dimensional system is one in which the load is distributed in one direction only, such as a slab bridge, in which bending occurs in only one direction, about a horizontal axis perpendicular to the longitudinal axis of the bridge. However, in a slab-stringer bridge, the bending of the slab takes place in two mutually perpendicular directions; such a system is classified as a two-dimensional system, which is much more efficient and economical than a one-dimensional system.The superstructure of a bridge can also be constructed as a three-dimensional system, which may be more efficient than one- or two-dimensional systems. Essentially, such a system consists of a slab (reinforced concrete or, preferably, prestressed concrete) supported on flat, skeletal, single- or double-layer, steel tetrahedrons (pyramidshaped trusses), resulting in a three-dimensional plane grid. These tetrahedrons are arranged in a horizontal plane in two parallel grids that are interconnected by vertical or inclined web members. The external loads are distributed among the various members of the tetrahedrons omnidirectionally in space. Such a system, shown in Fig. 1.57, was suggested by Taly in 1976 and is reported in the literature [Taly and Gan- gaRao, 1978; GangaRao and Taly, 1977, 1978]. Taly (1976] presents a comprehensive study of various patented steel tetrahedrons and of a prestressed concrete slab that can be used to build such a bridge, along with a stress analysis determined by using NASTRAN (computer program). The experimental continuous three-span (118, 131, and 118 ft) Roize Bridge over the Roize River near Grenoble, France, completed in December 1990, is based on a similar concept. The precast, pretensioned deck elements of this bridge were made from 11,500-psi concrete, although only 8700 psi was used for the design [Muller and Lockwood, 1992; Montens and OHagon, 1992; Muller. 1993],