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86-496: The McKinley Bridge is a steel truss bridge across the Mississippi River . It connects northern portions of the city of St. Louis, Missouri with Venice, Illinois . It opened in 1910 and was taken out of service on October 30, 2001. The bridge was reopened for pedestrian and bicyclists on November 17, 2007 with a grand re-opening celebration. Since December 2007, McKinley has been open to vehicular traffic as well. It

172-470: A Parker truss or Pratt truss than a true arch . In the Brown truss all vertical elements are under tension, with exception of the end posts. This type of truss is particularly suited for timber structures that use iron rods as tension members. See Lenticular truss below. This combines an arch with a truss to form a structure both strong and rigid. Most trusses have the lower chord under tension and

258-422: A closet rod sagging under the weight of clothes on clothes hangers is an example of a beam experiencing bending. On the other hand, a shell is a structure of any geometric form where the length and the width are of the same order of magnitude but the thickness of the structure (known as the 'wall') is considerably smaller. A large diameter, but thin-walled, short tube supported at its ends and loaded laterally

344-513: A couple or moment as they are equal in magnitude and opposite in direction. This bending moment resists the sagging deformation characteristic of a beam experiencing bending. The stress distribution in a beam can be predicted quite accurately when some simplifying assumptions are used. In the Euler–Bernoulli theory of slender beams, a major assumption is that 'plane sections remain plane'. In other words, any deformation due to shear across

430-550: A Parker truss vary from near vertical in the center of the span to diagonal near each end, similar to a Warren truss. George H. Pegram , while the chief engineer of Edge Moor Iron Company in Wilmington, Delaware , patented this truss design in 1885. The Pegram truss consists of a Parker type design with the vertical posts leaning towards the center at an angle between 60 and 75°. The variable post angle and constant chord length allowed steel in existing bridges to be recycled into

516-599: A common truss design during this time, with their arched top chords. Companies like the Massillon Bridge Company of Massillon, Ohio , and the King Bridge Company of Cleveland , became well-known, as they marketed their designs to cities and townships. The bowstring truss design fell out of favor due to a lack of durability, and gave way to the Pratt truss design, which was stronger. Again,

602-435: A conventional truss into place or by building it in place using a "traveling support". In another method of construction, one outboard half of each balanced truss is built upon temporary falsework. When the outboard halves are completed and anchored the inboard halves may then be constructed and the center section completed as described above. The Fink truss was designed by Albert Fink of Germany in 1854. This type of bridge

688-464: A length totaling 4,162.5 ft (1,268.7 m). The Bridge reopened to pedestrians and bicycles on November 17, 2007 and was fully reopened to traffic on December 17, 2007. Truss bridge The nature of a truss allows the analysis of its structure using a few assumptions and the application of Newton's laws of motion according to the branch of physics known as statics . For purposes of analysis, trusses are assumed to be pin jointed where

774-481: A limited number of truss bridges were built. The truss may carry its roadbed on top, in the middle, or at the bottom of the truss. Bridges with the roadbed at the top or the bottom are the most common as this allows both the top and bottom to be stiffened, forming a box truss . When the roadbed is atop the truss, it is a deck truss; an example of this was the I-35W Mississippi River bridge . When

860-477: A lower chord (functioning as a suspension cable) that curves down and then up to meet at the same end points. Where the arches extend above and below the roadbed, it is called a lenticular pony truss bridge . The Pauli truss bridge is a specific variant of the lenticular truss, but the terms are not interchangeable. One type of lenticular truss consists of arcuate upper compression chords and lower eyebar chain tension links. Brunel 's Royal Albert Bridge over

946-472: A new alignment took the route over Chain of Rocks Bridge in order to avoid leading traffic directly into the downtown St. Louis area. The Chain of Rocks Bridge was famous for having a curve in the middle. It is now open to pedestrians. The bridge was owned by the city of Venice, Illinois and operated as a toll bridge. After decades of disrepair due to the lack of toll revenues, the McKinley Bridge

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1032-789: A new span using the Pegram truss design. This design also facilitated reassembly and permitted a bridge to be adjusted to fit different span lengths. There are twelve known remaining Pegram span bridges in the United States with seven in Idaho , two in Kansas , and one each in California , Washington , and Utah . The Pennsylvania (Petit) truss is a variation on the Pratt truss . The Pratt truss includes braced diagonal members in all panels;

1118-459: A pin-jointed structure, one where the only forces on the truss members are tension or compression, not bending. This is used in the teaching of statics, by the building of model bridges from spaghetti . Spaghetti is brittle and although it can carry a modest tension force, it breaks easily if bent. A model spaghetti bridge thus demonstrates the use of a truss structure to produce a usefully strong complete structure from individually weak elements. In

1204-443: A transverse load is applied on it. In the quasi-static case, the amount of bending deflection and the stresses that develop are assumed not to change over time. In a horizontal beam supported at the ends and loaded downwards in the middle, the material at the over-side of the beam is compressed while the material at the underside is stretched. There are two forms of internal stresses caused by lateral loads: These last two forces form

1290-545: A variant of the lenticular truss, "with the top chord carefully shaped so that it has a constant force along the entire length of the truss." It is named after Friedrich Augustus von Pauli  [ de ] , whose 1857 railway bridge (the Großhesseloher Brücke  [ de ] ) spanned the Isar near Munich . ( See also Grosshesselohe Isartal station .) The term Pauli truss is not interchangeable with

1376-407: Is where J = m I A {\displaystyle J={\tfrac {mI}{A}}} is the polar moment of inertia of the cross-section, m = ρ A {\displaystyle m=\rho A} is the mass per unit length of the beam, ρ {\displaystyle \rho } is the density of the beam, A {\displaystyle A}

1462-451: Is where E {\displaystyle E} is the Young's modulus, I {\displaystyle I} is the area moment of inertia of the cross-section, w ( x , t ) {\displaystyle w(x,t)} is the deflection of the neutral axis of the beam, and m {\displaystyle m} is mass per unit length of the beam. For

1548-395: Is where I {\displaystyle I} is the area moment of inertia of the cross-section, A {\displaystyle A} is the cross-sectional area, G {\displaystyle G} is the shear modulus , k {\displaystyle k} is a shear correction factor , and q ( x ) {\displaystyle q(x)}

1634-700: Is a Pratt truss design with a polygonal upper chord. A "camelback" is a subset of the Parker type, where the upper chord consists of exactly five segments. An example of a Parker truss is the Traffic Bridge in Saskatoon , Canada. An example of a camelback truss is the Woolsey Bridge near Woolsey, Arkansas . Designed and patented in 1872 by Reuben Partridge , after local bridge designs proved ineffective against road traffic and heavy rains. It became

1720-519: Is a hybrid between a Warren truss and a double-intersection Pratt truss. Invented in 1863 by Simeon S. Post, it is occasionally referred to as a Post patent truss although he never received a patent for it. The Ponakin Bridge and the Bell Ford Bridge are two examples of this truss. A Pratt truss includes vertical members and diagonals that slope down towards the center, the opposite of

1806-559: Is accessible from Illinois Route 3 in Illinois and from the intersection of Salisbury and North 9th Street in the city of St. Louis. The bridge carried both railroad and vehicular traffic across the Mississippi River for decades. By 1978, the railroad line over the span was closed, and an additional set of lanes was opened for vehicles in the inner roadway. The McKinley Bridge was the first alignment of U.S. Route 66 across

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1892-430: Is an applied transverse load. For materials with Poisson's ratios ( ν {\displaystyle \nu } ) close to 0.3, the shear correction factor for a rectangular cross-section is approximately The rotation ( φ ( x ) {\displaystyle \varphi (x)} ) of the normal is described by the equation The bending moment ( M {\displaystyle M} ) and

1978-430: Is an example of a shell experiencing bending. In the absence of a qualifier, the term bending is ambiguous because bending can occur locally in all objects. Therefore, to make the usage of the term more precise, engineers refer to a specific object such as; the bending of rods , the bending of beams , the bending of plates , the bending of shells and so on. A beam deforms and stresses develop inside it when

2064-436: Is distributed along the length of the beam) The dynamic bending of beams, also known as flexural vibrations of beams, was first investigated by Daniel Bernoulli in the late 18th century. Bernoulli's equation of motion of a vibrating beam tended to overestimate the natural frequencies of beams and was improved marginally by Rayleigh in 1877 by the addition of a mid-plane rotation. In 1921 Stephen Timoshenko improved

2150-832: Is named after the K formed in each panel by the vertical member and two oblique members. Examples include the Südbrücke rail bridge over the River Rhine, Mainz, Germany, the bridge on I-895 (Baltimore Harbor Tunnel Thruway) in Baltimore, Maryland, the Long–Allen Bridge in Morgan City, Louisiana (Morgan City Bridge) with three 600-foot-long spans, and the Wax Lake Outlet bridge in Calumet, Louisiana One of

2236-466: Is only valid if the cross-section is symmetrical. For homogeneous beams with asymmetrical sections, the maximum bending stress in the beam is given by where y , z {\displaystyle y,z} are the coordinates of a point on the cross section at which the stress is to be determined as shown to the right, M y {\displaystyle M_{y}} and M z {\displaystyle M_{z}} are

2322-570: Is partly based on the Howe truss . The first Allan truss was completed on 13 August 1894 over Glennies Creek at Camberwell, New South Wales and the last Allan truss bridge was built over Mill Creek near Wisemans Ferry in 1929. Completed in March 1895, the Tharwa Bridge located at Tharwa, Australian Capital Territory , was the second Allan truss bridge to be built, the oldest surviving bridge in

2408-426: Is possible to calculate the bending stress at any point on the beam cross section regardless of moment orientation or cross-sectional shape. Note that M y , M z , I y , I z , I y z {\displaystyle M_{y},M_{z},I_{y},I_{z},I_{yz}} do not change from one point to another on the cross section. For large deformations of

2494-695: Is practical for use with spans up to 250 feet (76 m) and was a common configuration for railroad bridges as truss bridges moved from wood to metal. They are statically determinate bridges, which lend themselves well to long spans. They were common in the United States between 1844 and the early 20th century. Examples of Pratt truss bridges are the Governor's Bridge in Maryland ; the Hayden RR Bridge in Springfield, Oregon , built in 1882;

2580-457: Is required where rigid joints impose significant bending loads upon the elements, as in a Vierendeel truss . In the bridge illustrated in the infobox at the top, vertical members are in tension, lower horizontal members in tension, shear , and bending, outer diagonal and top members are in compression, while the inner diagonals are in tension. The central vertical member stabilizes the upper compression member, preventing it from buckling . If

2666-407: Is supported only at the ends and is fully independent of any adjacent spans. Each span must fully support the weight of any vehicles traveling over it (the live load ). In contrast, a continuous truss functions as a single rigid structure over multiple supports. This means that the live load on one span is partially supported by the other spans, and consequently it is possible to use less material in

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2752-525: Is the Victoria Bridge on Prince Street, Picton, New South Wales . Also constructed of ironbark, the bridge is still in use today for pedestrian and light traffic. The Bailey truss was designed by the British in 1940–1941 for military uses during World War II. A short selection of prefabricated modular components could be easily and speedily combined on land in various configurations to adapt to

2838-406: Is the area moment of inertia of the cross-section, and M {\displaystyle M} is the internal bending moment in the beam. If, in addition, the beam is homogeneous along its length as well, and not tapered (i.e. constant cross section), and deflects under an applied transverse load q ( x ) {\displaystyle q(x)} , it can be shown that: This

2924-536: Is the Euler–Bernoulli equation for beam bending. After a solution for the displacement of the beam has been obtained, the bending moment ( M {\displaystyle M} ) and shear force ( Q {\displaystyle Q} ) in the beam can be calculated using the relations Simple beam bending is often analyzed with the Euler–Bernoulli beam equation. The conditions for using simple bending theory are: Compressive and tensile forces develop in

3010-466: Is the cross-sectional area, G {\displaystyle G} is the shear modulus, and k {\displaystyle k} is a shear correction factor . For materials with Poisson's ratios ( ν {\displaystyle \nu } ) close to 0.3, the shear correction factor are approximately For free, harmonic vibrations the Timoshenko–Rayleigh equations take

3096-486: Is the neutral axis. Because of this area with no stress and the adjacent areas with low stress, using uniform cross section beams in bending is not a particularly efficient means of supporting a load as it does not use the full capacity of the beam until it is on the brink of collapse. Wide-flange beams ( Ɪ-beams ) and truss girders effectively address this inefficiency as they minimize the amount of material in this under-stressed region. The classic formula for determining

3182-770: The Australian Capital Territory and the oldest, longest continuously used Allan truss bridge. Completed in November 1895, the Hampden Bridge in Wagga Wagga, New South Wales , Australia, the first of the Allan truss bridges with overhead bracing, was originally designed as a steel bridge but was constructed with timber to reduce cost. In his design, Allan used Australian ironbark for its strength. A similar bridge also designed by Percy Allen

3268-621: The Dearborn River High Bridge near Augusta, Montana, built in 1897; and the Fair Oaks Bridge in Fair Oaks, California , built 1907–09. The Scenic Bridge near Tarkio, Montana , is an example of a Pratt deck truss bridge, where the roadway is on top of the truss. The queenpost truss , sometimes called "queen post" or queenspost, is similar to a king post truss in that the outer supports are angled towards

3354-1316: The Fort Wayne Street Bridge in Goshen, Indiana , the Schell Bridge in Northfield, Massachusetts , the Inclined Plane Bridge in Johnstown, Pennsylvania , the Easton–Phillipsburg Toll Bridge in Easton, Pennsylvania , the Connecticut River Bridge in Brattleboro, Vermont , the Metropolis Bridge in Metropolis, Illinois , and the Healdsburg Memorial Bridge in Healdsburg, California . A Post truss

3440-445: The Howe truss . The interior diagonals are under tension under balanced loading and vertical elements under compression. If pure tension elements (such as eyebars ) are used in the diagonals, then crossing elements may be needed near the center to accept concentrated live loads as they traverse the span. It can be subdivided, creating Y- and K-shaped patterns. The Pratt truss was invented in 1844 by Thomas and Caleb Pratt. This truss

3526-481: The River Tamar between Devon and Cornwall uses a single tubular upper chord. As the horizontal tension and compression forces are balanced these horizontal forces are not transferred to the supporting pylons (as is the case with most arch types). This in turn enables the truss to be fabricated on the ground and then to be raised by jacking as supporting masonry pylons are constructed. This truss has been used in

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3612-499: The United States , because wood was in abundance, early truss bridges would typically use carefully fitted timbers for members taking compression and iron rods for tension members , usually constructed as a covered bridge to protect the structure. In 1820, a simple form of truss, Town's lattice truss , was patented, and had the advantage of requiring neither high labor skills nor much metal. Few iron truss bridges were built in

3698-482: The Mississippi River to St. Louis from E. St. Louis, Illinois in 1910, the designer of the bridge was Polish-American engineer Ralph Modjeski . It was constructed by Missouri Valley Bridge & Iron Co . and Pennsylvania Steel Co . When the US Highway System was instituted in 1926, the McKinley Bridge then carried auto traffic on the famous Route 66 across the Mississippi River for four years until

3784-548: The Mississippi. It is commonly assumed that the bridge was named for President William McKinley ; but in reality, it was named for the builder, William B. McKinley , chief executive of the Illinois Traction System interurban electric railway, which accessed St. Louis via the bridge. The current alignment of the bridge carries two lanes of traffic on the inner lanes. The outer lane on the north side of

3870-685: The Pennsylvania truss adds to this design half-length struts or ties in the top, bottom, or both parts of the panels. It is named after the Pennsylvania Railroad , which pioneered this design. It was once used for hundreds of bridges in the United States, but fell out of favor in the 1930s and very few examples of this design remain. Examples of this truss type include the Lower Trenton Bridge in Trenton, New Jersey ,

3956-471: The United States before 1850. Truss bridges became a common type of bridge built from the 1870s through the 1930s. Examples of these bridges still remain across the US, but their numbers are dropping rapidly as they are demolished and replaced with new structures. As metal slowly started to replace timber, wrought iron bridges in the US started being built on a large scale in the 1870s. Bowstring truss bridges were

4042-461: The availability of machinery, and the cost of labor. In other cases, the appearance of the structure may take on greater importance and so influence the design decisions beyond mere matters of economics. Modern materials such as prestressed concrete and fabrication methods, such as automated welding , and the changing price of steel relative to that of labor have significantly influenced the design of modern bridges. A pure truss can be represented as

4128-406: The behavior of a slender structural element subjected to an external load applied perpendicularly to a longitudinal axis of the element. The structural element is assumed to be such that at least one of its dimensions is a small fraction, typically 1/10 or less, of the other two. When the length is considerably longer than the width and the thickness, the element is called a beam . For example,

4214-407: The bending moments about the y and z centroid axes, I y {\displaystyle I_{y}} and I z {\displaystyle I_{z}} are the second moments of area (distinct from moments of inertia) about the y and z axes, and I y z {\displaystyle I_{yz}} is the product of moments of area . Using this equation it

4300-414: The bending stress in a beam under simple bending is: where The equation σ = M y I x {\displaystyle \sigma ={\tfrac {My}{I_{x}}}} is valid only when the stress at the extreme fiber (i.e., the portion of the beam farthest from the neutral axis) is below the yield stress of the material from which it is constructed. At higher loadings

4386-583: The body, the stress in the cross-section is calculated using an extended version of this formula. First the following assumptions must be made: Large bending considerations should be implemented when the bending radius ρ {\displaystyle \rho } is smaller than ten section heights h: With those assumptions the stress in large bending is calculated as: where When bending radius ρ {\displaystyle \rho } approaches infinity and y ≪ ρ {\displaystyle y\ll \rho } ,

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4472-713: The bridge companies marketed their designs, with the Wrought Iron Bridge Company in the lead. As the 1880s and 1890s progressed, steel began to replace wrought iron as the preferred material. Other truss designs were used during this time, including the camel-back. By the 1910s, many states developed standard plan truss bridges, including steel Warren pony truss bridges. In the 1920s and 1930s, Pennsylvania and several states continued to build steel truss bridges, using massive steel through-truss bridges for long spans. Other states, such as Michigan , used standard plan concrete girder and beam bridges, and only

4558-406: The bridge deck, they are susceptible to being hit by overheight loads when used on highways. The I-5 Skagit River bridge collapsed after such a strike; before the collapse, similar incidents had been common and had necessitated frequent repairs. Truss bridges consisting of more than one span may be either a continuous truss or a series of simple trusses. In the simple truss design, each span

4644-428: The bridge from the city of Venice. Rehabilitation began in 2004 and the original plans for the repairs anticipated a re-opening in late 2005. However, the date was pushed back due to the addition of The Great Rivers Greenway Bikeway tie-in. The rehabilitated McKinley Bridge consists of the three original river truss spans (Spans 26-29, 519 ft (158 m) long each) and thirty-three steel plate girder spans, with

4730-545: The bridge will become an exclusive service lane, while the outer lane on the south side of the bridge will become a sidewalk and bike path. It is expected to carry 14,000 vehicles across the river daily, but total traffic across the river increased in 2014 by 7.4% over 2013 levels, and in April 2014, it was estimated that 17,000 vehicles use it daily. Built by the Illinois Traction electric interurban railroad to cross

4816-516: The center of the structure. The primary difference is the horizontal extension at the center which relies on beam action to provide mechanical stability. This truss style is only suitable for relatively short spans. The Smith truss , patented by Robert W Smith on July 16, 1867, has mostly diagonal criss-crossed supports. Smith's company used many variations of this pattern in the wooden covered bridges it built. Bending In applied mechanics , bending (also known as flexure ) characterizes

4902-732: The center, the opposite of the Pratt truss . In contrast to the Pratt truss, the diagonal web members are in compression and the vertical web members are in tension. Few of these bridges remain standing. Examples include Jay Bridge in Jay, New York ; McConnell's Mill Covered Bridge in Slippery Rock Township, Lawrence County, Pennsylvania ; Sandy Creek Covered Bridge in Jefferson County, Missouri ; and Westham Island Bridge in Delta, British Columbia , Canada. The K-truss

4988-497: The center. Many cantilever bridges, like the Quebec Bridge shown below, have two cantilever spans supporting a simple truss in the center. The bridge would remain standing if the simple truss section were removed. Bridges are the most widely known examples of truss use. There are many types, some of them dating back hundreds of years. Below are some of the more common designs. The Allan truss , designed by Percy Allan ,

5074-414: The compression members and to control deflection. It is mainly used for rail bridges, showing off a simple and very strong design. In the Pratt truss the intersection of the verticals and the lower horizontal tension members are used to anchor the supports for the short-span girders under the tracks (among other things). With the Baltimore truss, there are almost twice as many points for this to happen because

5160-600: The construction of a stadium, with the upper chords of parallel trusses supporting a roof that may be rolled back. The Smithfield Street Bridge in Pittsburgh, Pennsylvania , is another example of this type. An example of a lenticular pony truss bridge that uses regular spans of iron is the Turn-of-River Bridge designed and manufactured by the Berlin Iron Bridge Co. The Pauli truss is

5246-441: The direction of the beam axis under bending loads. These forces induce stresses on the beam. The maximum compressive stress is found at the uppermost edge of the beam while the maximum tensile stress is located at the lower edge of the beam. Since the stresses between these two opposing maxima vary linearly , there therefore exists a point on the linear path between them where there is no bending stress. The locus of these points

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5332-459: The dynamic Euler–Bernoulli beam theory by including the effect of rotational inertia of the cross-section of the beam. Timoshenko improved upon that theory in 1922 by adding the effect of shear into the beam equation. Shear deformations of the normal to the mid-surface of the beam are allowed in the Timoshenko–Rayleigh theory. The equation for the bending of a linear elastic, isotropic, homogeneous beam of constant cross-section under these assumptions

5418-484: The earliest examples is the Old Blenheim Bridge , which with a span of 210 feet (64 m) and a total length of 232 feet (71 m) long was the second-longest covered bridge in the United States, until its destruction from flooding in 2011. The Busching bridge, often erroneously used as an example of a Long truss, is an example of a Howe truss, as the verticals are metal rods. A Parker truss bridge

5504-461: The following are true: In this case, the equation describing beam deflection ( w {\displaystyle w} ) can be approximated as: where the second derivative of its deflected shape with respect to x {\displaystyle x} is interpreted as its curvature, E {\displaystyle E} is the Young's modulus , I {\displaystyle I}

5590-417: The form This equation can be solved by noting that all the derivatives of w {\displaystyle w} must have the same form to cancel out and hence as solution of the form e k x {\displaystyle e^{kx}} may be expected. This observation leads to the characteristic equation The solutions of this quartic equation are where The general solution of

5676-412: The needs at the site and allow rapid deployment of completed trusses. In the image, note the use of pairs of doubled trusses to adapt to the span and load requirements. In other applications the trusses may be stacked vertically, and doubled as necessary. The Baltimore truss is a subclass of the Pratt truss. A Baltimore truss has additional bracing in the lower section of the truss to prevent buckling in

5762-522: The original formula is back: In 1921, Timoshenko improved upon the Euler–Bernoulli theory of beams by adding the effect of shear into the beam equation. The kinematic assumptions of the Timoshenko theory are: However, normals to the axis are not required to remain perpendicular to the axis after deformation. The equation for the quasistatic bending of a linear elastic, isotropic, homogeneous beam of constant cross-section beam under these assumptions

5848-424: The section is not accounted for (no shear deformation). Also, this linear distribution is only applicable if the maximum stress is less than the yield stress of the material. For stresses that exceed yield, refer to article plastic bending . At yield, the maximum stress experienced in the section (at the furthest points from the neutral axis of the beam) is defined as the flexural strength . Consider beams where

5934-445: The shear force ( Q {\displaystyle Q} ) are given by According to Euler–Bernoulli, Timoshenko or other bending theories, the beams on elastic foundations can be explained. In some applications such as rail tracks, foundation of buildings and machines, ships on water, roots of plants etc., the beam subjected to loads is supported on continuous elastic foundations (i.e. the continuous reactions due to external loading

6020-574: The short verticals will also be used to anchor the supports. Thus the short-span girders can be made lighter because their span is shorter. A good example of the Baltimore truss is the Amtrak Old Saybrook – Old Lyme Bridge in Connecticut , United States. The Bollman Truss Railroad Bridge at Savage, Maryland , United States is the only surviving example of a revolutionary design in the history of American bridge engineering. The type

6106-451: The simplest truss styles to implement, the king post consists of two angled supports leaning into a common vertical support. This type of bridge uses a substantial number of lightweight elements, easing the task of construction. Truss elements are usually of wood, iron, or steel. A lenticular truss bridge includes a lens-shape truss, with trusses between an upper chord functioning as an arch that curves up and then down to end points, and

6192-730: The situation where there is no transverse load on the beam, the bending equation takes the form Free, harmonic vibrations of the beam can then be expressed as and the bending equation can be written as The general solution of the above equation is where A 1 , A 2 , A 3 , A 4 {\displaystyle A_{1},A_{2},A_{3},A_{4}} are constants and β := ( m E I   ω 2 ) 1 / 4 {\displaystyle \beta :=\left({\cfrac {m}{EI}}~\omega ^{2}\right)^{1/4}} In 1877, Rayleigh proposed an improvement to

6278-454: The standard for covered bridges built in central Ohio in the late 1800s and early 1900s. The Pegram truss is a hybrid between the Warren and Parker trusses where the upper chords are all of equal length and the lower chords are longer than the corresponding upper chord. Because of the difference in upper and lower chord length, each panel is not square. The members which would be vertical in

6364-464: The straight components meet, meaning that taken alone, every joint on the structure is functionally considered to be a flexible joint as opposed to a rigid joint with the strength to maintain its shape, and the resulting shape and strength of the structure are only maintained by the interlocking of the components. This assumption means that members of the truss (chords, verticals, and diagonals) will act only in tension or compression. A more complex analysis

6450-411: The stress distribution becomes non-linear, and ductile materials will eventually enter a plastic hinge state where the magnitude of the stress is equal to the yield stress everywhere in the beam, with a discontinuity at the neutral axis where the stress changes from tensile to compressive. This plastic hinge state is typically used as a limit state in the design of steel structures. The equation above

6536-481: The term lenticular truss and, according to Thomas Boothby, the casual use of the term has clouded the literature. The Long truss was designed by Stephen H. Long in 1830. The design resembles a Howe truss , but is entirely made of wood instead of a combination of wood and metal. The longest surviving example is the Eldean Covered Bridge north of Troy, Ohio , spanning 224 feet (68 m). One of

6622-582: The theory further by incorporating the effect of shear on the dynamic response of bending beams. This allowed the theory to be used for problems involving high frequencies of vibration where the dynamic Euler–Bernoulli theory is inadequate. The Euler-Bernoulli and Timoshenko theories for the dynamic bending of beams continue to be used widely by engineers. The Euler–Bernoulli equation for the dynamic bending of slender, isotropic, homogeneous beams of constant cross-section under an applied transverse load q ( x , t ) {\displaystyle q(x,t)}

6708-442: The top member is sufficiently stiff then this vertical element may be eliminated. If the lower chord (a horizontal member of a truss) is sufficiently resistant to bending and shear, the outer vertical elements may be eliminated, but with additional strength added to other members in compensation. The ability to distribute the forces in various ways has led to a large variety of truss bridge types. Some types may be more advantageous when

6794-552: The truss members are both above and below the roadbed it is called a through truss; an example of this is the Pulaski Skyway , and where the sides extend above the roadbed but are not connected, a pony truss or half-through truss. Sometimes both the upper and lower chords support roadbeds, forming a double-decked truss . This can be used to separate rail from road traffic or to separate the two directions of road traffic. Since through truss bridges have supports located over

6880-471: The truss. Continuous truss bridges were not very common before the mid-20th century because they are statically indeterminate , which makes them difficult to design without the use of computers . A multi-span truss bridge may also be constructed using cantilever spans, which are supported at only one end rather than both ends like other types of trusses. Unlike a continuous truss, a cantilever truss does not need to be connected rigidly, or indeed at all, at

6966-428: The upper chord under compression. In a cantilever truss the situation is reversed, at least over a portion of the span. The typical cantilever truss bridge is a "balanced cantilever", which enables the construction to proceed outward from a central vertical spar in each direction. Usually these are built in pairs until the outer sections may be anchored to footings. A central gap, if present, can then be filled by lifting

7052-430: The wood is employed for compression elements while other types may be easier to erect in particular site conditions, or when the balance between labor, machinery, and material costs has certain favorable proportions. The inclusion of the elements shown is largely an engineering decision based upon economics, being a balance between the costs of raw materials, off-site fabrication, component transportation, on-site erection,

7138-414: Was also easy to assemble. Wells Creek Bollman Bridge is the only other bridge designed by Wendel Bollman still in existence, but it is a Warren truss configuration. The bowstring truss bridge was patented in 1841 by Squire Whipple . While similar in appearance to a tied-arch bridge , a bowstring truss has diagonal load-bearing members: these diagonals result in a structure that more closely matches

7224-505: Was closed in 2001. The state of Illinois attempted to provide money to the city of Venice for repairing the bridge, but was unable to do so because of the outstanding taxes owed by the city. As a result, the City of St. Louis foreclosed on the bridge, delaying reconstruction efforts further. In an agreement reached in June 2003, the states of Illinois and Missouri agreed to take over ownership of

7310-405: Was named after its inventor, Wendel Bollman , a self-educated Baltimore engineer. It was the first successful all-metal bridge design (patented in 1852) to be adopted and consistently used on a railroad. The design employs wrought iron tension members and cast iron compression members. The use of multiple independent tension elements reduces the likelihood of catastrophic failure. The structure

7396-683: Was popular with the Baltimore and Ohio Railroad . The Appomattox High Bridge on the Norfolk and Western Railway included 21 Fink deck truss spans from 1869 until their replacement in 1886. There are also inverted Fink truss bridges such as the Moody Pedestrian Bridge in Austin, Texas. The Howe truss , patented in 1840 by Massachusetts millwright William Howe , includes vertical members and diagonals that slope up towards

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