the Warren truss

significant structures of the past Bridge historians and early textbooks generally call a truss with alternating compression and tension diagonals a Warren; however, sometimes it is called an equilateral truss since all panel lengths and diagonals are of equal length creating a series of equilateral triangles. When the panel lengths are shorter than the equal length diagonals, it was sometimes called an isosceles or isometric truss.

Figure 1. Commonly accepted Warren Truss.

Figure 2. Warren Truss with verticals to support top chord and deck structure.

By Frank Griggs, Jr., Dist. M. ASCE, D. Eng., P.E., P.L.S.

Dr. Griggs specializes in the restoration of historic bridges, having restored many 19th Century cast and wrought iron bridges. He was formerly Director of Historic Bridge Programs for Clough, Harbour & Associates LLP in Albany, NY, and is now an independent Consulting Engineer. Dr. Griggs can be reached at fgriggs@nycap.rr.com. When the span length increases and the height of the truss necessarily increases, the long compression members in the top chord need bracing to minimize buckling in the vertical direction. In this case, verticals are placed from the lower chord panel points up to the mid point of the chord member directly above. In addition, the deck structure stringers get longer requiring either heavier members or the addition of verticals from the top chord panel points dropping down to shorten panel lengths.

Neither of these truss styles are what James Warren and Willoughby Monzani patented in 1848 in England. They based their patent on similar trusses that were built in France by Alfred H. Neville and a patent that was granted in England to William Nash in 1839 on a similar design. Warren and Monzani were well known English engineers, and their design was for a truss that could be used as a deck or a through truss. They used cast iron for the top chord, and diagonals and wrought iron bars and links for the lower chord members. The top chord cast iron members were connected through cast iron junction blocks, and the cast iron diagonals and lower chord wrought iron members were connected with pins. The title of the patent application was Construction of Bridges and Aqueducts and was issued on August 15, 1848 with Patent #12,242. Their profile was rectangular. Even though Squire Whipple in the United States had published the method of determining loads in truss members under uniform and varying loads, this method had not made its way to England. It wasn’t until 1850 that W. B. Blood developed a method of analyzing triangular trusses, as Whipple had. Warren and Monzani’s patent stated,

The specification of this invention exhibits four different modes of building bridges, which it is stated may, with some slight modifications, be applied to the construction of aqueducts and roofing. 1)The bridge is built with cast iron side bands, rods, or plates, inclined towards each other, and combined so as to form a series of Vandykes [V shapes]. They are bolted at top to horizontal compression rods, and at bottom to horizontal tension rods, and carry a roadway at top or at bottom, or at both. 2)Or the bridge may be built of cast iron side angular frames (placed with the apices [point] downwards), which have their bases bolted together, end to end, and their apices bolted to horizontal rods. 3)Or, instead of the preceding modes of longitudinal construction, hollow castiron transverse frames may be employed, which are inclined, and bolted together at top, and are similarly attached at bottom to horizontal rods, bars, or plates.

4) Or wrought iron tie rods may be bolted at top to compression rods, and at bottom held together by the side of wooden girders, and the structure strengthened by means of stay rods.

Th e angles of the plates are regulated by longitudinal screw rods and nuts. It is clear they didn’t size their members or give details as to the load, either tension or compression in their diagonals. He didn’t even think of his web members as triangles but only connected VanDykes (V’s) between a compression member on top and a tension member on the bottom. Th ey had four claims as follows, 1) Th e mode of constructing bridges, aqueducts, or roofi ng with iron rods, bars, or plates, inclined towards each other, and connected together at top by compression band, and at bottom by tension band, so as to carry a roadway at top or bottom, or at both. 2) Th e mode of constructing bridges with cast iron angular frames bolted together at their bases, and having their apices bolted to horizontal compression rods. 3) Th e mode of constructing bridges with transverse hollow cast iron

Figure 4. Newark Dyke Bridge, cast iron A-frame on pier.

frames inclined towards each other, and bolted together at top and at bottom to horizontal plates. 4) Th e mode of constructing bridges with wrought iron rods inclined towards each other, and attached at top and bottom, as described. It appears their only claim to originality was in the use of triangles with top compression chords and lower tension chords. Th e fi rst major bridge, built by Joseph Cubitt in 1852 roughly to the patent, was the Newark Dyke Railroad Bridge of the Great Northern

ADVERTISEMENT–For Advertiser Information, visit www.STRUCTUREmag.org Railroad. In it he used alternating cast iron compression and tension diagonals with cast iron upper chords and wrought iron links for the lower chord. At the middle panel he had opposing cast iron members. Th e bridge crossed the Dyke on a sharp angle, requiring a span of 240 feet 6 inches. Cubitt said the Warren design was brought to him by C. H. Wild. He wrote,

Each girder consists of a top tube, or strut of cast-iron, and a bottom tie of wrought-iron links, connected together by alternate diagonal struts and ties of cast and wrought iron respectively, dividing the whole length into a series of equilateral triangles, of 18 feet 6 inches length of side.

Th ese girders rest on the apices of castiron A-frames, placed on the masonry of the abutments (Figure 4). Each pair is connected by a horizontal bracing at the top and the bottom, leaving a clear width of 13 feet for the passage of the trains…

Th e trusses are so arranged, that all compressive strains are taken by the cast-iron, and all tensile strains by the wrought iron; the strains, in all cases, in the direction of the length are of the respective parts, and all cross strain is avoided. Th e parts are so proportioned, that when loaded with

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Figure 5. End View of one of the two parallel Newark Dyke Spans. Note massiveness of cast iron members as well as the verticals to support the deck at mid panel points.

combination. But they are merely trusses with parallel chords and diagonals, or rather, oblique members, with only one series of obliques, and without verticals, except to concentrate weight upon the obliques from intermediate points along the upper or lower chord, according as the girder is loaded at such upper or lower chord. Whipple did not think there was anything new with what was being called a Warren Truss. In fact, in his 1846/47 book he wrote of trusses without verticals. He called this a “cancelled truss which dispenses with vertical pieces, except perhaps at the ends, or at the first bearing points from the ends.” He found, in fact, that a truss, his trapezoidal without verticals, used 8% less iron.

Figure 8. Whipple Plan 1846 but bridge historians call it a Double Warren Truss.

a weight equal to one ton per foot run, which considerably exceeds the weight of a train of the heaviest locomotive engines in use on the Great Northern, or on any narrow-gauge line, no tensile, or compressive strain on any part, exceeds five tons per square inch of section. It is clear that by 1852 Wild had taken the Warren configuration and, applying Blood’s method of analysis, calculated the load in each member so that it could be proportioned properly. An end view of the bridge showed, however, the hugeness of the members which was typical of English and European bridge design at the time. Over time, the bridge style was converted to all wrought iron with built up riveted members. In the United States, the Warren/Wild/Cubit design was known by our engineers. Many of them subscribed to the Proceedings of the Institution of Civil Engineers where Cubitt had published his article. Prior to 1848, Whipple had designed and built similar trusses on the New York and Erie Railroad and discussed them in his 1846/47 book on bridges. He included the plan shown in Figure 6. Not only did he design this span, he built several for the New York and Erie Railroad

Figure 6. Whipple plan for a bridge similar to the Warren Plan with inclined end posts. in 1848, the same year Warren got his patent in England. In an article in Appleton’s Magazine and Engineers Journal in January, 1851, he described some of his New York and Erie bridges and wrote,

These were wrought-iron skeleton girders upon the triangular plan, such as have since been called Warren girders, and by some regarded as a newly invented Several trusses that were patented in the United States incorporated the alternating tension and compression diagonals associated with the Warren Truss. The first was a wood and iron rectangular truss by A. D. Briggs in 1858 (#20,987) followed by Alber Fink in 1867 (#62,714) with a combination wood and iron trapezoidal truss with equilateral triangles with verticals dropping down to support the deck at mid panel points. He

wrote, “I adopt the triangular, system of bracing between the two chords, both because this system best avoids evils arising from the unequal expansion of a wrought-iron bottom and wooden top chord, and because it is the system of bracing having the least amount of material for equal strength with other systems.” In the same year, J. Dutton Steele (#63,666) received a patent for an Isometric Truss. He had been building them since 1863 and called it an isometric plan, as the diagonals were of equal length with a shorter panel length. He had Charles Macdonald write a long report comparing all of the standard bridge designs, including the Pratt, Howe, Whipple and Warren trusses. Macdonald concluded the only cost savings in a truss bridge are in the web members, as the top and bottom chord requirements were the same for most bridges. For a standard bridge span length of 165 feet, he determined the Howe trusses needs 54% more iron in the web and the Pratt needs 31% more iron than the Isometrical truss. He then compares the Isometrical truss with Linville’s double intersection truss and determines the isometrical uses 19% less iron in the web. He presents the results of a study by C. Shaler Smith in 1865 where he compared the Fink, Bollman, Triangular (Warren) and Murphy Trusses.

Figure 9. J. Dutton Steele patent drawing for an isometric plan.

Smith determined the Triangular and Murphy were more effi cient than either the Fink or Bollman trusses for both through and deck trusses. His conclusion stated the Isometrical Truss required less iron in the web system than any other trusses considered. In addition, he found the Isometrical Truss was, especially in wood, much easier to adjust in the event of wood shrinkage.

ADVERTISEMENT–For Advertiser Information, visit www.STRUCTUREmag.org In 1872, Whipple, in an article in the Transactions ASCE entitled “On Truss Bridge Building,” wrote that he had objections to Macdonald’s pamphlet and how he used the Whipple Double Intersection truss in his comparison, stating: “Now, Mr. Macdonald represents what he designates as the ‘Whipple Truss,’ with diagonals inclining only 30° from the vertical. I desire here

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Figure 10. Little Juniata Bridge, Pennsylvania RR, cast and wrought iron with verticals, Pony Truss ~1870. Figure 11. Bell’s Bridge, Delaware, Lackawanna & Western RR 1872, Double Warren or Whipple.

Figure 12. Warren, Isometric, Truss, Polygonal top chord, with verticals, all riveted steel bridge for BNSF Railroad over Verdigris River, Oklahoma~1960.

to enter my emphatic protest against the imputation of ever having tolerated any such practice.” He then got into the Isometric Truss (and the Warren style), writing:

But what of the Isometric? The name, at least, as applied to bridge trusses, is new, and euphonic [pleasing to the ear] withal.

This is a truss with parallel chords without vertical members in the web: one of the general types discussed and compared in my publication of 1847 with reference to

Fig. A., page 14…

I am not aware that there had existed any examples of the parallel chord truss without verticals, prior to their construction by me over 20 years ago, with the important exception of the plank lattice bridge. This was first known to me under the name of “Town’s Lattice Bridge,’” and it was a very cheap and serviceable bridge when properly constructed…

But somehow it occurred to me…that a plan in which every member of the web system should do something in the way of advancing the weight toward the abutments, might possess advantages over one having vertical members merely to transfer the action of weight directly from chord to chord without advancing it at all horizontally…

The Trapezoidal truss, with and without verticals, though depending upon combinations so old that “the memory of man” (especially the present generation) “runneth not to the contrary” still, perhaps, owes something to me for economical form and proportions…

These gentlemen [Macdonald and

Merrill] are pleased to term ‘The Whipple

Truss;’ and considering that the Isometric and the Post [with inclined posts] trusses are merely modifications (and not very

favorable modifications either) of a type of truss first used and thoroughly discussed by me. It is clear that Whipple believed that the Warren or Isometric trusses were simply extensions of trusses he wrote about in the 1840s, and built in the 1840s and 1850s. In an article on the Pratt Truss (STRUCTURE, May 2015), a case was made that the trusses called Howe and Pratt should really be called Whipple Trusses. A similar case is made here that the Warren Truss should really be called a Whipple Truss. The reasons are that Warren, when he developed his truss, did not know how to size his members nor could he distinguish between tension and compression in his web members. He never designed or built a truss with an inclined end post nor a truss with verticals. A truss as he patented it was never built. Whipple on the other hand had analyzed, designed and built trusses with various web members and inclined end posts prior to Warren’s patent. It is probably too late to change what most people call the various trusses, but it should be at least recognized that most of the truss patterns used in the late 19th and 20th century had their origins in the United States and Squire Whipple between 1841 and the 1880s. What were called the Warren trusses were built in the thousands as short span pony trusses with no verticals, longer spans with verticals, even longer spans with double intersections, and still longer spans with subdivided panels. They were originally built with cast and wrought iron members with pins and, later, with wrought iron members and cast iron joints with pins, and later fully riveted in steel. Polygonal top chords were also added in many trusses to extend the span length. J. A. L. Waddell used the pattern in many of his lift spans after the turn of the century. Several examples of the bridge style are shown in Figures 10, 11 and 12. ▪

By Larry Kahaner

The earthquakes that hit Nepal in April and May have once again focused the construction industry and world leaders on the devastating loss of life and property involved in seismic events. More than 8,600 people died in the two earthquakes that destroyed more than a half-million homes, leaving many residents exposed to the upcoming monsoon rains. Many governments are responding to seismic threats. “ e market for energy absorption technologies in seismic applications is expanding as global government requirements are changing to protect critical assets, economic loss and loss of life,” says Greg Herman, Sr. Project Manager at ITT Enidine Inc. (www.enidine.com) in Orchard Park, New York. “Today, new builds and structural retro ts must consider energy absorption devices to mitigate these issues. Seismic protection is no longer an afterthought. Energy absorption technologies are used on an increasing basis to alleviate wind and seismic concerns.” In discussing the company’s products, he notes: “Fluid Viscous Dampers (FVD’s) are devices that operate by converting kinetic energy into heat, typically over multiple actuations. FVD’s are velocity dependent devices; they do not provide damping force or sti ness to a structure unless subjected to external excitation. FVD technologies use the ow of internal uids and custom ori ce geometry to obtain linear and non-linear damping properties. While applying FVD’s as energy dissipation devices, a structure will increase its critical damping ratio and reduce the dynamic magni cation factor, thereby reducing the dynamic response of the structural system in the event of an earthquake.” Herman adds: “ ere are di erent designs and technologies for energy absorption as it relates to seismic damping applications. Selecting the appropriate technology is critical to providing the proper protection of the structure. ese selections are based on the application, as there are di erent requirements for bridge, building (in frame vs. base) and tuned mass damping systems.” He highlights these di erences: • Bridges and base isolation components are often exposed to wind, thermal and tra c excitation on a daily basis. FVD’s for these applications must be able to withstand harsh conditions and sustain a long lifespan. • For buildings, the excitation frequency is signifi cantly less than for bridges. FVD’s for these applications should be designed to endure long periods of static installation with features that promote extended life span. • For tuned mass damping systems, a linear damper is often recommended, as these applications require high energy dissipation in tight spaces and require a relatively high amount of seal travel over the design life. When it comes to cost, Herman says that FVD’s can be a price-e ective solution. “In reviewing the total cost of ownership, adding FVD’s for energy dissipation can often be a more cost e ective solution, especially when coupled with a supplier that represents reduced risk for any associated elements and integration into a project. Because FVD’s have the ability to reduce the stress and displacement of a structure, they require less material, reducing the customer’s total cost.” At Simpson Strong-Tie (www.strongtie.com) based in Pleasanton, California, Marketing Communications Project Manager Elizabeth Rajs is seeing an increasing demand for light-frame, multi-story wood frame buildings. “ ere are complicated design challenges speci cally associated with multi-story buildings that must withstand seismic activity or wind events. Our anchor Tiedown System for Shearwall Overturning Restraint and our Uplift Restraint System for Roofs address those challenges, and have become a popular continuous rod tiedown solution for these types of construction projects. Simpson Strong-Tie has everything engineers need to design the safest building possible with materials speci cally suited for the application.” e company has several new o erings, Rajs explains: • Th e Simpson Strong-Tie Strong-Rod Systems Design Guide (F-L-SRS15) is now available in print or for download at www.strongtie.com/srs. is new document guides designers through the speci c challenges and solutions available to address multi-story light frame construction shear wall overturning restraint as well as roof wind uplift restraint using

Simpson Strong-Tie Strong-Rod Systems. ree methods of speci cation are explained. • Th e Simpson Strong-Tie RTUD5 and RTUD6 ratcheting take-up devices are new additions to their cost-e ective line of products for ⅝ -inch and ¾-inch diameter threaded rod, respectively. Once installed on top of the BPRTUD5-6 bearing plate, a series of internal threaded wedges enable the device to ratchet down the rod as the wood structure shrinks but engage the rod in the reverse direction when under tensile loading, ensuring continuous engagement is maintained enabling the rod system to perform as designed. Unlike similar products, the RTUD can be attached using nails or screws. • Simpson Strong-Tie has thoroughly researched and tested practical solutions for concrete podium slab anchorage to provide designers with additional options when designing light-frame structures over concrete podium slabs. e use of the special detailing of anchor reinforcement shown in

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Anchor Kit product information. • For other foundation anchorage conditions, design tools, such as the Simpson Strong-Tie Anchor Designer Software, are available to help designers navigate the complex anchorage provisions contained in the ACI 318 reference design standard. Anchor products, including the Pre-Assembled Anchor Bolt (PAB), are also available to simplify speci cation. Rajs concludes: “Because no two buildings are alike, each project is optimally designed to the designer’s individual speci cations. continued on next page

Run-assembly elevation drawings and load tables are provided to the designer for approval.” (See ad on page 35.) “Although Taylor Devices (www.taylordevices.com)has been designing and manufacturing special dampers and motion control products for approximately 60 years, these types of devices have only been used in structures beginning in the mid 1990s,” says Alan Klembczyk, the North Tonawanda, New York company’s Vice President, Sales & Engineering.”Since that time, we have adapted more and more special spring and damping devices into structures that were previously qualified for classified military and aerospace applications.” Klembczyk says that Taylor Devices has more than 600 structural projects worldwide with these special devices, some of which include a new combination of damping and spring components in either a

Stand firm. Don’t settle for less than the seismic protection of Taylor Fluid Viscous Dampers. As a world leader in the science of shock isolation, we are the team you want between your structure and the undeniable forces of nature. Others agree. Taylor Fluid Viscous Dampers are currently providing earthquake, wind, and motion protection on more than 650 buildings and bridges. From the historic Los Angeles City Hall to Mexico’s Torre Mayor and the new Shin-Yokohama High-speed Train Station in Japan, owners, architects, engineers, and contractors trust the proven technology of Taylor Devices’ Fluid Viscous Dampers.

parallel or series arrangement. “Typical applications include new tall buildings, new medium-sized buildings, retrofits, large bridges, pedestrian bridges and various other structures. The great feature of these Taylor damping products is that due to its output proportional to input velocity, it is the only structural product in use today that functions out-of-phase with the structural response (allowing reduction of stress) and acceleration, along with the reduction of deflection that is provided by all energy dissipation products.” He says that since the company has developed specialized components with non-linear behavior, structural engineers can now engage the added benefits that an optimized product can offer. “Our devices can incorporate linear or non-linear damping exponents, linear or non-linear spring components, pre-loaded mechanisms for zero drift during small inputs, high cycle-life components with no fatigue failures over decades of use, friction-free devices, force limiting devices, shock transmission units and any combination of these attributes. Our ‘bag of tricks’ in solving structural and dynamic problems has grown for more than six decades,” says Klembczyk. As for topical projects, Klembczyk notes that the company has recently delivered more than 100 non-linear dampers for the new San Diego Central Courthouse Project. These dampers were modeled and analyzed by Skidmore, Owings & Merrill LLP (SOM) as having two distinct Force vs. Velocity regions; one being linear for low velocities experienced during wind events and one being non-linear for the higher velocity range that occurs during seismic events. Wind tunnel testing at RWDI in Guelph, Ontario, provided the site specific wind environment and analysis at SOM verified performance during both these wind and seismic inputs. “With this additional level of analysis performed, our devices enabled an optimized solution for both wind and seismic events,” he says. “Business has been very good,” Klembczyk adds. “Our sales and product lines are continuing to grow as more engineers are willing to take a close look at what benefits our products can offer. A relatively simple structural analysis can demonstrate the benefits of adding our devices to their structures. Oftentimes, it is a simple matter of taking Taylor Devices’ Fluid Viscous Dampers give you the seismic protection that first step for engineers you need and the architectural freedom you want. to realize what they may not have considered before.”▪

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S-FRAME Software Inc.

Phone: 203-421-4800 Email: info@s-frame.com Web: www.s-frame.com Product: S-CONCRETE Description: Used to view instantaneous results as you optimize and design reinforced concrete walls, beams and columns within one easy solution platform, or automate your workflow by checking thousands of concrete section designs in one run. Features comprehensive ACI 318 and other design code implementations, along with detailed design reports.

Product: S-FOUNDATION Description: Quickly design, analyze and detail building foundations with S-FOUNDATION, a complete foundation management solution. Run as a standalone application, or utilize S-FRAME Analysis’ powerful 2-way integration links for a detailed soil-structure interaction study. S-FOUNDATION automatically manages the meshed foundation model. Includes Revit and Tekla BIM links. Product: S-LINE Description: Everything you need to analyze, design and detail reinforced concrete beams. Check strength and serviceability requirements for short- and long-term (cracked section) de ection estimations, automatically generate pattern loading and load combinations with optional moment redistributions. Graphical output, including capacity envelopes on shear, moment, and torsion diagrams, provides clear, easy-to-read results.

Simpson Strong-Tie

Phone: 800-999-5099 Email: web@strongtie.com Web: www.strongtie.com Product: Redesigned Titen HD® Screw Anchor Description: e patented, high-strength Simpson Strong-Tie Titen HD screw anchor for concrete and masonry o ers optimum performance in both cracked and uncracked concrete, as required by the 2012 IBC for post-installed anchors. Newly redesigned, this anchor now features optimized thread geometry and is available in ¼-inch diameter.

Product: AT-XP® Anchoring Adhesive for Cracked and Uncracked Concrete Description: Formulated for high-strength anchorage of threaded rod and rebar into concrete under a wide range of conditions. AT-XP adhesive dispenses easily in cold or warm environments with little to no odor, cures fast and when mixed properly is teal colored for easy post-installation identi cation.

Strand7 Pty Ltd

Phone: 252-504-2282 Email: anne@beaufort-analysis.com Web: www.strand7.com Product: Strand7 Description: An advanced, general purpose, FEA system used worldwide by engineers, designers, and analysts for a wide range of structural analysis applications. It comprises preprocessing, solvers (linear and nonlinear static and dynamic capabilities) and postprocessing. Features include staged construction, a Moving Load module and quasi-static solver for shrinkage and creep/relaxation problems.

StructurePoint

Phone: 847-966-4357 Email: info@structurepoint.org Web: www.StructurePoint.org Product: spColumn and spSlab Description: spColumn: design of shear walls, bridge piers as well as typical framing elements in buildings and structures. spSlab: analysis, design and investigation of reinforced concrete oor systems.

Product: spMats and spWall Description: spMats: analysis, design and investigation of commercial building foundations and industrial mats and slabs on grade. spWall: design and analysis of cast-in-place reinforced concrete walls, tilt-up walls, ICF walls, and precast architectural and load-bearing panels. Tekla

Phone: 770-426-5105 Email: kristine.plemmons@tekla.com Web: www.tekla.com Product: Tedds Description: A powerful software that will speed up your daily structural and civil calculations, Tedds automates your repetitive structural calculations. Perform 2D Frame analysis, utilize a large library of automated calculations to U.S. codes, or write your own calculations while creating high quality and transparent documentation.

Product: Tekla Structures Description: Move from design-oriented to construction-oriented engineering and enable structural engineers proved additional services. rough our open and collaborative software environment, you can work with other disciplines and reduce RFIs. From concept to completion, Tekla software gives you collaboration and control.

Product: Fastrak Description: A powerful software that will speed up your daily structural and civil calculations. Using Tedds, you can access a large library of automated calculations or write your own while creating high quality and transparent documentation.

VERSA-LOK

Phone: 800-770-4525 Email: versalok@versa-lok.com Web: www.versa-lok.com Product: VERSA-LOK Retaining Wall Systems Description: A solid construction and unique pinning system that enables unparalleled design exibility for building everything from erosion control and waterway installations to beautiful residential and commercial hardscapes with curves, corners, stairs and columns. e Standard unit is available in traditional split-face or vintage weathered textures.

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