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A reprint from American Scientist the magazine of Sigma Xi, The Scientific Research Society This reprint of a copyrighted article is provided for personal and noncommercial use only. For any other use, including reprinting and reproduction, please contact the author at [email protected]. Engineering An Anthropomorphic Model Henry Petroski eing able to feel the forces in represents a cantilever beam whose Ban unusual structure, even if If seeing is believing, self-weight must be supported at the only by proxy through a model, is a shoulder alone. great advantage for engineers, students Railroad bridges employing the and laypersons alike. If we can actually feeling may be cantilever principle had been built in be part of the model, and feel the forces North America during the 1880s, but directly, all the better. Probably the most understanding the form was new to Britain, so Baker famous anthropomorphic model of a prepared a public lecture to explain major engineering work is that of the the nature of a cantilever bridge, trac- Forth Bridge, located near Edinburgh, rience would believe me. Where no ing its roots to centuries-old Oriental Scotland. This structure had its origins precedent exists, the successful engi- examples but not mentioning any in the need for fixed crossings of the neer is he who makes the fewest mis- contemporary American examples. firths (or estuaries) of the Forth and takes.” Fortunately for engineers, it is His 1887 lecture is an exemplar of the Tay rivers on the country’s east coast. precisely where no precedent exists form, and its highlight was an anthro- Without such crossings, rail traffic was that they tend to be the most careful pomorphic model—variously referred interrupted by the need to transfer roll- and hence successful. to also as a living model and a human ing stock to and from ferries at each cantilever—of one full span of the river’s shores. The railway engineer The Cantilever Comes to Britain structure that was being built across Thomas Bouch was commissioned to Baker’s design for the bridge was quite the Firth of Forth. design the two bridges, and construc- unusual for its time. It was based on the The apparatus for the model con- tion of the one across the shallower cantilever principle, which had roots in sisted of a pair of chairs, four wooden Firth of Tay was completed in 1878. It corbeled arches and vaults. Galileo was struts, two pallets of bricks, a swing- was not a particularly daring design, the first to provide a rational analysis of like seat and rope to connect some of and the bridge was remarkable only for a cantilever structure, understanding the components to each other. Three its length of almost two miles across the that if he could successfully determine men were required to complete the wide estuary. Unfortunately, the lon- a relationship between the geometry, tableau of the model. Two of the men gest and highest girders of the bridge material strength and load carried at sat upright in the chairs, and each of collapsed during a storm in December the end of a generic cantilever beam, these men grasped the tops of a pair 1879, killing 75 people who were on the then he could predict the behavior of of struts, the bottoms of which were train making the crossing at the time. beams of more complex design and notched to bear against the edge of A court of inquiry found that the thereby shed light on the hitherto in- the chair seat. The triangular arrange- structure was “badly designed, badly explicable spontaneous failure of mas- ment so formed on either side of each constructed and badly maintained,” sive structures like obelisks and ships. man represented the portions of the and its engineer was discredited. Con- Galileo’s analysis of the cantilever beam bridge structure cantilevered out from struction was halted on the suspen- was correct in methodology but flawed the bridge towers, which were rep- sion bridge that Bouch had designed in detail; still, it provided the basis for a resented by the torsos of the seated to cross the deeper Firth of Forth, and rational method of structural analysis men and their chairs. To the tops of subsequently an entirely new design that is taught to engineering students the inside struts were attached the was commissioned from the firm of to this day. The classic illustration for sides of the swing seat, which repre- the distinguished engineer Sir John what has come to be known as Galileo’s sented the suspended central portion Fowler and his young partner Benja- Problem has been widely reproduced of the bridge span across which the min Baker, who would be knighted and, although not strictly speaking an railroad trains would run. Each out- on the completion of the project. Bak- anthropomorphic model, provides a side cantilever, consisting of a man’s er would be the lead designer of the feel for the gross forces involved. A true arm and associated strut, was tied by bridge, and he would also confess to anthropomorphic version of the canti- rope to a pallet of bricks, which pro- the enormity of the task: “If I were to lever is readily produced by stretching pretend that the designing and build- one’s arm out horizontally and holding Henry Petroski is Aleksandar S. Vesic Professor ing of the Forth Bridge was not a a briefcase, backpack or similar load in of Civil Engineering and a professor of history at source of present and future anxiety one’s hand. Even without such a load Duke University. Address: Box 90287, Durham, to all concerned, no engineer of expe- at its extremity, the outstretched arm NC 27708-0287 www.americanscientist.org Copyright © 2013 by Henry Petroski. Requests for permission to reprint or 2013 March–April 103 reproduce this article should be directed to the author at [email protected]. When engineer Benjamin Baker was faced with the need to convince a skeptical public that a new type of bridge, the cantilever, was the right choice for spanning the Firth of Forth, near Edinburgh, Scotland, he prepared a model for a lecture presented at the Royal Institution in Lon- don. Using three men, chairs, sticks, rope and bricks for counterweights, he demonstrated the principles that would make the record-length span possible. The model was likely photographed at the construction site and shown by use of a photographic lantern slide. (Photograph by Evelyn George Carey from Mackay, The Forth Bridge: A Picture History.) vided a counterweight to balance half legs into compression. In the world. The North British Railway, no the weight of the suspended central Forth Bridge you have to imag- doubt at least in part to allay fears that span plus half the weight of the third ine the chairs placed a third of a might have kept paying passengers man, who occupied the suspended mile apart and the men’s heads from booking travel across the soon-to- seat. In Baker’s lecture demonstration, to be 300 ft. above the ground. be-completed bridge, surely would not a large drawing of the bridge span was Their arms are represented by have discouraged Baker from giving displayed behind the human model, huge steel lattice members, and his lecture, in which he would empha- thereby making it self-evident—if it the sticks or props by steel tubes size that, in spite of the public’s con- was not already—what parts of the 12 ft. in diameter and 1¼ in. thick. fusion of the two, the Tay and Forth model corresponded to what parts of bridges were quite distinct. the bridge. In Baker’s own words: Baker’s lecture incorporating the The lecture was delivered on May human model was prompted by sev- 20, 1887, at a weekly evening meeting Two men sitting on chairs ex- eral factors. One was that the Tay of the Royal Institution in London. In tended their arms and supported Bridge that collapsed (and was rebuilt, addition to clarifying the location of the same by grasping sticks butt- reopening in 1887, the year of the lec- the Forth Bridge, which is about 35 ing against the chairs. This repre- ture) was on the same rail line that the miles south of the Tay, Baker gave a sented the two double cantilevers. new-style bridge would carry over the sense of its enormity and thereby the The central girder was represent- Forth. There was thus public anxiety difficulty of the task of erecting it. His ed by a short stick slung from one about the safety of the line generally. challenge in preparing his lecture, he arm of each man and the anchor- The other factor prompting the lecture admitted, was that he “had to consider ages by ropes extending from the was the unfamiliarity of the bridge how best to make a general audience other arms to a couple of piles of form that was being erected over the appreciate the true nature and direc- brick. When stresses are brought Forth. Although steel cantilever rail tion of the stresses on the Forth Bridge, on this system by a load on the bridges were not absolutely new, this and after consultation with some engi- central girder, the men’s arms and one under construction near Edin- neers on the spot, a living model was the anchorage ropes come into burgh was novel to Britain and was arranged.” Although Baker did not tension and the sticks and chair to have the longest spans of any in the claim that the idea was wholly his, the 104 American Scientist, Volume 101 Copyright © 2013 by Henry Petroski.