HOMEWORK ASSIGNMENT 6 Exercise 1: Arch Forms (10 points) Sketch the ideal form for an arch under a concentrated load, Q applied at midspan. (Ignore the effect that the dead weight of the arch would have on the form.) Exercise 2: Reactions (20 points) For a) and b) calculate the vertical and horizontal reactions at each support.

a) b) Exercise 3: Bending Moments (30 points) For arch a) in Exercise 2 draw the bending moment diagram due to the vertical loads and the bending moment diagram due to the horizontal reactions. On these two diagrams label the maximum moment and the moment at the quarterpoints. Draw the bending moment diagram that results when you add the first two diagrams together. On this diagram label the maximum moment and the zero moment locations.

Exercise 4: Critical Discussion (25 points) A recent article by a Princeton alumnus, Professor D. Paul Gauvreau (who studied under D. P. Billington and C. Menn), compared two pedestrian bridge proposals to traverse two sets of rail lines in downtown Toronto, Canada. The first proposal was a steel truss designed by an engineering firm. Due to the site’s proximity to the historically significant Fort York, the aesthetic quality of the truss was deemed insufficient and a second call for proposals was made. The lowest bid was for an inclined arch, which at $22 million was $4 million higher than the allotted budget. Of the two proposals, Gauvreau says, “Neither is ideal. The inclined arches, the primary designers of which were architects, create visual impact through an indirect and extravagant structural system. Whatever aesthetic value it may claim is diminished by the fact that its form is derivative of the large number of recently built inclined arches. (In the Toronto area alone, it would have been the third such bridge.) The positive characteristics we might attribute to the truss (more efficient flow of forces, greater economy) appear unconvincing in the light of its prosaic appearance. It was as if its designers, in this case engineers, did not particularly care about how this bridge would look.” Good designers typically use reference works to initiate their designs (as they improve, they will begin to use their own projects as references). Find a bridge covered in class that would be appropriate for this site. Assume either three spans of 70 m (210 ft) or one span of 200 m (600 ft). Keep in mind that this is a bridge for pedestrians and that certain systems are only appropriate for certain spans. How could an engineer adapt your chosen concept to this site? How does your design compare to the ‘prosaic’ and ‘extravagant’ concepts discussed by Gauvreau? Keep your response to 300-400 words and 2 sketches.

‘Prosaic’ Steel Truss Design

‘Extravagant’ Inclined Arch Design

D.P. Gauvreau (2012) "Design Education for the 21st Century," in Festschrift Billington 2012, E.M. Hines, S.G. Buonopane and M.E.M. Garlock, editors, International Network for Structural Art, pp. 92-121.

Exercise 5: Analytical Problem – Final 2009 (15 points)

Maillart designed the Vessy bridge with a span-to-rise ratio of 11.9.

a) Assuming the 184 foot span has a uniformly distributed dead load of 3 kips/foot,

solve for the horizontal and vertical reactions.

b) Draw the bending moment diagram for concentrated live loads applied simultaneously at each quarter point. Neglect the dead load and do not forget to indicate maximum and minimum locations on your diagram.