By Williams, Harry Edwin; Dym, Clive L
Analytical Estimates of Structural Behavior.
summary: Analytical Estimates of Structural habit
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3 displays a log–log plot of nave height against church length for a variety of medieval cathedrals and churches in England and on the European continent. We note that as church lengths (and thus size) increase, the nave heights increase in absolute terms but fall off in relative terms. That is, as churches get longer (and bigger), their naves get relatively smaller. Further, although we do not give the data to buttress this assertion, the larger churches tend to have narrower naves. Why do the nave height and width not increase with church size?
Such analyses are, however, considered more as aspects of three-dimensional elasticity theory than of structural analysis, so they are not discussed here. indb 35 05/01/12 12:17 PM 36 Analytical Estimates of Structural Behavior One-Dimensional Structural Elements In the first category we discussed, in which the loads and their attendant principal structural responses have the same directions, we are usually talking about structural elements that can be modeled as one-dimensional structures. These structures act in pure tension, as ropes or some of the bars in a truss, or they act in pure compression, again in truss bars and in columns, although columns deserve a category of their own.
Inasmuch as this cable requires only a statement of equilibrium regarding its uniform axial stress (or its net axial force), we need to stipulate only one reaction force, or its dual, at each end. At the top end, since it represents the suspension point from which we are hanging the cable and its load, there is only one reaction force, and it must balance the tension in the cable. At the other end, we could require the force we want the cable to carry (say, a weight W) or we could require that the cable be stretched by a known amount (say, Δ).