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Analytical estimates of structural behavior by Williams, Harry Edwin; Dym, Clive L

By Williams, Harry Edwin; Dym, Clive L

Analytical Estimates of Structural Behavior.

summary: Analytical Estimates of Structural habit

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Indb 37 05/01/12 12:17 PM 38 Analytical Estimates of Structural Behavior The final one-dimensional structure is the frame. In the same way that an arch has behavior in common with both the cable and the beam, the frame has its roots in beam behavior combined with bar-like aspects. 1(e). If the topmost frame element is something like a simple beam, it will need vertical supports at its ends to transmit its vertically applied load to the ground (through the frame’s two vertical members). Thus, the vertical legs of the frames, though they might act largely as beams, must exhibit bar-like (or column-like) behavior to carry the vertical loads down to the ground.

In many physical models, the cosinusoid is linked to or compared with unity. 39) because its value is being compared to unity, not to zero. For example, had we been sloppy in translating this assumption when evaluating the pendulum’s potential energy, we would have wrongly found that potential energy to be zero. This kind of behavior is ubiquitous in engineering and physics, perhaps because much of the same mathematics is fundamental to modeling in those fields. For example, catenaries are found in bridges and in measuring tapes.

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? The answer lies in the geometric scaling of surface areas and enclosed volumes. The relevant scaling issue is the change of a church’s enclosed area as it is made longer (and larger). A longer church has a longer perimeter. In buildings of constant shape, the surface area of the enclosing wall increases linearly with the perimeter length, while the enclosed volume increases with the square of the perimeter length.

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