By Williams, Harry Edwin; Dym, Clive L
Analytical Estimates of Structural Behavior.
summary: Analytical Estimates of Structural habit
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3(c) we show shell structures (or simply shells), which reflect combined behaviors that arise because they are curved surface structures. In fact, shells are often described as curved plates, but their behavior is more complicated because a shell’s curvature couples the in-plane normal stresses to the transverse shear stresses. Further, the in-plane normal stresses have two components: one uniform, like the axial stresses in bars and arches, and a second that varies linearly through the thickness, like the bending stresses in beams and plates.
For this discussion, we will denote such dominant stresses by σn for normal stresses and by τs for shear stresses. We also note that each of these elements is far longer than it is deep or wide. Stated otherwise, the depth h and the width b of each of these elements are small compared to its length L, and “small” typically means less than 1/10. 1 One-dimensional structural elements and dominant stresses: (a) cable; (b) bar; (c) beam; (d) arch; (e) frame. (Dym, C. L. 1997. Structural Modeling and Analysis.
Why is that so? Simply because the speeds involved in all of these calculations are far, far smaller than c, the speed of light in a vacuum. 080 × 109 km/hr! These scaling ideas not only extend the ideas discussed earlier about dimensionless variables but also introduce the notion of limits. indb 14 05/01/12 12:17 PM Mathematical Modeling for Structural Analysis 15 life and in normal engineering applications of mechanics. A box of candy is not expected to weigh any more whether one is standing still, riding in a car at 120 km/hr (75 mph), or flying across the country at 965 km/hr (600 mph).
Analytical estimates of structural behavior by Williams, Harry Edwin; Dym, Clive L