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2: Simple Tensile and Shear Structures

Last updated

Mar 15, 2021
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- 1.4: Stress-Strain Curves
- 2.1: Trusses

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The modules in this section will outline some of the basic concepts of materials mechanical response by restricting the geometry to a case of simple uniaxial tension. Many of the atomistic and mechanistic concepts in our materials-oriented approach to solid mechanics can be introduced in this way, without the mathematical and conceptual complications that more realistic gemoetries entail. Subsequent modules will extend these concepts to geometrically more complicated situations, and introduce gradually the mathematical language used by the literature of the field to describe them.

2.1: Trusses
This page covers the analysis and application of trusses in structural engineering, focusing on their design, stability, and response to loads. It explores concepts such as static equilibrium, the energy method (including Castigliano's theorem), and matrix structural analysis to calculate forces and deflections. Various analytical methods, including finite element analysis, are emphasized for their efficiency in solving truss problems.
2.2: Pressure Vessels
This page covers the application of Mechanics of Materials to analyze two-dimensional stress and strain in thin-walled pressure vessels like pipes and airplane cabins. It discusses the importance of design to prevent failures, focusing on biaxial tensile stresses, deformation concepts including the Poisson effect, and the behavior of compound cylinders under pressure.
2.3: Shear and Torsion
This page covers the mechanics of torsionally loaded shafts, emphasizing shearing stresses and strains crucial for power transmission in engineering. It explains the relationship between shear stress, shear strain, and torque, highlighting the advantages of hollow shafts for efficiency. The text also compares solid and annular shafts, discusses methods for calculating angular displacements, and presents the energy method using Castigliano’s theorem.

Thumbnail :Simplified model of a truss for stress analysis, assuming unidimensional elements under uniform axial tension or compression. (CC0; Krishnavedala via Wikipedia)

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