in the name of god. For NMAA and Kardan University Faculty of Engineering. Lecture by : LT “Sayed Dawod karimi” email@example.com 0799560376. Lesson #05 Strain. 1. Lesson Objectives At the conclusion of this lesson, you should be able to do the following:
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For NMAA and Kardan University
Faculty of Engineering
Lecture by :
LT “Sayed Dawod karimi”
they did not have to allow for as much uncertainty in their design, and so they were able to use considerably less steel in the building. Less steel made the structure lighter and more economical than any previous skyscraper had been. However, the building was also much more flexible than it should have been. It was susceptible to much larger deformations than older, heavier buildings had been, and so even in light winds, the tower flexed and twisted far more than anyone had anticipated. Because window glass is itself very stiff, the windows were unable to flex along with the building frame, and they simply popped out of their mountings. It is important to note that the structural design was, in fact, safe. The stresses in the structural
members were within allowable limits. Nonetheless, the building failed to fulfill its intended function because of excessive deformations.
where dh and dw are the changes in height and width dimensions, respectively. It is important to note that, while there are two different expressions for lateral strain, a given axially loaded member with a given applied load has just one value of lateral strain. The lateral deformations might be different in the two lateral directions—but the lateral strain is always the same in both directions.
It is important to recognize, however, that this equation is rarely applied in the form shown above. Because Poisson’s Ratio is a material property, it is usually obtained from reference tables like Table A-17 and A-18 in your textbook. The equation above is typically used to calculate lateral or longitudinal strain for a given material.
At any given magnitude of load, this steel specimen experiences some normal stress, s, which is equal to the load divided by the cross-sectional area of the specimen. At the same time, this load causes the specimen to elongate. If we measure the elongation, we can calculate the corresponding longitudinal strain, e, as the measured deformation divided by the original length.
We will examine stress-strain curves in more detail next lesson. For now, it is only necessary to note two key characteristics of the example curves shown in Figure 4-28. First, a stress-strain curve always starts at the origin. This is expected, because zero load results in zero deformation, and so zero stress should result in zero strain.
The linear relationship between stress and strain in the elastic region of the stress-strain curve is one of the most important concepts underlying all of structural mechanics. This linear relationship is called Hooke’s Law, named after the great British scientist Robert Hook, and can be expressed mathematically as