L35_Columns-fall 10

L35_Columns-fall 10 - EAS 209-Fall 2010 Instructors:...

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Unformatted text preview: EAS 209-Fall 2010 Instructors: Christine Human Lecture 35 Stability of Columns In preceding chapters, we have been concerned with two main design criteria: Strength the ability of a structure to support a given load without experiencing excessive stress, < all . Deflections the ability of a structure to support a given load without undergoing excessive deflections Chapter 10 is concerned with stability - the ability of a structure to support the applied loading, without undergoing a sudden change in configuration. Todays Lecture: Develop Eulers Buckling Formula Understand the effect of end conditions on buckling load Todays Homework: 12/20/2010 1 Lecture 35 Stability of columns EAS 209-Fall 2010 Instructors: Christine Human Buckling For the design of columns in compression, the cross- sectional area of the column is selected such that allowable stress is not exceeded specified maximum deformation is not exceeded In addition, we must consider another possible failure mode. We must ensure that the applied load P is less than P cr , the critical load that causes buckling. 12/20/2010 2 Lecture 35 Stability of columns all A P = spec AE PL = P cr is load that causes buckling. P>P cr P<P cr EAS 209-Fall 2010 Instructors: Christine Human To gain some insight into the stability of columns, we will consider a simplified model composed of two rigid rods and a torsional spring. In the straight column, the forces are aligned and the structure is stable. If we add a small perturbation at C, there will be a moment at C that is resisted by the spring. Is the spring stiff enough to return the deflected column the original vertical position? YES system is stable NO system is unstable. Column will continue to deflect to the right, until equilibrium is reached....
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L35_Columns-fall 10 - EAS 209-Fall 2010 Instructors:...

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