Student:Lamyaa MohsinBuckling of thin platesAdvanced Theory of ElasticityFILS, M I, STRUCTURAL ENGINEERING1In the calculation of critical values of forces applied in the middle place of a plate, the same methods as in the case of compressed bars can be used.

The equation for the buckled plate is

How presentation will benefit audience: Adult learners are more interested in a subject if they know how or why it is important to them.Presenters level of expertise in the subject: Briefly state your credentials in this area, or explain why participants should listen to you.2Buckling of Simply Supported Rectangular Plates Uniformly Compressed in One Direction.

Assume that a rectangular plate (Fig. 1) is compressed in its middle plane by forces uniformly distributed along sides x = 0 and x = a.

The Navier solution for the deflection way may be used:The strain energy of bending in this case is

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3The work done by the compressive forces during buckling of the plate, will be

Thus Eq. (2), for determining the critical value of compressive forces, becomes

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The first factor in this expression represents the Euler load for a strip of unit width and length a. For a plate of a given width the critical value of the load is smallest if the plate is square. In this case

The critical load, with m = 1, in expression (e), can be finally represented in the following form:

For other proportions of the plate the expression (g) can be represented in the form

Let us assume now that the plate buckles into two half-waves and that the deflection surface is represented by the expression

For calculating the critical load we can again use Eq. (g) by substituting in it a/2 instead of a. Then

in which k is a numerical factor, the magnitude of which depends on the ratio a/b. this factor is presented in Fig. (2) by the curve marked m = 1. The transition from m to m + 1 half-waves evidently occurs when the two corresponding curves in Fig. 2 have equal ordinates, i.e., when

From this equation we obtain

Substituting m = 1, we obtain

At this ratio we have transition from one to two half-waves. By taking m = 2 we find that transition from two to three half-waves occurs when

From Eq. (6) the critical value of the compressive stress is

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Steel thin plate: a = 15 mb = 5 mh =50 mmSAP2000 Model