{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

06_PlateTheory_05_RectangularCoordinates

06_PlateTheory_05_RectangularCoordinates - Section 6.5 6.5...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 6.5 Solid Mechanics Part II Kelly 149 6.5 Plate Problems in Rectangular Coordinates In this section, a number of important plate problems will be examined using Cartesian coordinates. 6.5.1 Uniform Pressure producing Bending in One Direction Consider first the case of a plate which bends in one direction only. From 6.3.11 the deflection and moments are 2 2 2 2 ) ( , ) ( ), ( dx w d D x M dx w d D x M x f w y x ν = = = (6.5.1) The differential equation 6.4.9 reads D x q dx w d ) ( 4 4 = (6.5.2) The corresponding equation for a beam is EI x p dx w d / ) ( / 4 4 = . If ) ( / ) ( x q b x p = , with b the depth of the beam, with 12 / 3 bh I = , the plate will respond more stiffly than the beam by a factor of ) 1 /( 1 2 ν , a factor of about 10% for 3 . 0 = ν , since ( ) b EI Eh D 2 2 3 1 1 1 12 ν ν = = (6.5.3) The extra stiffness is due to the constraining effect of y M , which is not present in the beam. 6.5.2 Deflection of a Circular Plate by a Uniform Lateral Load A solution for a circular plate problem is presented next. This problem will be examined again in the section which follows using the more natural polar coordinates. Consider a circular plate with boundary 2 2 2 a y x = + , (6.5.4) clamped at its edges and subjected to a uniform lateral load q , Fig. 6.5.1.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon