By Maan H Jawad
Review This e-book is written essentially for pro engineers drawn to designing plate and shell constructions. It covers simple facets of theories and provides examples for the layout of elements as a result of inner and exterior so much in addition to different a lot resembling wind and useless a lot. quite a few derivations are stored quite uncomplicated and the consequent equations are simplified to a degree the place the engineer could practice them on to layout difficulties. extra intricate derivations and extra normal equations could be present in the literature for these drawn to a closer wisdom of the theories of plates and shells. The examples given all through this publication are meant to teach the engineer the extent of study had to in attaining a secure layout in response to a given required measure of accuracy. This ebook can also be applicable for complex engineering classes.
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Additional resources for Design of Plate and Shell Structures
The tank is full of water on one side of the partition. The material is SA 240-304 and the temperature is 100jF. Assume the partition ABCD to be simply supported on all four sides. 1-16 In Example 1-2, what modifications must be made to Eq. (1) if the thickness of the plate is variable and is a function of x and y. 1-17 Discuss the modifications that have to be made to the differential equation and boundary conditions if the corners of a simply supported plate are allowed to curl up due to applied pressure.
Thus, if the load in Example 1-4 is triangular in distribution as shown in Fig. 1-18, then it can be expressed as pm ¼ po x a and Eq. (1-49) becomes pm ðyÞ ¼ 2 a Z a 0 po x mkx 2po ðÀ1Þ mþ1 sin dx ¼ mk a a m ¼ 1; 2; . . Problems 1-11 Find the expression for Mx, My and Mxy in Example 1-4. 1-12 A channel weir is approximated as a simply supported rectangular plate and is subjected to triangular loading. Find the expression for the moments. 1-13 An internal zirconium bulkhead is loaded as shown. Find the expression for the moments assuming the plate to be simply supported.
Sinusoidally loaded plate. 22 Bending of Simply Supported Rectangular Plates Figure 1-13c. Corner reinforcement. boundary conditions of the plate. Hence, a deflection of the form w ¼ C sin kx ky sin a b ð2Þ satisfies the given boundary conditions. Substituting Eq. (2) into Eq. (1) gives C¼ Dk 4 po 1 1 þ a2 b2 2 and the expression for w becomes w¼ Dk 4 po 1 1 þ a2 b2 2 sin kx ky sin : a b Substituting this expression into Eq. (1-17) gives Mx ¼ k2 po 1 1 þ a2 b2 2 1 A kx ky sin sin þ a2 b2 a b ð3Þ Boundary Conditions My ¼ k2 Mxy ¼ po 1 1 þ a2 b2 2 23 A 1 kx ky sin sin þ a2 b2 a b po ð1 À AÞ kx ky 2 cos cos : a b 1 1 k 2 2 þ 2 ab a b The maximum value for moments Mx and My occurs at x = a/2 and y = b/2.