By Maan H Jawad
Review This publication is written basically for pro engineers attracted to designing plate and shell buildings. It covers easy elements of theories and offers examples for the layout of parts as a result of inner and exterior quite a bit in addition to different a lot corresponding to wind and lifeless a lot. numerous derivations are saved particularly uncomplicated and the consequent equations are simplified to a degree the place the engineer could observe them on to layout difficulties. extra problematic derivations and extra normal equations should 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 e-book 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 booklet can also be applicable for complicated engineering classes.
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Additional resources for Design of Plate and Shell Structures
The positive value of R indicates that the corners have a tendency to lift up and a downward force is needed to keep them in place. This action must be considered when designing cover plates and concrete slabs. An example of the reinforcement at the corners of a concrete slab is shown in Fig. 1-13c. 1-7 Double Series Solution of Simply Supported Plates The first successful solution of a simply supported rectangular plate subjected to uniform load was made by Navier (Timoshenko 1983) in 1820. He assumed the load p in Eq.
Where l X Jm ðyÞ ¼ Bm cosh m ¼ 1;3;... þ 4po a 4 m 5k 5D Cm ¼ Case 2 mkx a mkð y À b=2Þ mkð y À b=2Þ þ Cm ð y À b=2Þ sinh a a 2a 3 po m 4 k 4 D cosh mkb 2a 4a 4 po þ mkpo a 3 b tanh mkb 2a : Bm ¼ m 5 k 5 D cosh mkb 2a The boundary conditions are B2 w2 ¼ w2 jy ¼ 0 ¼ w2 jy ¼ b ¼ 0 By 2 y ¼ 0 ð3Þ Plates with Various Boundary Conditions and 45 2 l X B w2 B2 w2 mkx ÀD þA ¼ Mm sin : 2 2 By Bx a m ¼ 1;2;... y¼b Substituting the function w2 ¼ l X fm ðyÞ sin m ¼ 1;2;... mkx a into the differential equation j4w2 = 0 gives fm ðyÞ ¼ Am sinh mky mky mky mky þ Bm cosh þ Cm y sinh þ Dm y cosh : a a a a Substituting the deflection expression into the first three boundary conditions gives Bm ¼ Cm ¼ 0 mkb ; a Am ¼ ÀDm b coth and from the fourth boundary condition we get Mm DTm Dm ¼ À where Tm ¼ Hence, w2 ¼ l X Mm DT m m ¼ 1;2;...
2Þ Single Series Solution of Simply Supported Plates 31 The homogeneous solution for the deflection is obtained from Eq. (1- 46). Referring to Fig. 1-17, the deflection in the y-direction due to uniform load is symmetric about the x-axis. Hence, the constants Am and Dm must be set to zero mky since the quantities sinh mky a and y cosh a are odd functions as y varies from positive to negative. Also, m must be set to 1, 3, 5, etc. in order for sin mkx a to be symmetric around x = a/2. Hence, wh ¼ l X mky mky mkx sin Bm cosh þ Cm y sinh a a a m¼1;3;...
Design of Plate and Shell Structures by Maan H Jawad