By Maan H Jawad
This publication is written basically for pro engineers drawn to designing plate and shell buildings. It covers simple points of theories and provides examples for the layout of parts because of inner and exterior so much in addition to different quite a bit, corresponding to wind and useless lots. numerous derivations are stored particularly uncomplicated and the consequent equations are simplified to a degree the place the engineer can follow them on to layout difficulties. extra complex derivations and extra basic equations are available within the literature for these attracted to a better 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 achieving a secure layout in keeping with a given required measure of accuracy. This e-book can be acceptable for complex engineering classes.
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Extra resources for Design of Plate and Shell Structures
N¼1;3;... mn½ðm=aÞ 2 þ ðn=bÞ 2 2 ð1Þ The bending and torsional moment expressions are given by Eq. (1-17) and are expressed as 16po Mx ¼ 4 k " l X l X m¼1;3;... n¼1;3;... org/about-a 26 Bending of Simply Supported Rectangular Plates Figure 1-15. Shear and Moment distribution in a uniformly loaded square plate. ) " # l l X 16po X mkx nky My ¼ 4 Gmn sin sin k a b m¼1;3;... n¼1;3;... " # l l X 16po ð1 À AÞ X mkx nky Mxy ¼ Hmn cos cos k4 a b m¼1;3;... n¼1;3;... ð3Þ ð4Þ where Fmn ¼ Gmn ¼ Hmn ðm=aÞ 2 þ Aðn=bÞ 2 mn½ðm=aÞ 2 þ ðn=bÞ 2 2 Aðm=aÞ 2 þ ðn=bÞ 2 mn½ðm=aÞ 2 þ ðn=bÞ 2 2 1 ¼ : ab½ðm=aÞ 2 þ ðn=bÞ 2 2 The maximum values of deflection and bending moments occur at x = a/2 and y = b/2.
3Þ ð4Þ where Fmn ¼ Gmn ¼ Hmn ðm=aÞ 2 þ Aðn=bÞ 2 mn½ðm=aÞ 2 þ ðn=bÞ 2 2 Aðm=aÞ 2 þ ðn=bÞ 2 mn½ðm=aÞ 2 þ ðn=bÞ 2 2 1 ¼ : ab½ðm=aÞ 2 þ ðn=bÞ 2 2 The maximum values of deflection and bending moments occur at x = a/2 and y = b/2. A plot of Eqs. (2), (3), and (4) is shown in Fig. 1-15 for a square plate. The figure also shows a plot of M1 and M2 obtained from Mohr’s circle along the diagonal of the plate. M1 becomes negative near the corner of the plate. This is due to the uplift tendency at the corners.
2-4a are at x ¼ 0; w ¼ 0 and B2 w ¼0 Bx 2 at x ¼ a; Mx ¼ 0 and Vx ¼ 0 at y ¼ 0; w ¼ 0 and B2 w ¼0 By 2 at y ¼ b; w ¼ 0 and Bw ¼ 0: By Equation (7) satisfies all of the above boundary conditions except Bw ¼0 By y ¼ b and Vx jx ¼ a ¼ 0: These two boundary conditions are used to determine the two unknowns in Eq. (7). l l l X X X dJm mkx dKm mkx nk nky sin sin ¼ 0: ð8Þ þ þ Ln cos dy dy a a b b y ¼ b m ¼ 1;3;... m ¼ 1;2;... n ¼ 1;2;... In order to solve this the last term needs to be expressed in terms À expression, Á .