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The thin rectangular plate (Fig. 1, not to scale) with sides 6 m and 4 m of thickness 112 mm 1s subjected the stresses Ox, Oy and Txy. An Airy stress function is proposed to be: $(x, y) = Ax° + Bx y+Cxy², with A= B =C =1 (a) Determine the values of stresses (Or, Gy and Ty) at point (x.y) which satisfy the stress function (b) Draw a stress element showing the stresses on the four faces of the element (Use the face bounded b the X- and Y-axes with a line representing a face, that is, a 2-D stress element). (c) Neglecting body forces, determine the resultant normal and shearing forces on the right face of the plat that are consistent with o (Use the face bounded hy the Yand V aves with a line anting a fce the

The thin rectangular plate (Fig. 1, not to scale) with sides 6 m and 4 m of thickness 112 mm 1s subjected the stresses Ox, Oy and Txy. An Airy stress function is proposed to be: $(x, y) = Ax° + Bx y+Cxy², with A= B =C =1 (a) Determine the values of stresses (Or, Gy and Ty) at point (x.y) which satisfy the stress function (b) Draw a stress element showing the stresses on the four faces of the element (Use the face bounded b the X- and Y-axes with a line representing a face, that is, a 2-D stress element). (c) Neglecting body forces, determine the resultant normal and shearing forces on the right face of the plat that are consistent with o (Use the face bounded hy the Yand V aves with a line anting a fce the

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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The thin rectangular plate (Fig. 1, not to scale) with sides 6 m and 4 m of thickness 112 mm is subjected to the stresses ox, Oy and txy. An Airy stress function is proposed to be: $(x, y) = Ax° + Bx'y+Cxy, with A=B=C =1 (a) Determine the values of stresses (ox, Oy and txy) at point (x_y) which satisfy the stress function (b) Draw a stress element showing the stresses on the four faces of the element (Use the face bounded by the X- and Y-axes with a line representing a face, that is, a 2-D stress element). (c) Neglecting body forces, determine the resultant normal and shearing forces on the right face of the plate that are consistent with o (Use the face bounded by the X- and Y-axes with a line representing a face, that is, a 2-D stress element). 112 mm 4 m 6 m Fig. 1 Biharmonic Equation ô*o(x, y) ôx o*o(x.y) ô*¢(X.y)=v*o(x,y) =0 +2 where o(x.y) is defined as: ô*o(x,y) o o(x, y) ôxcy
Transcribed Image Text:The thin rectangular plate (Fig. 1, not to scale) with sides 6 m and 4 m of thickness 112 mm is subjected to the stresses ox, Oy and txy. An Airy stress function is proposed to be: $(x, y) = Ax° + Bx'y+Cxy, with A=B=C =1 (a) Determine the values of stresses (ox, Oy and txy) at point (x_y) which satisfy the stress function (b) Draw a stress element showing the stresses on the four faces of the element (Use the face bounded by the X- and Y-axes with a line representing a face, that is, a 2-D stress element). (c) Neglecting body forces, determine the resultant normal and shearing forces on the right face of the plate that are consistent with o (Use the face bounded by the X- and Y-axes with a line representing a face, that is, a 2-D stress element). 112 mm 4 m 6 m Fig. 1 Biharmonic Equation ô*o(x, y) ôx o*o(x.y) ô*¢(X.y)=v*o(x,y) =0 +2 where o(x.y) is defined as: ô*o(x,y) o o(x, y) ôxcy
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