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
Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter7: Analysis Of Stress And Strain
Section: Chapter Questions
Problem 7.2.27P: -27 A square plate with side dimension of 2 in. is subjected to compressive stress a and tensile...
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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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