# HW9 - 13.3 The thin square plate shown in Fig. P13.3 is...

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13.3 The thin square plate shown in Fig. P13.3 is uniformly deformed such that x = +1,400  , y = −650  , and xy = +1,200 rad. (a) Determine the normal strain n in the plate. (b) Determine the shear strain nt in the plate. Fig. P13.3 Solution (a) From the geometry of the plate, the n axis is rotated 45° clockwise from the x axis; therefore, = −45°. The given strain values are: 1,400 με 650 με 1,200 μrad x y xy   Substitute these values into the normal strain transformation equation [Eq. (13.3)] to obtain the strain in the n direction: 22 cos sin sin cos (1,400 με)cos ( 45 ) ( 650 με)sin ( 45 ) (1,200 μrad)sin( 45 )cos( 45 ) 225.000 με 225 με n x y xy          Ans. (b) The shear strain nt is found from the shear strain transformation equation [Eq. (13.5)]: 2( )sin cos (cos sin ) 2[(1,400 με) ( 650 με)]sin( 45 )cos( 45 ) (1,2 00 μrad)[cos ( 45 ) sin ( 45 )] 2,050.000 μrad 2.050 μrad nt x y xy            Ans.

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13.5 The strain components x , y , and xy are given for a point in a body subjected to plane strain. Determine the strain components n , t , and nt at the point if the n-t axes are rotated with respect to the x-y axes by the amount and in the direction indicated by the angle shown in either Fig. P13.5 or Fig. P13.6. Sketch the deformed shape of the element. x = +520  y = −650  xy = +750 rad = 35° Fig. P13.5 Solution The n axis is rotated 35° counterclockwise from the x axis; therefore, = +35°. The given strain values are: 520 με 650 με 750 μrad x y xy   Substitute these values into the normal strain transformation equation [Eq. (13.3)] to obtain the strain in the n direction: 22 cos sin sin cos (520 με)cos (35 )
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## This note was uploaded on 02/08/2011 for the course ME 650:291 taught by Professor Weng during the Fall '11 term at Rutgers.

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HW9 - 13.3 The thin square plate shown in Fig. P13.3 is...

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