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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 )
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 7

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online