- #1

Dell

- 590

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in the following question,

E=65 GPa

V=0.3

find the new length of the arc BD??

i have found the stresses

[tex]\sigma[/tex]xx=-56Mpa

[tex]\sigma[/tex]yy=0

[tex]\sigma[/tex]xy=-28Mpa

using hookes law i can find the strains

[tex]\epsilon[/tex]xx=-8.615e-5

[tex]\epsilon[/tex]yy=2.58e-4

0.5*[tex]\epsilon[/tex]xy=[tex]\gamma[/tex]=-1.12e-3

but how do i calculate the change in the arc using this? i would know how to solve this if i had some kind of angular strain- i need to use a polar system not Cartesian. is there any way to do this?

also how do i know the new angle DAB? i know that the XY axis' new angle is 90.06417, and the n,t system (axes tilted 45 degrees to XY) is also 90.06417 but how do i find DAB,? generally is there any way of knowing how the axis is strained, for example, has the X axis dropped 0.06417 degrees, or the Y axis opened up 0.06417 degrees, or a bit each??

in this specific case can i say that since there is no yy strain the x-axis stays at the same angle?

DA*=DA(1+[tex]\epsilon[/tex]tt)=4.999569cm

AB*=5.0012923cm

E=65 GPa

V=0.3

find the new length of the arc BD??

i have found the stresses

[tex]\sigma[/tex]xx=-56Mpa

[tex]\sigma[/tex]yy=0

[tex]\sigma[/tex]xy=-28Mpa

using hookes law i can find the strains

[tex]\epsilon[/tex]xx=-8.615e-5

[tex]\epsilon[/tex]yy=2.58e-4

0.5*[tex]\epsilon[/tex]xy=[tex]\gamma[/tex]=-1.12e-3

but how do i calculate the change in the arc using this? i would know how to solve this if i had some kind of angular strain- i need to use a polar system not Cartesian. is there any way to do this?

also how do i know the new angle DAB? i know that the XY axis' new angle is 90.06417, and the n,t system (axes tilted 45 degrees to XY) is also 90.06417 but how do i find DAB,? generally is there any way of knowing how the axis is strained, for example, has the X axis dropped 0.06417 degrees, or the Y axis opened up 0.06417 degrees, or a bit each??

in this specific case can i say that since there is no yy strain the x-axis stays at the same angle?

DA*=DA(1+[tex]\epsilon[/tex]tt)=4.999569cm

AB*=5.0012923cm

Last edited: