Dell
Nov4-09, 11:37 AM
in this question, i am given the function for the xx stress as seen in the diagram below:
http://lh6.ggpht.com/_H4Iz7SmBrbk/SvG3wUaPVAI/AAAAAAAAB6w/sMKXVGWomi8/Capture1.JPG
i am asked to sketch the stress distribution, which i have done
http://lh3.ggpht.com/_H4Iz7SmBrbk/SvG3wPYlmdI/AAAAAAAAB6s/rd9T_ED6MK0/Capture.JPG
now i am asked to find the value of C which will give me the maximum value for Mo, which as far as i can see is Moment about the z axis.
what ive done is
Mz= -ʃʃ {(σxx)*y} dA
now i know that there are 3 options,(3 functions for σxx) but i know that for y>=c and y<c the function for σxx is constant and -ʃʃ {y} dA is 0,(2nd area moment)
therefore i think i must find it where -c<y<c,
-ʃʃ {(-σy/c)*y} dA= σ/c * ʃʃ {(y^2} dA
=σ/c * ʃʃ {(y^2} dydz [(z from -b/2 to b/2), (y from -h/2 to h/2)]
and i get
Mo=(σ*h^3*b)/(12c)
now how do i find thevalue for c that will give me the maximum Mo?? if c=0 Mo is infinite ??
i thought maybe to find the derivative and compare to 0 but by what? y? z? either way i dont see how that would help, since i am looking for the maximum "c" value, then i thought maybe dMo/dC but i dont think so.
http://lh6.ggpht.com/_H4Iz7SmBrbk/SvG3wUaPVAI/AAAAAAAAB6w/sMKXVGWomi8/Capture1.JPG
i am asked to sketch the stress distribution, which i have done
http://lh3.ggpht.com/_H4Iz7SmBrbk/SvG3wPYlmdI/AAAAAAAAB6s/rd9T_ED6MK0/Capture.JPG
now i am asked to find the value of C which will give me the maximum value for Mo, which as far as i can see is Moment about the z axis.
what ive done is
Mz= -ʃʃ {(σxx)*y} dA
now i know that there are 3 options,(3 functions for σxx) but i know that for y>=c and y<c the function for σxx is constant and -ʃʃ {y} dA is 0,(2nd area moment)
therefore i think i must find it where -c<y<c,
-ʃʃ {(-σy/c)*y} dA= σ/c * ʃʃ {(y^2} dA
=σ/c * ʃʃ {(y^2} dydz [(z from -b/2 to b/2), (y from -h/2 to h/2)]
and i get
Mo=(σ*h^3*b)/(12c)
now how do i find thevalue for c that will give me the maximum Mo?? if c=0 Mo is infinite ??
i thought maybe to find the derivative and compare to 0 but by what? y? z? either way i dont see how that would help, since i am looking for the maximum "c" value, then i thought maybe dMo/dC but i dont think so.