Maths proof

hacktavist

Hello, I don't know if this is frowned upon but i'm wondering if anyone can help me out with this proof.

I've tried my best to sub everything in but I cant solve it.

Thanks

Mike...

hacktavist wrote: »

Hello, I don't know if this is frowned upon but i'm wondering if anyone can help me out with this proof.

I've tried my best to sub everything in but I cant solve it.

Thanks

pass

ArmCandyBaby

Is that not to do with plane stress? Better off postion in the engineering forum I'd say - some of the students probably have it in their notes.

Fremen

Have you given us everything we need to know to solve it?
Seems like Tau_xz is not defined.
I guess Sigma_1,2 is the definition of Sigma_1 and Sigma_2, where one takes a plus sign and one takes a minus, right?
The right hand side of the Sigma_1,2 equation is the quadratic formula, if that's any help.

seandoiler

Fremen wrote: »

Have you given us everything we need to know to solve it?
Seems like Tau_xz is not defined.

it's most probably a misprint, i think it should be Tau_xy.... O.P. it should work out easily if you sub in and work out

hacktavist

Ah yes I did type that wrong it should be tau xy. sorry.

hivizman

In the second formula, define the first term (Sigma_x +Sigma_y)/2 as a and the second term (the square root expression) as b.

Then Sigma_1 = a + b, Sigma_2 = a - b, and you have:

A = [Sigma_1]^2 = a^2 + 2ab + b^2
B = [Sigma_2]^2 = a^2 - 2ab + b^2
C = [Sigma_1]*[Sigma*2] = a^2 - b^2

Hence A + B - C, which is the expression under the square root sign in the first formula, is

a^2 +3b^2 . . . [Expression 1]

But a = Sigma_x/2 and b^2 = [Sigma_x/2]^2 +[Tau_x,y]^2

So the above Expression 1 is 1/4*[Sigma_x]^2 +3/4*[Sigma_x]^2 +3*[Tau_x,y]^2

Simplifying, this gives [Sigma_x]^2 + 3* [Tau_x,y]^2, and substituting this into the first formula gives the required result.

Sorry the notation isn't very pretty.

hacktavist

Thanks alot! explained perfectly!