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Brendanmcg
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Homework Statement
DIAGRAM ATTACHED AT BOTTOM
Q. The following statements are true for an element in plane stress state. (this is 2D)
(1) one of the principle stresses is 40Mpa;
(2) σx= -2τxy; (the algebraic values)
(3) in x'oy' with θ=30°, the two normal stresses σx'=σy'
Determine:
(a)σx,σy,τxy;
(b)the principle stress state, and sketch it on an element;
(c)the maximum in-plane(xoy) shear stress state and sketch it on an element;
(d)the absolute maximum shear stress.
Homework Equations
ok i haven't been given a set of equations specifically for these questions because its a course work, but my tutor heavily implied i should use Mohr's circle, I've been trying and i have identified I am going to have to obviously use Trig relationships and Algebra but apart from that I am totally lost. il insert the transformation equations i think might be useful. But obviously doing this with Mohr's circle the majority aren't really needed.
Pinciple Stresses
σx'= (σx+σy)/2 +(σx-σy)/2 cos2θ+τxysin2θ
τx'y'= -(σx-σy)/2 sin2θ+τxycos2θ
max/min in-plane normal stress:
σ1,2=(σx+σy)/2 +/-√((σx-σy)/2)^2 + τxy^2
the bit that's taking the sq root is obviously R in Mohr's circle
Max in-plane Shear Stress
τmax=R
Max in-Plane shear stress orientation:
tan 2θs= -(σx-σy)/2τxy θs1=θp1-45°
The Attempt at a Solution
Any question i have done like this before all principle stresses have been given, I am pretty lost without them... trail an error has led me to believe σy=40Mpa but apart from that I've been drawing Mohr's circles and getting lost in algebra and trig... HELP PLEASE! if any more info is needed just ask. its due in on tuesday and I've wasted 5days on dead ends... it surely couldn't be as hard as I am making it.
Homework Statement
Homework Equations
The Attempt at a Solution
Attachments
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