Identifying Stress in Three Rods: A Practical Approach

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The discussion focuses on calculating stress and deflection in three supporting columns under a load. The key point is determining the load at which the outer columns deflect by 0.3 mm, with no stress in the interior column at that point. The approach involves calculating strain based on the displacement of the top cap and ensuring the forces in all columns equal the total load. If the calculated displacement is less than 0.3 mm, it indicates the middle column is not bearing any load, simplifying the calculations for the outer columns. The collaborative input from participants helped clarify the solution process.
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Homework Statement



See attached - not the yellow engineering paper.


Homework Equations



PL/AE = deformation


The Attempt at a Solution



See attached


I can't figure out what the heck I'm doing wrong - my work is a little scattered because I was kind of thinking while doing it...
 

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Looks like the outside columns equally support the portion of the load up to the point where their deflections equal 0.3 mm. Calculate what that load is for that deflection, and the stress in the outside columns (no stress or deflection in the interior column) under that load. Then the remainder of the load will be divided equally amongst the 3 columns.
 
Another way of doing it is to let the displacement of the top cap be x downwards.

Then assuming all the columns take some load, the strain in the end posts is x/125 and the strain in the middle post is (x-0.3)/125. Find the force in each column corresponding to the strain, and get an equation for x by saying the forces in the 3 columns sum to the total load.

If x comes out as less than 0.3, then the middle column did not take any load, in which case finding the load in the two end columns is easy!
 
I did it the way PhantomJay said and it worked like a charm! Thanks you guys!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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