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ginrummy
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Homework Statement
http://img.waffleimages.com/5b5524d885644e9f1c76a800c4b0701a0606268a/problem6.jpg
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I am given this drawing and stress v strain diagram, and am told to find the deflection, ∂, at 4 (the end of the beam), if P = 50 kN.
Homework Equations
When solving by geometry:
E = stress/strain
∂ = PL/AE
F = k∂
k = AE/L
The Attempt at a Solution
Using the stress v strain diagram provided, I solve for the elastic modulus (Young's modulus):
E = (700x10^6 N/m^2)/(.35) = 2x10^9 N/m^2
Take the moment about point A to solve for tension in the cable, T2:
(clockwise is positive) ∑MA= 0= (1.4 m)(-T2 N)+(2.2 m)(50,000 N) => T2= 78,571.43 N
From there, I do a compatibility sketch. Unfortunately I do not have software on my computer to draw up a diagram to post, but it is a right triangle, with the length of the bar as the "height," and ∂4 and ∂2 serving as the bases in a similar triangle relationship.
Therefore:
(∂4/2.2)=(∂2/1.4) leading to ∂4=(2.2/1.4)∂2
Therefore, using the Hooke's Law equation:
T2= k2∂2 => ∂2= T2/k2
k2= AE/L= [(1.25x10^-4 m^2)(2x10^9 N/m^2)]/3m => k2= 83,333.3 N/m
Therefore:
∂2= 0.943 m
∂4= 1.48 m
These deflections seem WAY too high to be correct. I feel confident that I'm using the right process, but there has to be some mistake I'm making somewhere.
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