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NEGATIVE_40
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Homework Statement
The 30mm diameter A-36 steel rod (E=200x10^9 Pa) is subjected to the loading shown. Determine the displacement of end A with respect to end C. (see attached picture)
Homework Equations
[tex] \delta = \frac{PL}{EA} [/tex] (eq. 1)
where delta is the deflection, P is the internal force, E is Young's modulus and A is the cross sectional area.
[tex] \delta_{A/C} = \delta_C - \delta_B [/tex] (eq. 2)
The Attempt at a Solution
I first turned the two forces at B into a single force of +48kN. Since [tex] \sum F_x = 0 [/tex] I determined the reaction A to be 42kN. I then took a cut at a point between A and B, and determined the displacement of B by eq.1 giving -0.1188mm (to the left). Similarly I then took a cut between B and C and determined the displacement of C and found a dispacement of -0.3819mm. Then by eq. 2 the displacement of A relative to C is -0.2632mm. This answer is incorrect though.
I spoke to my tutor about this earlier today, and he told me I could move the reaction at B to any point along the line of the beam (so any where between A and C). Doing this I found an internal force of -42kN (compression), which by equation 1, for the whole beam, gives a displacement of -0.2971mm, which is also wrong.
The stated answer in the back of the book is -0.772mm (is the textbook's answer correct?) I've been trying all sorts of combinations on this problem for days now, and am no closer to solving it. Any help would be appreciated!