本帖最后由 泼墨 于 2013-12-19 19:24 编辑
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" ^, e5 c# y8 h- cTwo metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular
- u1 n; U% ] e# |! x! p* Fto block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the
+ A5 c7 B$ a4 W) z. o$ ]$ fother end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface.
' D0 c i7 d8 ~" eRelated dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular
4 n) P$ [* z' m7 K8 Dcross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially 4 u$ W: z- c& B& Z+ ^4 n( z
straight. - y* P: o9 t+ V* s, U
Neglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial . Y) C. S% z* s/ p! ^$ y: v
elongation or compression of beams a and c .
8 A5 s$ X- |8 B7 N1 O3 sUsing elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled / B. `4 f! E* o' L' \8 |
for 10 mm in the indicated direction. + y: y7 ~1 w8 c& t/ W
Use Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should S5 U% `. i1 X: N# [, M
also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure 4 s6 g3 f- e0 A' P' p9 N) b
looks realistic. , c0 s4 B" F8 S+ T1 c
Please also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs , \& B; J2 |5 g, k& q @
which pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall # x; W# M2 c# S" x+ ~2 V0 q6 e
surface at one end.
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发表于 2013-12-19 19:22:36
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