本帖最后由 泼墨 于 2013-12-19 19:24 编辑
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Two metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular
( L# i, o7 y4 @, P3 y& ]% n1 X, |to block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the
y+ y% [6 H- M# Lother end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface. ) m- k1 |- C9 K$ i
Related dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular
+ c: } y2 B3 s5 B. e2 H. c2 ^5 Zcross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially 3 m$ v: X9 t; L- R& D- I6 \% ^- a
straight. 9 u6 T. ?2 p9 [3 t0 _) r% _! g5 ]
Neglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial
8 G7 D2 z: N6 n# G1 V% l4 Y- m8 Melongation or compression of beams a and c . 6 F& U% o' l6 Z; v# e# h- n
Using elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled
_0 P1 A) m: ffor 10 mm in the indicated direction. # ?: o5 v: U. ]8 x
Use Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should & D/ B# `" j1 u/ @' O
also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure ( f/ _* W |( Q+ J3 y- _/ v1 d
looks realistic.
9 \; r; P' G3 h# R/ D2 I+ M9 qPlease also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs
& Q' Y! w! D" {# m# j e5 H4 d& awhich pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall . W! l R4 i* f# S ]5 }- f
surface at one end.
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发表于 2013-12-19 19:22:36
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