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本帖最后由 潑墨 于 2013-12-19 19:24 編輯
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7 }0 @/ r* V! Y7 y8 |- rTwo metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular / N; b+ O% k1 _2 I: ` S' ~
to block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the 3 t% {( t4 I" r/ ?
other end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface.
* N: }% Z( J) x# {- N% HRelated dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular
/ A: n8 U% H* c0 u" m: M; Gcross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially
$ ^) a/ x+ D9 U4 u' v, ustraight. 1 ~+ n% a0 j+ w; i9 T c
Neglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial 2 b& G& s& O. {8 w: k2 D
elongation or compression of beams a and c . K) T( o( _/ T* x/ ^, Z
Using elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled
9 t; n4 V: K [" C8 }* Hfor 10 mm in the indicated direction. : A: J/ z L/ U( t
Use Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should
# q2 ]9 m% K- M. z9 a8 I: U) `also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure " k9 |0 f+ W) [8 n' m0 j- l& s
looks realistic.
1 f( d5 D+ u4 N" N5 rPlease also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs
8 e8 [% L4 O% W, y& S$ h; uwhich pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall
+ U7 Z3 o; u: s# dsurface at one end.
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