本帖最后由 泼墨 于 2013-12-19 19:24 编辑
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. B4 K% X. x. T( i: tTwo metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular
% j+ m3 d1 |4 T& }8 W( Zto block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the
) ^+ @. V% N# d$ ~, D% }6 nother end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface. , c9 M' l, d* }
Related dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular
3 L" u5 Y1 d9 i) W- Y7 `9 d; _/ Hcross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially - s* m& G/ Q+ T- g- t; E, O( G
straight. / z" z ~2 c0 p) H+ S
Neglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial 4 X# i: T9 ]: t3 b2 J- j3 Y. ~5 j$ {
elongation or compression of beams a and c .
' {% S% t# e& x' W& k2 Z. f2 `5 c" TUsing elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled 2 }" v; t6 G" C) g2 U' V0 [# ~
for 10 mm in the indicated direction.
: D2 e, w4 s; P) @4 r x9 `Use Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should ! B* ] N9 [* @0 a5 M& [) C
also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure " P8 A3 O. Q* p4 g9 [
looks realistic. % ^0 g1 B0 l: Q0 N
Please also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs $ b5 M1 W1 y9 O
which pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall 6 ^5 _# J, w. i1 Y7 m( d
surface at one end.
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发表于 2013-12-19 19:22:36
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