本帖最后由 泼墨 于 2013-12-19 19:24 编辑 + o! v, f5 b( W
9 f7 V4 k U: R, i- D0 y! pTwo metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular . H) ~( L0 g6 h9 h8 @& ^: T
to block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the
8 i# w4 @' B* R6 |$ Rother end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface. 7 i% c. u% ]; O I
Related dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular
) ?# V' \# n9 Ncross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially # I% w% \5 u. j# X+ {1 B
straight.
0 m3 G$ M0 }5 `+ Z1 i f9 pNeglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial 2 D$ X2 o' u5 t; V5 e6 e
elongation or compression of beams a and c .
% R9 d% w' T. ]1 I9 H2 _2 @Using elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled
9 z# i$ T3 N9 s4 k9 Wfor 10 mm in the indicated direction. 9 g* E* R- ~) m& e/ |/ b3 O
Use Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should / a, P5 o1 z) w% r7 S) P- k
also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure
, D( ~8 ~4 f7 i8 [4 B5 n+ ylooks realistic.
: I% {! p9 J8 N' |# f2 wPlease also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs
5 P5 C6 K6 G/ z9 s4 U5 e$ P: Mwhich pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall 9 S( n0 K! o8 }5 k. H
surface at one end.
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发表于 2013-12-19 19:22:36
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