本帖最后由 泼墨 于 2013-12-19 19:24 编辑
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2 a6 H. N- p7 j7 dTwo metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular , I# r1 r6 X/ [+ m
to block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the 2 p, U; M( A0 y. t$ }% N; V
other end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface. 1 ~' v$ D' w9 j* z6 _) r& x1 q' V
Related dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular ( ]6 g) c" H$ o$ o2 z3 \
cross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially , X9 F- z) ]7 R9 Z
straight.
$ ~% w" v' {8 t. u, e7 |Neglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial
; I; z' c& @6 xelongation or compression of beams a and c .
& n& ^( n7 J* a. KUsing elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled
$ M6 g# L+ R' @* v' Gfor 10 mm in the indicated direction. ' F8 R+ e! N. {; Z1 z4 R( ]: z
Use Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should , _, w( h0 b4 X# u, B
also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure : I8 w3 n4 X @) J6 J" s) A
looks realistic. 8 u0 N1 ^- E! d% }( m2 F3 l
Please also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs " Y* ~' r: g4 W/ @: F
which pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall
3 y- t' p# c, y4 Q7 f2 Ssurface at one end. 4 u' ~3 ?8 c! G+ I, j" Z) U c" g
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发表于 2013-12-19 19:22:36
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