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
( b' {5 o: Z& P& yto block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the
/ f7 n; M0 L/ p" [- eother end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface. " f% c+ Y4 y3 Z/ o1 ]# A# K
Related dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular
; _. T% o5 R" }" R+ Gcross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially 2 S5 O) J( n+ t- N( Z
straight.
/ a7 A2 w4 k9 V7 uNeglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial
6 p, f& I0 I( xelongation or compression of beams a and c .
$ l" u! z, {2 }- O# n2 @* ?% CUsing elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled 4 } p4 Q! [7 j5 x# f/ q' J& {
for 10 mm in the indicated direction.
6 Q1 X N/ W5 T/ T. N% BUse Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should
& _0 ~# c* B' q7 xalso plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure " R; G$ ` i; i1 d) H, q1 p
looks realistic. 0 N) I" m1 M9 R1 |4 V
Please also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs
% q4 i) \" v. J' Zwhich pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall
8 s) X) n( T5 `5 ?) }* ?' r: o" v6 ~surface at one end.
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发表于 2013-12-19 19:22:36
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