本帖最后由 泼墨 于 2013-12-19 19:24 编辑 # L y% V. q+ e
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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
: Z: ?$ L3 Y1 I& b8 W5 mto block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the 7 v% F5 e. _* A X. O
other end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface.
1 I3 i9 F, G1 E! ~7 S0 p) p5 vRelated dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular 0 v/ E4 L1 I& Y8 }4 G0 O" h
cross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially ' I u3 E# E7 M% P8 _
straight. 6 H! ]: p9 C: A
Neglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial + {+ c" Q$ |) a3 m' l3 z" R9 W7 V& T, ^
elongation or compression of beams a and c . ) ?, o2 u# {2 g; o4 M. T4 ~
Using elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled : z3 |1 ~/ X- J0 A- F
for 10 mm in the indicated direction.
* x+ \% _: D/ N% k4 c* s) ~* mUse Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should
; G ^0 c' J1 y" B$ talso plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure
# m* ~2 a, m5 blooks realistic. ' f& H; k, r8 q% L7 F4 L$ L8 N: W
Please also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs . U. R$ m4 [1 r- x) D/ E' [
which pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall 3 F8 y0 U0 U; @" S4 {- m5 J8 h
surface at one end.
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发表于 2013-12-19 19:22:36
