本帖最后由 泼墨 于 2013-12-19 19:24 编辑 ( U1 f) B& B) ]
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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
, O. M, x7 W5 K! |) ito block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the ( E6 ~* |# b3 P
other end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface. 6 E% \7 c2 E% T# w
Related dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular
/ R+ ]% L: o* ucross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially * B/ J) O; u1 @0 ~1 C: u
straight.
- h Q3 X5 T {0 rNeglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial ! D: k- s* X. T- i) B5 u
elongation or compression of beams a and c . 2 H% D4 C. {+ z
Using elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled - E& \, |; _: h/ N( }* X/ l4 I9 F/ Y
for 10 mm in the indicated direction.
& Y( Y) R2 \4 ]- ~1 S! s8 ^Use Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should
) {9 H% V+ Q9 Dalso plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure
( f% w% x4 q- X0 p: j) hlooks realistic. ; N- q ?6 J L( T X4 r5 f
Please also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs
( I6 ]1 y8 w' S; o6 b1 k; _which pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall
, i. P- k! ?; ]2 G4 [surface at one end.
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发表于 2013-12-19 19:22:36
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