本帖最后由 潑墨 于 2013-12-19 19:24 編輯 9 a( s( ^6 P4 A7 S! ]7 s
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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
$ y3 p. _8 a6 w) yto block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the
% O; i7 a/ Q. c3 g: D$ ^other end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface.
: s$ r' S% |4 mRelated dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular ! H/ W% B- `+ P- I$ g5 E& R
cross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially
/ F f7 b' J) j' L5 P# o- s1 C+ ?straight.
: G- N; F+ @% i9 oNeglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial 4 q+ E. Z, p" l# Q) C3 J8 |
elongation or compression of beams a and c .
; x% ]$ f# R7 ?+ v; aUsing elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled 0 O/ u. _! G9 h2 [% L
for 10 mm in the indicated direction.
1 k! ?. @* \) b1 K$ }: m5 A8 EUse Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should
* d+ u+ u$ i/ e$ J _* G- Xalso plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure 3 q r, i+ o& ^: i
looks realistic. . x9 B7 S4 ? F# K; O5 Y+ i9 ^% ^" ?
Please also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs
: A. I: Y7 `( Z7 ?# a" T! jwhich pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall
; S& e1 ` |7 w1 }7 bsurface at one end. + I' R2 @$ j8 l; w+ |9 [
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發表于 2013-12-19 19:22:36
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