本帖最后由 泼墨 于 2013-12-19 19:24 编辑 6 Q3 D$ s1 C+ B' }8 d: o
2 h8 ^9 l( n. b/ l4 }# JTwo metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular
# ?. v" o0 Z, h6 ^+ u6 b5 Vto block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the
! j9 s- q, Z/ ^; ?% k" Gother end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface.
- F# Y |* S. O% i' _Related dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular ) k0 f9 e: s2 U9 w. H
cross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially
: E& P9 o7 P, [% W6 I# Jstraight.
. w% o6 V7 |7 Y6 ]6 [- [Neglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial $ g! ~9 t2 S. q0 O. m
elongation or compression of beams a and c . ! k$ o* ?9 V% S8 S1 v* |
Using elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled # _. C* y" G% {3 U% ]- @- ^
for 10 mm in the indicated direction. 7 z* W" ?$ e6 @( v
Use Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should ! ^% {: Y7 P4 w2 f' Z* }
also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure
0 ?2 |( b9 E D& Q8 Xlooks realistic. % [- m9 h1 e6 |- D0 R
Please also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs
% L, v! W; V" B% Ywhich pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall
! D* Y; T1 e* k) P: ]6 Esurface at one end.
y: f' j* U. V O/ z7 _/ n5 ` |
发表于 2013-12-19 19:22:36
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