本帖最后由 泼墨 于 2013-12-19 19:24 编辑
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8 j: C- V% a% d r0 P: G& w# |& O$ K; CTwo metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular
x3 C8 l3 y1 G: f! T/ Wto block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the
9 g& n" Z) }! A p& }. Z; r. |other end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface.
) ?+ b$ _. Q# eRelated dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular
# a5 G& e8 _. Bcross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially
; ~8 E- I+ t1 J; f4 r) ]: Tstraight.
0 F, u$ v; A6 R- K4 WNeglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial 8 {3 O. n4 {) ?8 X$ ^& J& V
elongation or compression of beams a and c .
" _: r. L q5 o! O7 I0 \Using elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled
! g* i( e: l4 g% nfor 10 mm in the indicated direction.
3 j8 j/ M; [" H" lUse Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should 0 S9 g) o* R! Z
also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure ! S5 J6 \, |3 \, A9 I/ |
looks realistic. 2 s( a5 n- Q' I0 G* s1 |4 X
Please also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs
0 G5 U) q. N2 D) O. f/ ]4 Z& u/ ?6 cwhich pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall ' t! W8 n% f) k) s4 p5 |0 _' C9 A
surface at one end.
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发表于 2013-12-19 19:22:36
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