本帖最后由 泼墨 于 2013-12-19 19:24 编辑
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" E7 D/ `: B* S4 _+ M1 V7 L2 yTwo metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular * C& x0 V, C% W! S# g
to block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the 2 H$ M+ e4 x5 B1 h
other end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface.
# t9 H+ ^9 K$ }. {9 U* URelated dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular . v5 L# A' g5 T8 o8 s+ N
cross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially & d. Q3 `7 j& {1 Z1 E
straight.
4 n# n4 L# c; ]6 kNeglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial
& x& J$ `; ^& Telongation or compression of beams a and c . . m8 W y- G. o: F' ?9 R0 O
Using elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled
0 r" }; `' t# C5 W2 ifor 10 mm in the indicated direction. ; c' a- a1 B c6 V- D$ b* ^
Use Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should 1 z: s! b6 b' L! R; J" N3 A
also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure 0 `) r7 ? K; p$ i
looks realistic.
% @( [0 x' q- ]: B& D' M! p. R# |4 BPlease also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs & R2 b2 E! _7 R( i, x
which pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall 4 x" W' l' P2 t2 {7 |7 ]" \: b* P
surface at one end. $ i4 F; T2 j; g& t w
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发表于 2013-12-19 19:22:36
