本帖最后由 潑墨 于 2013-12-19 19:24 編輯 ( O* k' X+ g7 t" b& _
; _+ t" f7 N2 Q+ \& c8 QTwo metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular
- c! K6 Y/ J- b+ g j( u8 s% U" Kto block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the 5 N. o, J: @7 z
other end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface. 9 r: t! P9 Z$ C' D
Related dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular
% _0 ]* k* f0 k$ icross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially , v& O* p: S5 y5 v
straight.
: f* \, r; `$ ^Neglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial
* X+ f+ [$ i4 P8 r2 |9 l5 q$ |6 ~elongation or compression of beams a and c .
, b8 a; U1 j% _$ U9 ]/ wUsing elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled
0 _& Q- C" B3 y0 _- l% C( f$ Ufor 10 mm in the indicated direction.
% D) o6 R2 V; K1 A0 wUse Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should . f) z, z% }2 g! C% ^
also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure 9 |2 \" g1 z1 s" k& u( z' z
looks realistic.
" |0 Y+ S% I* b: Y5 x$ C: yPlease also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs 8 Y' V. f+ u$ z0 \
which pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall
0 ~" H" E' j0 N5 b4 l6 _- ?' j: d3 wsurface at one end.
5 k1 d7 p a! Q# W7 R |
發表于 2013-12-19 19:22:36
QQ好友和群
QQ空間
