本帖最后由 泼墨 于 2013-12-19 19:24 编辑
# Z& T# h' y/ @& n' ^9 V
+ Q9 Y6 h/ D" g$ `- P. C- dTwo metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular % O- ]% T+ _; K3 k- {2 E7 N5 T
to block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the 7 m4 z) U$ |$ U; e. k
other end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface. % a; g7 l/ [* a$ l
Related dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular
5 {" J: X5 ~9 X& ]' scross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially
/ s# Z0 O4 \* r; g* l' j( tstraight.
8 l0 x) J7 U1 ?3 c8 JNeglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial : U$ B$ T$ ^- @9 F/ a
elongation or compression of beams a and c .
6 I5 {% j: H% f9 d$ RUsing elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled ! |4 T7 {" X2 ^/ q3 B, x1 c5 Z
for 10 mm in the indicated direction.
0 V7 }7 d) ~! u0 Z3 l/ ZUse Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should + y3 A0 C! h1 |& R
also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure
2 p2 @# k' C% I; n$ `$ L+ alooks realistic. 8 W D) h! a c+ `( y1 H" F, g& v
Please also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs 3 D# p6 F% P- h: ~( Q/ L9 `
which pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall
$ n+ k s0 A7 e& x& t( Ssurface at one end.
* f2 Q4 |7 I, D+ f- ~# R4 P* C1 ` |
发表于 2013-12-19 19:22:36
