本帖最后由 泼墨 于 2013-12-19 19:24 编辑 8 J6 K6 [, j3 N2 j( l4 G3 Z
( [6 u; V$ w) o! N' m, M3 xTwo metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular
1 J D: a+ d4 H2 M4 }$ Q! T1 h: Gto block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the ' U8 ~; a2 Z* U) X: z t
other end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface. 0 x$ }( Q0 W; w9 I4 @! n& q
Related dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular
1 V2 l' W' ^ X# [# _+ ] }cross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially - r+ U* D9 q/ a3 K! o/ ~0 p
straight. " }, x: o! H0 W3 L- |7 p! n Z8 U
Neglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial
9 g; j4 e( O3 v( z+ `' Qelongation or compression of beams a and c .
3 V( L3 \- |! M' _; `/ ^# ^Using elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled
; ^6 b9 a, X M* W* jfor 10 mm in the indicated direction. ! D' q, q. s# |5 ]
Use Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should # }; f2 I5 ~5 K: `& r8 J! t3 {
also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure
. N2 ?# [* J" m( y7 hlooks realistic. ' b- u y( g2 Y3 E+ n b+ s% e
Please also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs
! t5 M3 G% d* L! ^+ X. Iwhich pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall 2 t U* M& B* \7 }! ^0 ]; C3 ]3 R: h
surface at one end. 0 O! A$ r2 u% l D3 |: v, W! i2 c$ m
|
发表于 2013-12-19 19:22:36
