本帖最后由 泼墨 于 2013-12-19 19:24 编辑 ) e6 |1 w; k2 E* g
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Two metallic beams a and c are fixed to a block as shown below. Both beam a and beam c remain perpendicular
& W4 n% I; w, C) }+ c; |: {8 Rto block b at the connecting points. Beam a is attached to a wall and it remains perpendicular to the wall at the
9 i8 z" C& d e! B% Bother end. Beam c is passed through a hole in the wall. Direction of the hole is perpendicular to the wall surface.
( v9 F' N! t% e+ R8 O% wRelated dimensions are shown on the diagram. The diagram is in millimeter. Beams a and c have a circular 2 x+ U4 h8 @& z
cross-section with a diameter of 0.7mm. The Young’s modulus is 70 GPa. Both beam a and beam c are initially
/ G4 _ C) b* @, V c! A5 B6 @straight.
7 f( J2 n: A7 n# x& F$ W5 I& `3 U1 `Neglect gravity. Assume a perfect linear relationship between stress and strain for beams a and c . Neglect axial 0 Z' L3 E' D0 l# u; w
elongation or compression of beams a and c .
) |% } q6 t, i$ ~( uUsing elliptic integrals, derive relevant entities to predict the final shapes of beams a and c when beam c is pulled 3 P3 n3 e) v' U, e& l6 }
for 10 mm in the indicated direction.
0 v7 y$ @9 u6 ~% s0 e+ KUse Matlab to implement your derivations and plot the deflected shapes of beams a and c in a figure. You should
' e& e; A( {. o5 X) N: {also plot block b at the desired position. Please make sure your plot has a correct X-Y scale so that the figure ! k, ?$ }( a) Y4 E( Y
looks realistic.
! H% u+ y- x |: m6 m" YPlease also compare how close the deflected shapes of beams a and c are to circular arcs, by drawing circular arcs
}3 X' h8 f8 ?- h1 z nwhich pass through the two ends of beams a and c . The circular arcs should also be perpendicular to the wall
- P/ C) k8 D- l' |' Esurface at one end.
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发表于 2013-12-19 19:22:36
