Solutions 3

Solutions 3 - 4-3 The A~36 steel column is used to support...

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Unformatted text preview: 4-3. The A~36 steel column is used to support the symmetric loads from the two floors of a building. Determine the loads P1 and P; if A moves downward 0.12 in. and 8 moves downward 0.09 in. when the loads are applied.'l‘he column has a cross.sectional area of 23.4 inz. Inter-d For“: .' As shown on FBI). Displacement: Forpoiu A -2P (IM) 3 —; -0,|2 ' ,8 —'—_.. 6‘ AE " (23.4) 29.0! 10’) .4". *muzmz: (23.4) 29.0! Iﬂ'l B B 2:215:29. +9: lli ForpohtB P, 3 PL . -2(P. +P.)(I2Hl2l p a —; -01” I ——'_ 6‘ 2A5 a (23.4» 29.0mm ‘ 4' 20.062511“. w, R: Solvngqs. ll]:ndl2ly'¢ﬂs: r. =1onup .m ﬂ.=-.2f,’ 5 . map Ans g‘n—zafﬂ) 4-15. The assembly consists of three titanium rods and a rigid bar AC.'l'he cross-sectional area of each rod is given in the figure. If a vertical force P = 20 kN is applied to the ring F. determine the vertical displacement of point F. E" = 350 GPa. PL ”(10’ W) ‘I—. AB (GOXIO‘XSSOXK’) Inn PL mo’xzooo) -—.ﬂ. .0!” 5‘ as 45(10‘X350Xl0) ' '"' PL 2000’le 8932—- _..___ . um .43 vsuo‘xasoxw) "m 6. - [9159+ gmlﬂm - l.092 Inn 5: ' 5n 4* 5m a LM+ 1.14” I 2.23 Illll A. l. (4” 4.01:! a 0.1; "M *4—24. The rod has a slight taper and length L. It is suspended from the ceiling and supports a load P at its end. Show that the displacement of its end due to this load is 6 - PL/(wErer). Neglect the weight of the material.The modulus of elasticity is E. L-t-xo. 2; ‘0 . Ln '1 't '2 “'l ’1 r; -r. r.L+(n-r.)x 1h . + — us r(x) an L x- L L Aw - 5w. + (r; - nm’ x. ’7 8f Pd: .PL’ 1. 8:: — gal.) A(x)£ TE 0 mt. + (r,- "ml .-P_L’.__I__.l‘. -_£_ _.__ -L, n ¢ RE (r; -r;)(r.L+(r; -f|)£) o 35“: -7.) r.L+(r3 -r.)l. ’1'. P _ PL’ l 1 PL’ r. - r; #30; - r.) rzL nL REV; - r.) anL PLz - r. PL IE"; - I.) an]. tEru'. QED ...
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