CH9(1-42)

CH9(1-42) - @T|ih ?i <14 Lqirupdwlrq dqg dvvxpswlrqv...

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±²@T|ih ³´?i <14 Lqirupdwlrq dqg dvvxpswlrqv surylghg lq sureohp vwdwhphqw Ilqg whuplqdo yhorflw| ri eorfn Vroxwlrq I vkhdu @ Z vlq ± ² @ I vkhdu @D v @ Z vlq ±@O 5 ² @ ³gY@g| @ ³ ± Y@ ± | W θ F shear L L y ru Y @ ² ± |@³ Wkhq Y @+ Z vlq ±@O 5 |@³ Y @ +533vlq43 @ 3 = 63 5 , ± 4 ± 43 7 @ 43 5 Y @6 = ;9 p2v :5<
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<15 Lqirupdwlrq dqg dvvxpswlrqv surylghg lq sureohp vwdwhphqw Ilqg g|qdplf ylvfrvlw| ri rlo Vroxwlrq Vdph vroxwlrq surfhgxuh dssolhv dv lq Sure1 <141 Iurp wkh vroxwlrq wr Sure1 <14/ zh kdyh ± @+ Z vlq ²@O 5 |@Y ± 7 3 ± +8 @ 46, @ 6 5 , ± +3 = 35 @ 45, @ 3 = 8 ± @8 = :3 ± 43 6 oei0v2iw 5 :63
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<16 Lqirupdwlrq dqg dvvxpswlrqv surylghg lq sureohp vwdwhphqw Ilqg g|qdplf ylvfrvlw| ri rlo Vroxwlrq Vdph w|sh ri vroxwlrq surfhgxuh dssolhv dv lq Sure1 <14 dqg <151 Wkhq ± @+ 5 3 ± +8 @ 46, @ 4 5 , ± 8 ± 43 7 @ 3 = 45 ± @6 = 53 ± 43 5 Q ² v2p 5 :64
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<17 d, Xsshu sodwh lv prylqj wr wkh ohiw uhodwlyh wr wkh orzhu sodwh1 e, Plqlpxp vkhdu vwuhvv rffxuv zkhuh wkh pd{lpxp yhorflw| rffxuv +zkhuh gx@g| @3,1 :65
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<18 d,1 Wuxh e,1 Idovh f,1 Idovh g,1 Idovh h,1 Wuxh :66
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<19 d, E| vlplodu wuldqjohv x@| @ x pd{ @ ± | y y U max U U ru x @+ x pd{ @ ± | , | x 3 = 6 @ 3 = 335, | p2v @ 483 | p2v y @3 e, Iru ²rz wr eh luurwdwlrqdo Cx@C| @ CY@C{ khuh Cx@C| @ 483 dqg @ 3 1 Wkh htxdwlrq lv qrw vdwlv³hg> ²rz lv urwdwlrqdo 1 f, Cx@C{ . Cy@C| @ 3 +frqwlqxlw| htxdwlrq, Cx@C{ @ 3 dqg @ 3 vr frqwlqxlw| lv vdwlv³hg 1 g, Xvh wkh vdph irupxod dv ghyhorshg iru vroxwlrq wr Sure1 <04/ exw Z vlq ± @ I vkhdu = Wkhq Y I v @OZ |@² I v @ YOZ²@ ± | I v = 6 ± +4 ± 3 = 6, ± 7 @ 3 = 335 I v @4 ; 3Q :67
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<1: Ydolg vwdwhphqwv duh +f,/ +h,1 :68
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<1; Wkh vkhdu irufh lv wkh vdph rq wkh zluh dqg wxeh zdoo> krzhyhu/ wkhuh lv ohvv duhd lq vkhdu rq wkh zluh vr wkhuh zloo eh d juhdwhu vkhdu vwuhvv rq wkh zluh 1 :69
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<1< Dvvxph d olqhdu yhorflw| glvwulexwlrq zlwklq wkh rlo1 Wkh yhorflw| glvwulexwlrq zloo dsshdu dv ehorz= Ehfdxvh wkh orzhu sodwh lv prylqj dw d frqvwdqw vshhg/ wkh vkhdu vwuhvvhv rq wkh wrs dqg erwwrp ri lw zloo eh wkh vdph/ ru ± 4 @ ± 5 ² 4 gY 4 @w 4 @ ² 5 gY 5 @w 5 ² 4 ± + Y ² Y orzhu , @w 4 @ ² 5 Y orzhu @w 5 4 @w 4 ² ² 4 Y orzhu @w 4 @ ² 5 Y orzhu @w 5 Y orzhu + ² 5 @w 5 . ² 4 @w 4 ,@ 4 @w 4 Y orzhu @+ 4 @w 4 , @ + ² 5 @w 5 . ² 4 @w 4 , :6:
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<143 Lqirupdwlrq dqg dvvxpswlrqv surylghg lq sureohp vwdwhphqw Ilqg wrutxh uhtxluhg wr urwdwh glvf1 Vroxwlrq ± @ ²gy@g| ± @ ²u$@ ± | gW @ ugI gW @ u³gD gW @ u + ²u$@ ± | ,5 ´ugu D y dr Plan View w Wkhq W @ ] u 3 gW @ ] u 3 3 + ²$@ ± | ,5 ´u 6 gu W @+ 5 ´²$@ ± | , u 7 @ 7 m u 3 3 @5 ´²$u 7 3 @ +7± | , Iru ± | @3 = 334 iw> u 3 @9%@3 = 83 iw> $ @4;3 ± 5 ´@ 93 @ 9 ´ udg2v ² = 45 oei0v2iw 5 W 5 ± 3 = 45 ± 9 3 = 334,+3 = 8 7 @ 7, W @ 555 iw0oei :6;
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<144 Lqirupdwlrq dqg dvvxpswlrqv surylghg lq sureohp vwdwhphqw Ilqg wrutxh uhtxluhg wr urwdwh glvf1 Vroxwlrq Wkh sureohp lv wkh vdph w|sh dv Sure1 <143> wkhuhiruh/ W ± 5 ±²$u 7 3 @ +7± | , zkhuh u @3 = 43 p> ± | @5 ² 43 6 p> $ @ 443 udg2v> ² @9Q ³ v2p 5 W ± ² ; ² 43 ² 43 7 @ +7 ² +5 ² 43 6 ,, @ 9 = 5; Q ³ p :6<
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<145 gW @+ ±x@v , gD ± u @ ±u$ vlq ² 5 ³u 5 gu@ + vlq ² , @5 ³±$u 5 gu@´ W ±$@´ ,+5 6 @ 6, m u 3 3 @+5 @ 6, 6 3 ±$@´ r β θ T ω r 0 :73
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<146 Lqirupdwlrq dqg dvvxpswlrqv surylghg lq sureohp vwdwhphqw Ilqg irufh uhtxluhg wr sxoo sodwh1 Vroxwlrq Yhorflw| glvwulexwlrq= V=0.4 m/s Irufh @ ±D @ ² + gY@g| , D @+ 3 = 95 ± +3 = 7 @ 3 = 335, ± 4 ± 5, ± 5 I @ 7<9 Q :74
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<147 Lqirupdwlrq dqg dvvxpswlrqv
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This note was uploaded on 12/09/2009 for the course CE 2200 taught by Professor Deng during the Spring '09 term at LSU.

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CH9(1-42) - @T|ih ?i &lt;14 Lqirupdwlrq dqg dvvxpswlrqv...

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