Class_notes_week15_16

Class_notes_week15_16 - a??? {u W k , 4. W A w row!»...

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Unformatted text preview: a??? {u W k , 4. W A w row!» \.,_«_5 WE gr,“ y 10.1 Knowing tha: {he torsional spring at B is Of constant K bar AB is rigid, determine and thai the the critical load PU. 19.4 Two rigid bars and BC are connected by a pin at C as shown. Knowing that the torsional spring at B is of constam K, determine the critical load PCr far the system. ‘ . £4,463 1 No 7%: flmfi’ dig/firm}: 13g 35$ fivaww‘g Guggemmg m CR7 PM (fig’flv iflf “We €3bé€rmm( 715402 i5 wziewqu, J WM? , 9/ 5 WW): Pg» if? \ 2 '- m UJ ,FCY-f: W E MOI/1 ( I; i j: HM,“ ’ 1‘ «2 W113 a mzvaagmg \, / { émtkzbiéfldj”, Yaw {:3 A ($5? aymjwé UL Poiagafin “‘ W“ [3w] Par“) g a r 3 a :. 9 ‘ * ‘u‘wr (5)0nefixed end, ‘ ((1) Both ends fixed. (in) Both and; A iIu-xeu one inned end P , . i L l a SAMPLE PROBLEM “10.1 An aluminum column of iength L and rectangular cross sectien has a fixed end B and supports a centric load 212A. Two smooth and inunded fixed plates te— strain end A from moving in nne of the vertical planes of symmetry of the col‘ mm, but allow it to move in the other plane. (a) Determine the ratio (1/1: of the two sides of the crass section corresponding tn the most‘efficient design against buckling. (37) Design the most efficient cross section for the column, knowing that L = 2031., E = 10.1 X 106 psi, P z: 5 kips, and that a factor ef safety of 2,5 is required.- SOLUTlON h Buckling in xy Plane. Referring to Fig. 1018, we note that the effec~ live length ’ef the column with respect to buckling in this plane, is L, = 0.71., The radius of gyration 'rz of the cross section is obtained by writing I J‘ba3 2 . and, since I1 "2 Ar?a r3 = = lid—b“ 2 £13 yz = a/Vfi The effective slendemess ratie of the column with respeet to buekling in the lane is _ W p is 0.7L _ (1} i} .7 [1/ VI 12 _ Buckling in xz Plane. The effective length of {he column with respect to buckling in this plane is L: = 2L, and the correspnnding radius of gyration is r, = b/V’ii, Thus, L m “i (2). 2‘}; Wm - n. Mast Efficient Design. The most effigien: design is that for which the cfitical stresses Corresponding tn the two possibie modes of buckling are equal, Refening to Eq, (1013’), we note that this will be the ease if the two values ebtained above for the effective slendemess ratio are equal, We write 0.7L “ 2L _ L? a/V. 12 b/x/ii \f x a a and, solving fur the ratio a/b, g = j)— ; é 0.35 4 I). Design for Given Dam. Since ES. = 2.5 is required, Por = (1513,)? = (2.5)(5 Rips) = 125 kips ' Using a = 0,35b; we have A = ab = 0,3552 and 12,500 lb 035:»? Making L = 20in, in Eq. (2), we hava Lc/ry = 138.61%, Substituting for Pet 0-“ = :4— = . E, LE/r, and 9'“ inte Eq, (10.13”), we write 'n'ZE _ 1250515 __ «200.1 >< 105m) (Lg/r)2 ‘ 0.35221 (1386/11): b = 1.6mm a = 0.355 = “0.567121: «1 l l i s' l E 10.11 A column of effective length L can b: made by gluing together identical planks in either of the arrangements shay/n. Dctcrmizxe the ratic of tha critical load using the arrangement a to the critical load using the arrange- ” " mam bk 5 _ v Ii. i L. ’ ‘ ' +l l4“ [1/3 i (a) Fig. 3310.11 ; _.L_;_.c._;~JW-.;-.:._x.;.. .. .a.w.....vx_;_me4..._._4.;. 10,21 Caiun’m AB emits a centric load P of magnitude 15 kips. Cables BC and 82) are tau: and pfavent motion 0f point B. in the .152: pianc, Using Buicr’s formula and a factor of safety 0f’2.2, and neglecting the tension in the 035353, determine the maximum allowable length L. Use E = 29 X 205 psi. ‘ g”: ” 3 L15... 11,. .3, .. L‘i’ -._-r..-,..___41_._ p.” y g N I t I x' i i 1 “MMMMMW¢Tflmw_ ;L+jx M— W10><22 L1 LQM l $71.;iyuvifljfl_ r..___,).-w. 1...... m-.. " €‘g3'r;i_§j%:i;;§;j: I I l'l ‘ w L fBLEOx of safcsty is the same with raspect to buckling in the xz and ya planes. (b) Using the ratio found in pan a, design tha cross section of the column so that the factor of safety will be 3.0 when P = 4.4 kN, L = 1 m, and E = ...
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This note was uploaded on 05/20/2010 for the course CE 3400 taught by Professor Moorthy during the Spring '09 term at LSU.

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Class_notes_week15_16 - a??? {u W k , 4. W A w row!»...

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