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Unformatted text preview: Tutorial 7 r‘x _ \ W' Problem 12-13 compute the maximum slope and maximum defleotion of the beam. E1 is constant. 11-43 75 Determine the elastic curve for the cantilevered beam, which is subjected to the couple moment M0. Also compute the maximum slope and maximum deflection of the beam. E1 is constant. val E1531 = “Max + C, (1) dx . _ -._M9x2 , ’ Ely — 2 + C,x + C2 . (2) v, 1 Boundary conditions: I £2)- : at 'x I 0 dx . From Eq. (1), CI = 0 y = O at x =0 Fran) Eq. (2), C2 2 0 £12_—M0x dx EI dy —ML 9 :,__ _L=H____9.._ "m dx " EI Ans The negative sign indicates clockwise rotation. _ — Moxz ' A y 2E1 “5 . m fl 2E1 ns Negative sign indicates downward displacement. ( f.) 31—7. W13. Determine the equation of the elastic curve for the beam using the X coordinate. Specify the slope at A and the maximum deflection. E1 is constant. ‘v .19» Solution 12414 M. (El) MC!) :Ma("xz) L . me E 933 = Mow-E) 51% = Margin c1 _ {1; EH: :— MM; "EL” C1: + C1 . ‘(23 Bbundarycundifions: . 9:0 51 1:0 bzflflxtL meEq.{2). . L2 L2 M9}. 11(2 6} z 51‘ 3 (3} has I; :2 Jig—{31.13 ~— xa - 2L5) {4) An} Subéfimuex m w. 7 «mm - .1} ' 11.,” = Eli-MD Ana: 1- C) Problem 13—9. A11 A—36 steel column has a length of 9 m and is pinned at both ends. If the erossusectional area has the dimensions shown, determine the critical load. Est = 200 GPa, UyéZSO MP3,. F—ZOOmm—el _L - ‘ 'TIOmm l ="‘10mm T Solution 13—9 3 actian Prapmies .- A =33 (0.17} 43.19 ((1.15) s: 55g( 113") m1 I; = film-2) (03‘?) «2 iimm (-0.153) = 22.24533 (_ m") m4 9:: [Pcaauwfll +«-—-(9.xs}(um’) =1334533Ufl‘) m {Cflflwfi’} ‘ Critézc! Buffing Land : K = ‘1 for pin sappcrfltd ends mm. Amiyflig gum“: fumalm '33-‘52 p—_......2.. “. {KL}: - afii£®£1093f13345$3fl 122} {1(9)}z 3- 325229.27 N = 325 22: AM Criticai Stress 3 Eukr’x famuhis may 2355:: if a}, a: a? . ‘0': P“ 31522987 25913m226=155m2 0K! f“ A 352(12): ” at } Problem 13—17 The W310 x 129 structural A-36 steel column has a length . of 4 m. If its bottom end is fixed Supported While its top is free, determine the largest axial load it can support. Use a factor of safety with respect to buckling of 1.75. E = 21-0 era, 5,, = 250 MP3... w Solution 13-17 -W310x129 ‘Aslesoomml' Ix: 308(106) mm“ 13,: 100(106) mm‘ (controls) K = 2.0 2 2 3 6 P“: a»: £1: = 2: (210x10 )(moleo ) 3 323817 m (KL) [10(4000H ' P: __13,_,_ .7. 323827 =1850.44kN Ans ES 1.75 Check 3. oq— 3 = W =112.15 War: a} A 16500 OR ' 48331~Mechanics of Solid _ _ . StudentGuide, Tutorial and Assignm-t Problems: PROBLEMS ON DEFLECTION OF BEAMS 11-1 For the beam and loading shown, determine (a) the equation of the elastic curve for portion BC of the beam; (b) the deflection at mid—span; (c) the slope at B- Y t P=wL/5 E lq—L/2——>l<———- L ——>] Figure.11—l 11-2 A cantilever beam is 4 m long and carries a concentrated load of 40 kN at a point 3 m fi'om the support. / (a) Determine by using integrati n, the vertical fleetion of the free end of the cantilever 1f E165 MNmz. (b) How would this value clian e If the szme to load were uniformly distributed met the porti of th] cantilever ' support? 1‘ l r 1' i OkN t l i Figure 11—2 57 fl *muv \Iw' ’ 43331—Mechanicsof501id ‘ ' I . Smdthuide, Tutorial andAssigumcnzProblems_ PROBLEMS ON DEFLECTTON 0F BEAMS 11-1 For the bean: and loading‘shom determine (a) the equation of the elastic curve for portion BC of the beam; (b) the deflection at mid-span; (c) the slope at B. - ' 11-2 A cantilever beam is 4 111 long and carries a concentrated load of 40 kN at a point 3 In from the support. (a) Determine by using integration1 the vertical deflection of the free end of the cantilever 1f EI 65 MNmZ. (b) How would this value change if the same total load were applied but - miformly distributed over the portion of the cantilever 3111 from the support? 40kN Figure 11-2 57 ’ *mw g2: 1L=uamflmmas\ —._—-7,..‘—H:.‘i W %: Sgt-53L -.-.- _- 5.533-1-13’fi \Md’fl; DBL-L. 3 - . m . '7; #6:“) = ‘3 .35 ‘A‘tD—S'Oliwsa ‘ %, m " Lot.“ ___ #333,); \ong 34‘ .‘ ‘3 E1 ‘ 7 05 *59w0 (=- '3 “3-" -— 2:021, fikwa 2 --2.o*+é "mm ’ SW5 =. ._.__. ______, __ _._ ___.,.,_.._—.— H... u. _. ..._.... _.—.——._—_—.-__._ .__.._._.__ _________~_________.._.—_———--_________.. ___._—.—___—._‘.- .——-b--.——-_- flout-mm .- ----- —______w—_.._.——---——-—-—— __ -_____._...___.— —.-——.—. -.. __.—-. w...“ ____.._......._ _. .- ...— um“ —-.¢.._..- ._.......—_._._— ._-.—.—_ .._.._ w} GE’L -—. - _ ....—-—-....——.-..——-——___.. _.__.. _ ___.. __ .— _ a... ....__.._—-— .- _—........_...._ u— — 7 3 \3.72-Bf;l0%r¢ 3 Lfib‘S 7: £09 '2 0 65—1“). 3 x10 T‘ng. 13-2. The column consists of a rigid member that is pinned at its bottom and attached to a spring at its top. If the spring A ‘ . is unstretched when the column is in the vertical position, determine the critical load that can be placed on the coiumn. £+ 2M1. =0. PLsine—(fl-Sifl 8Xst 3F“ P=kLcose Sinceflis small cosfl=1 13—3 The. leg in (3) ms as a column and can be modeled (b) by the two pin-connected members that are attachad lo a torsional spring having a stiffness k (torquca‘rad). Determine lh: crisica] buckling load. Assume the bone malaria] is n‘gid. l— 2 A! M18] (”MA = 0; —P(6)(§} + 2H) = o Require: 4 Ru: 1 Am '865 ...
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