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Unformatted text preview: Tutorial 7 r‘x _ \ W' Problem 1213 compute the maximum slope and maximum deﬂeotion of the beam. E1 is constant. 1143 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 = MowE)
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.,” = EliMD 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; = ﬁlm2) (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 A36 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 = 210 era, 5,, = 250 MP3... w Solution 1317 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 Assignmt Problems: PROBLEMS ON DEFLECTION OF BEAMS
111 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 112 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 111 For the bean: and loading‘shom determine (a) the equation of the elastic curve for portion BC of the beam; (b) the deﬂection at midspan; (c) the slope
at B.  ' 112 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 112 57 ’ *mw g2: 1L=uamﬂmmas\ —._—7,..‘—H:.‘i W %: Sgt53L .. _ 5.533113’ﬁ \Md’ﬂ; DBLL. 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.——_ ﬂoutmm .
 —______w—_.._.——————— __ _____._...___.— —.——.—. .. __.—. w...“ ____.._......._ _. . ...— um“ —.¢.._.. ._.......—_._._— ._.—.—_ .._.._ w}
GE’L —.  _ ....——....——...————___.. _.__..
_ ___.. __ .— _
a... ....__.._—— . _—........_...._ u—
— 7 3
\3.72Bf;l0%r¢ 3 Lﬁb‘S 7: £09 '2 0 65—1“). 3 x10 T‘ng. 132. 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—(ﬂSiﬂ 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 pinconnected 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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