Quiz 4 B - 10 Points(3 3(b 3(C 4 Your Section#2 Your Name...

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Unformatted text preview: 10 Points (3) - 3 (b) - 3 (C) - 4 Your Section #2 . . . . . . . Your Name: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ENGRD 202 — MECHANICS OF SOLIDS Quiz #4/ B — Lecture #1 Wednesday, November 29, 2006 1. Shear—Moment Diagram. rI‘he figure at right shows a simply—supported beam which is supported at A and B and which is subjected to a uniformly distributed force of 4kips/ft starting at 10ft from A and extending to the right end of the beam. (a) Draw the free body diagram for the beam and determine the reaction forces. A simply—supported beam with a distributed load. (b) Draw the shear force diagram for this beam. (0) Draw the bending moment diagram for this beam. For parts (b) and (0) please indicate the maximum/ miniman values of V and M in each section of your diagrams. Your drawings MUST be clear enough to differentiate constant, linear, quadratic or other power law portions of the diagrams. Alternatively, you can also provide the functional forms of V(a:) and Mr . Bx: 0 SchD :7 Ay+fiy~120¢o E;MA_:—D a”) 3987 aimuj 7-D -.=7 By: 1924*? Ayféoac U”) 05%!” 7M 20 Bipv [0‘5 25:90 20 «‘VSO P9 szdflci‘p) -29x+M=P =5) m :ZOX @th 9,0 Arman) Afr—D V: 20a4x+v0 2.. 7: ... , ‘ ,20x+\£(xP,pxml,) \f so Mam) k ‘9'“ =0 1(x1-207H-rw) a m: ,«lxza purge-u lea/ff” * " g“. 20»¥(5C—~ro)+prv-V :0 ’— v Va [towwxfic—Wl 2.9123“? "mm? 2m, :0 P; azmc+¢(>e—rp)(x:°) , (xv-3‘0) IW+M=U MT:- ZDX —'2\(1+UW .3243? 4. fwx..3§170 M a; ,zw-a. may: , 22m: Ki‘pri’t M ,.— e—‘TM 29”? V 15 Points 2. Stresses in Beams. The figure at right (a) ' 2 shows a simply-supported “Inverted (b) ' 3 T—beam” loaded with a distributed load of : 3 10 [lb extending 6 on the beam from (G) _ 4 its left end at which point there is also a point load of Ba) [1b] applied. Finally at the far right of the beam is another 3w [lb] point load as shown in the figure. The corresponding shear and bending moment diagrams are also given. Details of the beam’s “Inverted T” cross—Section are also depicted. Note the units on all the axes! (12 [in] E 1[it-]; V[lb]; M[ft-lb]) Recall that the shear and flexure stresses in a beam can be found from: . M y Shear and moment diagrams for a 7-09) E It and (Icy) : I simply—supported “Inverted T—beain”, - loaded as shown. (a) Determine the location of the neutral arts of the “Inverted y T—beam” (specify this relative to the y’-z’-coordinate system "*1 l F45“ _ Whose origin is at the bottom of the beam’s oross—sectiOn). (b) Determine the moment of inertia of the beam about its neutral arm’s, NA. (c) What is the value of the maximum tensile flexure stress in the beam and where does it occur? (ct—y coordinates, a: is along the beam’s length, 3; is alOng its height, measured Jfrom the neutral axis.) Cross—section of T—beam. (C) What is the value of the maximum compressive flexure stress in the beam and Where does it occur? (as—y coordinates) (d) What is the value of the shearing stress at the point denoted as Point ‘A’ located in the web just above the flange of the beam’s cross-section? ‘ F: (“Goa-ht 3"(m-1) a 20+ [no gr I (YE-D) an WWW MW: If“: t. ( "WJ + 31.(l°'2)-+efzfiwgl-JLE‘Cma) wthA ' 6 ¢ 5'33I‘MV quiznle'DG: 11.27.06 [C ) 40k 0 Wit/Mm V0“?th Sl’l/‘QJU'O: (Yrs- 11:2? 2W<CWP$= fix” ‘ Céflffvmz’r‘v’q”, MW? + Kw [#45] (a) (ngfi 0 = - we» m c» yaw .j: :2 #— (WQW) {/Zihjéglah) ' FML ,__ _ ‘ 3‘33 Aw " + A él‘” [/%,,L) T 12.4qu Wfl/e J/weyf .02 F— W W"QJC%‘)(+KFM) @ ’7“: ‘7 Pk $33 Fla“ = % [mm 5953/. my Cowprle/Cwe sin/rm- ,_.—-——-—'—'—r (a 79V a5. WW- (I) «r v#. Ce) Wvétmmm s’WMw/«fi Wm, M“ QWMA (7‘ :2 1—62 ' “1"” @fihA 5(3K240) 7—6Dh/l3 1* 64271921 7‘ ' VW: —-SWUAJ @éfxé‘WJ- 1:: (F SN)(ED Mg) 11L:— '2th m c M a \ $DT5’25’IW '7: pr 55 7-1 __ w [p I) [m < J‘Awfi/W «5%de ...
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