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(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 7D .=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(x1207Hrw)
a m: ,«lxza purgeu lea/ff” * " g“. 20»¥(5C—~ro)+prvV :0
’— v Va [towwxﬁc—Wl
2.9123“? "mm? 2m, :0 P; azmc+¢(>e—rp)(x:°) , (xv3‘0) IW+M=U MT: ZDX —'2\(1+UW .3243? 4. fwx..3§170 M a; ,zwa. may: , 22m: Ki‘pri’t
M ,.— e—‘TM
29”? V 15 Points 2. Stresses in Beams. The ﬁgure at right (a) ' 2 shows a simplysupported “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[ftlb]) Recall that the shear and ﬂexure stresses in
a beam can be found from: . M y Shear and moment diagrams for a
709) 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 crosssection? ‘ F: (“Goaht 3"(m1) a 20+ [no gr I (YED)
an WWW MW: If“: t. ( "WJ + 31.(l°'2)+efzﬁwglJLE‘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 71 __
w [p I) [m < J‘Awﬁ/W «5%de ...
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