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Unformatted text preview: for brass, and 10x106 psi for aluminum. The beam is
kipin about a horizontal axis.
a) Find the maximum stress in each of the three metals.
b) Find the radius of curvature (p) of the beam.
c) Would p increase, decrease, or interchanged? (You do not need to do any calculations to
explain your answer.) lWW“)?(Zn—Wanna 7': (u)(.s>’+(m(s)m‘f ’ ‘1
,0957 7; z 2.3M? +3654 = QIH’ In ‘ (Iz,aw)(lz€) r .  : €51  f
V t n _. 4/Immpm  a; ‘0) 2"“, 4. Pg], .
" z, .7  . ‘
brass: 02 = W : 4,170 ’05; she! = 0: =8) (12.0»)(ac) M = 91/3 5/
146’? > I l’  'M __ _ 541 " loll/o‘)(z.1é&) > f m ’ I It ‘ (
—‘ ' n l
to El [21000 f 6&2: or If ’ i ' I ‘ ’\CWS‘€ L
a) Mglwnsmj 60155 W a/mmm «MAM n I ntor 'I'Aa Sada?” S», )9 New“ mare“: . A steel beam with a W200 X 52 cross section is ﬁxed at one end and resists an axial load of
500 RN and an unknown horizontal load P at the end of the cantilever. The two loads act
through the centroid of the section. The yield stress of the material is 350 MPa. The self
weight of the section may be neglected. What is the allowable load P that can be applied to
the section, using a factor of safety of 2.5 against yield? (See following page for properties
of the section.) ‘1 y 753 Appendix C. Properties of RolledSteel Shapes T?
(SI Units) 11 X X
Continued from page 751 J— '“’
W Shapes Y
(WideFlange Shapes) ' L I)!!! 9.“ W310 X 143 18200 323
107 13600 3] l
74 9480 310 81.2 531 77.3
23.4 228 49.7 38.7 4940
32.7 4180 313
23.8 3040 l .92 37.6 2 l .4 67 8580
58 7420 252
49. l 6250 247
44.8 5720 ' 18.8 l85 350.3
15.1 150. 49.2 v 3.5» o * 1 ‘ '; ' : : . 91. was;
Wl30 X 28.l 3580 [3 “56 55.2
~ 23.8 30l0 127 I39 54.] 3.” 49.0 32.] w100x19.3 2480 106 90.0 43.9 l.6l '31.3 25.5 ‘i'A Wideﬂange shape is designated by the letter W followed by the nominal depth in millimeters and the mass in kilograms per meicn 3.81 59.5 32.6 * k W'ﬂknﬂiﬂ 13.2111. mmmmnmwm ,.4« r 1 ww «(v  u 5, 3. A 6 foot long ski is designed to distribute the weight of the skier on the snow. The skier’s
weight can be assumed as a point load at the middle of the ski. If the skier (including all
gear) causes a load of 180 lb on each ski, and the distribution of force (upward) of the snow
on the ski can be written as w(x) = —i§[x— <x—1.5~>‘ — < x—4.5 >‘],
where x is in feet from the leading edge of the ski, and wo is a constant with units of pounds per foot: a) Determine the value for we. b) Sketch w(x). c) Determine the expressions for shear and bending moment using singularity functions. d) Sketch the shear and bending moment diagrams, and identify the location and
magnitude of maximum bending moment. 4. The beam shown consists of two 4” x 1” boards, which are nailed together as shown. The
nails have a diameter of V4” and an allowable stress of 20ksi. Determine: ,a) the maximum shear force? M 4M6 W b) the maximum shear stress in the section?
. c) the nail spacing to resist the maximum shear? d) if the nail spacing is varied to reﬂect the shear force at each section, how many nails
are required" between the point loads? *  P=2kips ﬁrm: _
b ‘ 3ft —>l«—’ i sit—4+~ ~3ft ,QH'R&.:P=1\L~P‘ ' . 3 2g" 3(114X3)‘+61uXo.s)
.Lmlfvww I91 yes ' ' 8 ‘ 4"——l ' I = P75
L g VG  ‘
(l WNW  I; .(%P+(Hx3vp.7s)L+(t+_)t_nl3
I + QOJS'O 25>z‘
.~. Isrz act I _ ‘ ‘ .15) =S28fn3
0mm ‘ls Isl x37 ‘
(W: its”) {0581163 wa ') :
c9 mamas) =5 a: V9 dag) = 055 L/m
’ I 1847 ...
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 Spring '08

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