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Unformatted text preview: Prob. 6.24. Couples M, are applied to a steel strap of length
L = 30 in. and thickness 1: = i in. to bend it into the form
of a circular are, as shown in Fig. P622. The deﬂection 6
at the midpoint of the are, measured from a line joining the
tips, is 3.5 in. (a) Determine the radius of curvature, p, of
the strap, measured from the center of curvature C to the
heutral axis of the strap (which passes through the center
of the cross section of the strap). (b) Calculate the maximum
extensional strain, em in the curved strap. 4} fat/1w 05 («n/a 14m: h/z. QWW ll/z {i/IONA
at“ = /0 6w = /. 75200” 5/. 6—451. P6.22 A [’/0/Z¢) ¢=E7 f=/’(/’Cor¢)
vol/ear 5,2” 3.570, =/0 [/ (al{':;;")]
JE/ur [Ar algae 744/10: 710/ / =j/,‘f4/h. ——> J=£faaz,h. I4: = ——‘—“ = A ‘idlél/o" 7,7. Prob. 6.37. A timber beam consists of four planks fastened
together with screws to form a box section 5.5 in. wide and
8.5 in. deep, as shown in Fig. P6.37. If the ﬂexural stress at
point B in the cross section is 900 psi ('1‘), (a) determine the
ﬂexural stress at point A in the cross section; (b) determine the stress at point C in the cross section; and (c) determine " ' 5 5 m
the total force on the top plank. NA . ___  A
2.0 in. " J [/l 1.5 m.
0.75 in. . 2.5 in. 15 in
l.5 In.
P6.37 duejco s mmeb’lj, cwbro'ld isin middle, of cross—Seceionﬁo
7T: ‘4. in. __M93
53' I Ii O’A=_ I @3015 =%)ﬁwﬁi = " FLOO g? 9mm .
05:ng = (3.412353 = (%‘F2Mﬁooﬁi 0: = 67W
; 0'4
1.5m. 553m. 1.5m m 2.15m.
O’(Lj=2.?5 in) =(2.25in)‘loo P5; = — H .
l'+ooEsi+Iloo§' ' .
2 ‘(L.5m)(5..5m) “(Krakow
0' Fm = ' “00 psi (L5in)(5.5in) +
= — ' _U_5_kuzi Prob. 6329. For beam A15 in Fig. P6348, (a) sketch shear and moment diagrams, and (b) determine the maximum
ﬂexural stress in the beam. /4) 2164/ doc/moman/a/‘z I’de Ega/%/n’amr
475w), =0: ~//é,;o)/7/f) $5104!)
—/z Lad/2,44 f a £44 ,A/ =0
3} ’ / [ff/kl
“Mime =0: (/éq'o mm '(Z£I}I)/Z;4/J
My Mm  H123 'ﬂ‘ =0 0'25
ﬂ} = / 7f/4/ryf ﬂ] MdX/I‘YH/m 7481mm / {ﬂed MJ
4;" T 6 : Mil /Z
= /7. 3/44 m. t : (é Mufti/e ’M/HMJ
a” mam 0', ¢ ' = //I W“ 6;” = W5 A; I’l’l’ol). 6.335. Determine the maximum uniform distributed
load. w, that can be applied to the beam with overhang
shown in Fig. P6.335. The allowable stress (magnitude) in
tension or compression is 150 MPa, and the beam is a W310 x
97 (see Table D2 of Appendix D). P6.335, P6.336, and P6341 " beam Worm ?(éM)B =0: AJHml‘ w(lpm¥)ml= o A3: W(i.5m)
'1 A C 19(EMlA‘o: woomYSml " Bﬁ‘imk'o B B.j = w(4.5ml ‘1 A B
l K—tj—Zm—ﬁklmak—‘JZM—H —2w — — — —" Mn!th =  :FromTalole, D2, al= 502mm and "1:222:00") mm“
__ = M =‘NmaLZJrﬂd ZIz z. 25‘] o
WMAx ‘ (Zmzlg
zgxmmzzzugbl mm‘l (2m2l(508 mm} = /08./Z kNgm UAHOW WW: Wm w = 1.5 kips/ﬁ
I"Prob. 6.49. From Table D.1 of Appendix D, select the
lightest wideﬂange steel beam that may be used for the
application shown in Fig. P6.49. The allowable stress (mag
nitude) in tension or compression is 0.... = 20 ksi. P = 20 kips
P6.4«9 ft/cc/ ﬁfé/rr/ r/a/ Jam .
Z ,‘I’én'um,’
f“ [fl/kr/ 4 26:0: {Db/'4,  fob/’4; 5% =o
T4 =  /o A}, “(Z/WC to:
MC *[3041241)//0//) [mud/12 ﬂ) =0 M . —60 MW
MW *1 leyll ’ 60 A,;.,£/ 19//0wd!/c ' {/Z/crf 09/1» : I 304,th ﬂ’3 0' ﬁt /%/rf/M¢m £7
mfg/Ia 51/! a/ ﬂ/wJ/M a «Zr/pa . "(If/")5 ‘0 I' ‘ l’I’I'ol). 6.415. An inverted structural steel tee beam is sup ‘1 [“Av ported by a pin at A and rests on a toilet at B, as shown in _f
Fig. P6.415a. What is the maximum load P that can be hung from the beam at C if the cross section of the tee has the 554i" dimensions shown in Fig. P6.415b, with t, = 0.420 in., and l the allowable bending stress (in tension and compression) is 03... = 20 ksi? L5.02in.J17
wonm Ml/mum /0¢a/,
+(’(2’M)6 =0!
H} (10/!) 1‘ F/fff)=0
l9; 5' ’ {P /lI/'u) @(w/H « P//5’ﬂ)=0
45/.{P MW = /M//a//:/ r 5? 4/474! 7, e an!» #276,514): 3.6%.
7’, = $70.4: )=0.z/ ,2. ﬂ. = {a.¢zrz.)/6.57rrh.l — [.7465th '71=/0,4z/h.)/£ozlh,)=z, watt/2‘ é'ﬁ‘h'L. ’ I I a: '2.
" ﬂ; 1* l ’
7: 7 z: =Z/7f5’m (~— '  E
was 1 L— —11 '1‘
 aﬂM. 5”“ é%m%Z;%mc£ﬁnz = Mm Jam (57’ AM/ We Ms. W)
4/1th [ : 27, 267/34 p _. (Mind/w.sz
{57/102 1%,) {mm
5 /. 67/5, IP= [67Z/Ikr [44/44/144 Mic/x) . ' f L
: o’in */M,.;,)(4,o7,>.,s{Mim) , I
,t I: [M3, ; /£oZ/h./(o,~fl/}.J/Z./B'Oll/y]
IL z wow/27‘ r 0’. 20m" = M, 2457 ,a‘ ...
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This note was uploaded on 04/28/2008 for the course CVEN 3161 taught by Professor Xi,yunping during the Spring '06 term at Colorado.
 Spring '06
 XI,YUNPING

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