Problem 9.3 YI I L Wo A x L A [)(":L..) j-=-O] ['J(-::L;):1;", 0 1 ""DX ~ TM J :5 x '1. IIJOXI ~ ~3'\ A loE~ {J V [116= L..) .)' ': 0] (Q.) EiASfi Co C:tJ~lIe- (6) j @ ?t-= D: CC) *- @ ~= 0 : 9.1 through 9.4 For the loading shown, determine (a) the equation of the elastic curve for the cantilever beam AB, (b) the deflection at the free end, (c) the slope at the free end. LJ.s e ~Neeo. boi t AI a +.::> L MJ" -::.0: M... w;:. f M -= - ~ 'dr-a ': 0 dZy -= .-.l.. ~x.$ cH., 6 L £ .1' ~ - -.L wo')!,'f C rJ?t, - 2"f L + I ,.-- , w.x!" c::I ,,= - - ~ + C~ + C ~ r~o L I 1 r"X- = L 6.: (;) ] .. - ,;L Wo L:! -'- C L' .) h . ,11.." T'" I c. - J... ,01 L '3 I - ~... VVg EI - - -L hI L '" ..d- ..1 L '1 C - j - I~o ¥Vo +.t 'I VVo + z - 0 C2 - -doWe) Ly. ~r= II~~~.I Co'(~S - -5 1..~?t. + If LS ) ~ h. .vJ. . \I k -:: ~~ iI L (-; ~., ~ L ~ I' - - WoL'f - ""0L" -J, I:fA - 30 cI JA - 30EI ~ !L I -= h,.. W L3 -2..- 'J.~EI e - woL" A- ~tIEX A.. .......
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Problem 9.3
YI
I
L
Wo
A x
L
A
[)(":L..) j-=-O]
['J(-::L;):1;", 0 1""DX
~ TM
J :5x
'1.IIJOXI
~ ~3'\
A loE~ {JV
[116= L..) .)' ': 0]
(Q.) EiASfi Co C:tJ~lIe-
(6) j @ ?t-= D:
CC) *- @ ~= 0 :
9.1 through 9.4 For the loading shown, determine (a) the equation of the elasticcurve for the cantilever beam AB, (b) the deflection at the free end, (c) the slope atthe free end.
LJ.se ~Neeo.boi t AIa
+.::>L MJ" -::.0: M... w;:. fM -= - ~ 'dr-a
': 0
dZy -= .-.l.. ~x.$cH., 6 L
£.1' ~ - -.L wo')!,'f CrJ?t, - 2"f L + I
,.-- , w.x!"c::I ,,= - - ~ + C ~ + C~ r~o L I 1
r"X-=L 6.: (;) ] .. - ,;L Wo L:! -'- CL' .) h . ,11.." T'" I
c. - J... ,01 L'3I - ~... VVg
EI - - -L hI L'" ..d- ..1 L'1 C -j - I~o ¥Vo +.t 'I VVo + z - 0
C2 - -doWe) Ly.
~r= II~~~.I Co'(~S - -5 1..~?t. + If LS )~
h. .vJ. . \Ik -:: ~~ iI L (-; ~., ~ L ~I'
- - WoL'f - ""0L" -J,I:fA - 30 cI JA - 30EI~
!LI
-=h,..
W L3-2..-'J.~EI e - woL"A - ~tIEX A.. .......
Problem 9.7
L
('1(:;>..) Y::D] [1f:L...Iy =oJ
~J
wiL-
l _un !rk-~
r<J!I
wL
w
~ MA )
V~ X ~
[-x.=L..,) ,]'=oJ
(Q..) EJ)e..s+;c. cVV"\Ie
9.7 For the beam and loading shown, determine (a) the equation of the elastic curvefor portionAB of the beam, (b) the slope atA, (c) the slope at B.
~x U.s~r1j -FV'€eboly ABC
4-) :2M8= 0: - RAL+(wL'(~) -(wLX~) : 0
RA ':: t wL
FDV" porfiC>1I\ ~B (o4!')b4!L)
+, 2M,J"= 0 ~ - RAx.. + (w~"l.1:) -= 0
tv) = t wL~ - ~w'i/-
Er ~ ': ..L w l-x. - J..v.J?~.~~"L'" ~
EI ~ - .lwli - J.wi!. -4 L~ . '8 6 '
I L 3 \ '1ET::f -= ~., W ')( - ;?'i w-x.. + C, ~ -t C-z.
[X= °", j :oJ -: 0= 0-0+0 +Cz. C2, = 0
0::- ii w l 'f - ~\'fw L't + C, L + 0 :: 0 C :: 0I
vJ ( ,. 'f )J =- - L?l-~~L/EI
b - -Y:L. ( 3 Lx.?.- 4';(.3)A' :?~ EI
(0 !; ~~ L).
(6 ) ~ J ,,:::0~
(c.) :tL d ~ = Lch6
..
£IA ~ DG"= 0 ~
:hI
- - wL.3h B - ;<tjEI
e - wL'!g - i4EI ~ 411
Problem9.12 9.12 For the beam and loading shown, (a) express the magnitude and location of themaximum deflection in terms ofwo, L, E, and I. (b) Calculate the value of themaximum deflection, assuming that beam AB is a W 18 x 50 rolled shape and thatWo = 4.5 kips/ft, L = 18 ft, and E = 29 X 106 psi.
Problem9.15 9.15 Knowing that beam AE is a W 360 x 10I rolled shape and that Mo= 310 kNm,L = 2.4 m, a = 0.5 m and E = 200 GPa, detennine (a) the equation of the elasticcurve for portion BD, (b) the deflection at point C.
:Mo Mo
Use c.Q~i; VIu; -l "I
aVlJ SjWlYhef~1
F~oW\ Sft,)lh'c.s j
bDVV\J~"1 Gc,"IJd i O"" c<.,-t BbovV\4e.."'1 c.:;>"".,..f1t ,'O"" ~ C.