Moment Diagram Examples

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29 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

84 εμφανίσεις

6-29.TheT-beamissubjectedtotheloadingshown.Draw
theshearandmomentdiagrams.
2kip
200Ib/ft
I
A.~...
r--6ft+- 9ft.
9ft
1
Prob.6-29
Ic¥/r.~
Cp
rG:..
10
c)J6
~-f
1~4sr
2
~4-
,-,"."<III
J/14 <::..<L-f
r~/t?r/7 4e?4V-I,
J
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NAME
DATE
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6-29.TheT-beamissubjectedtotheloadingshown.Draw
theshearandmomentdiagrams.
2kip
200lb/ft
~
A
*-
".
V}
'.".'-".""",..
6ft'9 ft
3.//(,}/(
w~-~'
9ft
-=r
.3
J
I('
o.~?
Prob.6-29
EN 1739862C
*6-28.Drawtheshearandmomentdiagramsforthebeam,
anddeterminethe shearand momentin the beamas
functionsofx.
2oo-2oo(x-3)
1
[
200
]
-2
3(x-3) (x-3)-V =0
{
100
2
}
V = -3x +500 N
Support
Reactions:AsshownonFBD.
Shear andMoment Functions:
For 0S x <3m
+iIF,=0;
v = 200N
200- V =0
(+IMNA =0;
M -2oox =0
M = (2oox} N.m
For 3m<x S 6 m
+iIF,= 0;
Set V = 0,
x =
3.873m
2OONI..
,'iI;J 1'~"':'~3B
ADS
-t (Z40)('5)::300f,J
ZOO(3J
=
bOO II
ADS
+~tn
1/11""
0.5""700N
ZOON
ADS
V
F=1hM
,zOo/J
ZoONf
;!'"
H~;(-J~iX-3)
ZO
.
O(~-JJ
I
i:1f=l!
~
M
I~
~
~IMNA
=0;
1
[
200
] (
X-3
)
M +2 3(x-3) (x-3) 3
(
X-3
)
+2oo(x-3)
T
-2OOx=0
{
100 J
}
M =
-9x +500x -600
N.m ADS
WN)
Substitute x = 3.87 m,
M=691N.m
M(N.m)
Zoo
:a,")
{,
.;((/11)
"
3 03.67
"
6
-700
6-29.TheT-beamissubjectedtotheloadingshown.Draw
theshearandmomentdiagrams.
!I
'L
-c..- ~I..
L
,L.-
(,1 Z.
'f
~
~
,3!<.if'
o.ZJ.9J=/.8<;
/eip
I
()
f
'1
1,9.dJ
-;--
49Jt
o.h~~t'f
M(Kip.Jt)
/.1.0
I [;,,9
\
0 I"
-tl-
/,'7
-2.00
-1,z.O
238
.
..
.
PROBLEM
CtV/£
"~
I
,2..I
EN 173 986 2C
..
,c-,
PROBLEM
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ENGINEERING
NAME
DATE
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,/2,
H;300
I
SJ!Q
EN 1739862C
....
.
*6-20.Drawtheshearandmomentdiagramsforthebeal11Jn
.
»
anddeterminetheshearandmomentthroughoutthebeanooi~.
asfunctionsof x.:(
2kip/ft
.
10kip
8kip
:>
.
'
.
'
.
.';
.
~!f
.
Y~
~
~:
Y
.
'.
.
\
.
:
.
.
-J
~[;
~x
4ft
6ft
Prob.6-20
*6-20.Drawtheshearandmomentdiagramsforthebeam,
anddeterminetheshearandmomentthroughoutthebeam
asfunctionsofx.
Support Readion$:AsshownonFBD.
Shearand Moment Function:
-
J.~..
~
..w"'tf..:'",:."""",'I)
r-'--;
,I i
f ---!
j
For 0::;:r:< 6 Ct
+i U;
=
0;
30.0-2:r:-V=0
V={30.0-2:r:}kip
Ans
0-rMNA=0;M+216+2:r:G)-30.O:r:=0
M={-xz+30.O:r:-216}kip.ft
Ans
For 6 ft <:r:::;10 ft
."",,)~/.l.OKif/O~:P 81::;p
Nb,('~)~'J'
31tt/t ~3j~
i
"fit 1
""tj
p~r
M
tr ~ I)
30.0/:ip
-t ~
8/:ip
ttdr*
V I'/o-x
I
+i1:Fy=0;
v =S.OOkip
Ans
I/O:;P) [2...l<..J- 3'
L'
304__(
M(I:iP'10
V-S=O
(+1:MNA=0;
-M-S(IO-x)-4O=O
M ={S.00:r:-120}kip.ft
Ans
6-21.Drawtheshearandmomentdiagramsforthebeam,
anddeterminetheshearandmomentthroughoutthebeam
as f,'1.ctio:1sof x.
Support Reaction$:AsshownonFBD.
Shear and Moment Function:
For 0::;x <8 ft
+i1:Fy=0;
7.60- O.SOO:r:- V =0
V ={7.60- O.SOO:r:}kip
Ans
(+
1:MNA=0;M +44.S+0.S00:r:G)-7.60x=0
M ={-0.4OOxz+7.6O:r:-44.S}kip.ft Ans
For S Ct <:r:::;16 Ct
+i EFy
=
0;
V-1.20=0
V = 1.20kip
Ans
t1:MNA =0;
-M -1.20(16-:r:)=0
M = {1.2Ox-19.2} kip.ft
Ans
V(Kip)
I
7.60
0
0
/'JI'1
- 2../If.
~('1'f
':.72-
,.zo
8
234
;t,(Jt)
10
+-32"
"
"
10_X(jt.)
-40.0
-216
-~ l.~-
...J""*"':"".'."".,""."",;..,,,+~!
)
~..-L..~
1).2'/%)::f...47 ¥"
~(r+--i
76oKJ~/iJt
,---+~~.t
4"q.~!V)M
7.{'OJ:iP~
M(d~
)1'/6->:'\
'r
1
M (J{;p.Jt)
16
j:.(JI)"
e
'":xC.II:)
-#.6
fli
bbt!../G
r G;
d
6-9.Drawtheshearandmomentdiagramsforthebeam.
Hint:The20-kiploadmustbereplacedbyequivalentload-
ingsatpointContheaxisofthebeam.
15kip
A~4ft-L
4ft
J
Prob.6-9
,"
.
~ Drawt~eshearandmomentdiagramsforthebeam.
Hint:The20-kiploadmustbereplacedbyequivalentload-
ingsatpointC ontheaxisof thebeam.
"C ~~"'1
~...''--.
A.'..
~4;.-L4Cll4nJ
~'Sk;f
1-4/t
IS
d) Kip
~
~,
f
~It.
t
2tl'it
r
.1.3$kif
~
""7/(;'
'/CKif)
r
.
t)'"
-.4-~~
H(~~
..
.
~
6-18.,Drawtheshearandmomentdiagramsforthebeam.
It.is supportedbyasmoothplateatA whichslideswithin,
thegrooveandsoit cannotsupportaverticalforce,although
it cansupportamomentandaxialload.
w
L
Prob.6-18
T
.'
PROBLEM
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ENGINEERING
NAME
DATE
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EN 173 986 2C
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EN 173 986 2C
6-18.Drawtheshearandmomentdiagramsforthebeam.
It issupportedbyasmoothplateatA whichslideswithin
thegrooveandsoitcannotsupportaverticalforce,although
it cansupportamomentandaxialload
f
f~
~
L
-wI!'
14
-r
Cr
!!
!I:
I!I!!f
w/...
M
"
wI:"
7:
L
1'-
'J:.
0
L
0
SUPPQrtReactions:
FwmtheFBD of segmentAB
6-19.Draw the shear and momentdiagramsfor the
compoundbeam.
5k.~'m
~
""""""""".
,
"""""""""'D
",':4""'"18''r C
T
2m--;-lm-r-lm,
FromtheFBD of segmentBD
5.oo{I)+10.0(0)-Dy(l) =0
Dy=5.00kN
(
+rMc
=
0;
Cy-5.00- 5.00-10.0=0
Cy=20.0kN
+i L1';=0;
5(2)=10.0kN B'f 5(2.).10'o~
.
~
-t--t:-i
~ c~ J)~
~1:/';=0;
Bx=0
FromtheFBD of segmenlAB
~
L1:;
=
0;
Ax=0
V(/CN)
M(F.tJ.tn)
Shearand Moment Diagram:
10.0
;&.so5.00
$.'",)
'I-
-10.0
I'
233
tI>
(+rM =0'
By (2) -IO.O( I) =0
By =5.00 kN
\A'
+i1:1';=O;Ay
- 10.0+5.00=0
Ay =5.00 kN