1. T.Chhay
PaBdabrbs;Fñwm
Deflection of beam
1> kMeNag nigm:Um:g;Bt; Curvature and bending moment
enAeBlFñwmsamBaØmYyrgnUvkMlaMgbBaÄrxageRkA kugRtaMgTaj)anekIteLIgenAEpñkxagelIénGkS½NWt
nig kugRtaMgsgát;enAEpñkxageRkam. sésEdlrgkarTaj lUtEvgCagmun ÉsésEdlrgkarsgát; rYjxøICag
mun. EdlkarenHeFVIeGayFñwm mankMeNag b¤dab. CaTUeTA bøg;NWtRtUv)aneKeGayeQμaHfa ExSeGLasÞic
(elastic curve). enaHkaMkMeNagRtUv)anKNnatamrUbxageRkam³
eKman HD' CabMErbMrYlragBIRbEvgedIm C' H O Center of
curvature
enaHeK)an bMErbMrYlrageFob ε = C ' H = JF
HD' HD'
tamc,ab;h‘Ukm:UDuleGLasÞic E = εs dθ
R= Radius of curvature
HD' ( R = OJ = OF )
⇒ sb = Eε = E ( )
JF
Elastic curve
kñúgkrNIkMeNagmantMéltUc/ eRbobeFobRtIekaN G
D' FH nigRtIekaN JOF eK)an
A' B'
c HD'
= J F
R JF c
dθ
c
⇒ sb = E
R C' D' Segment of
H
mü:ageTot tamsmIkarkugRtaMgm:Um:g;Bt; dl
loaded beam
dx
M .c
sb =
I
c c
⇒E =M
R I
1 M
⇒ =
R EI
R=
EI
M
b¤
2> PaBdab nigmMurgVil Deflection and rotation angle
θ
eday k = R = ddl
1 Y
dθ M
⇒ =
dl EI dθ
eday tan θ = dy
dx
R dθ=θ1−θ2
dl
d d2y
⇒ tan θ = 2
dx dx
dθ d 2 y
⇒ (1 + tan 2 θ ) = θ1 θ2
dx dx 2 X
PaBdabrbs;Fñwm 99

2. T.Chhay
d2y dy dθ
⇒ 2
= [1 + ( ) 2 ]
dx dx dx
2
d y
dθ 2
⇒ = dx
dx 1 + ( dy ) 2
dx
mü:ageTot dx
dl dl
=
1
= 2
1
2
=
1
dx + dy 12 [1 + ( dy ) 2 ] 12
( )
dx dx 2 dx
2
d y
dθ dθ dx
dUcenH k=
dl
= ( )( ) =
dx dl
dx 2
dy 3
[1 + ( ) 2 ] 2
dx
kñúgedaytMél dy 2
( ) →0
dx
dθ d 2 y
⇒k = =
dl dx 2
d2y M
⇒ 2 =
dx EI
b¤ y' ' =
M
EI
sMrab;krNI TisedArbs;GkS½ Y eLIgelI
EtebITisedA Y cuHeRkamenaH
2
⇒
d y
dx
=−2
M
EI
b¤ y' ' = − EI
M
Edl y CaPaBdab
eday dy = tan θ = θ edaysar θ CamMurgVilmantMéltUc
dx
d 2 y dθ M
⇒ = =
dx 2 dx EI
b¤ y' = EI
M
PaBdabrbs;Fñwm 100