1. The document discusses member design under compression and bending forces. It provides equations and diagrams for determining the plastic centroid, axial load capacity, moment capacity, and balanced or interaction conditions of members.
2. Safety provisions for member design include minimum reinforcement ratios and load factors that are applied to nominal member strengths based on material properties and cross section details.
3. Diagrams show load-moment interaction curves indicating regions of failure by compression, tension, or balanced flexure for members designed based on provisions in the document.
14. T.Chhay NPIC
edaysareKBi)akkñúgkarTsSn_TaynUvmuxkat;ssrfa tension failure b¤ compression failure
eK)ansnμt;fa enAeBl e < 2d enaHssr)ak;eday compression failure EdlRtUvepÞógpÞat;enAeBleRkay.
3
edIm,IKNna nominal load strength P eKeRbIeKalkarN_sþaTic. karviPaKmuxkat;ssrsMrab;kar)ak;eday
n
karsgát; compression failure eKGaceRbIsmIkar P − C − C + T = 0 nigsmIkar
n c s
P e'−C (d − ) − C (d − d ' ) = 0 nigdMeNaHRsaymYykñúgcMeNamdMeNaHRsayxageRkam.
a
n c s
2
8>1> dMeNaHRsay Trial solution
dMeNaHRsayenHRtUv)ansegçbdUcCMhanxageRkam³
!> KNnacMgayeTAGkS½NwtsMrab;muxkat; balanced section c b
600d t
cb = (-3)
600 + f y
@> kMNt; P edayeRbIlkçxNÐlMnwg
n
Pn = Cc + Cs − T (-10)
#> KNna P edayKitm:Um:g;Rtg;EdkrgkarTaj A
n s
a
Pn e' = Cc (d − ) + Cs (d − d ' ) (-11)
2
Edl e' = e + d "kñúgkrNITUeTA
b¤ e' = e + d − enAeBl A = A'
h
2
s s
Cc = 0.85 f 'c ab
Cs = A's ( f 's −0.85 f 'c )
T = As f s
$> edaysnμt;tMél c > c KNna a = β c . snμt;
b 1 f 's = f y
%> KNna f s
⎛d −c⎞
f s = ε s Es = 600⎜ t ⎟ ≤ fy
⎝ c ⎠
^> CMnYstMélEdlrkeXIjeTAkñúgsmIkarCMhan @ nigCMhan # edIm,Irk P nig P . RbsinebI n1 n2
P ≈ P eRCIsyktMéltUcCageK b¤mFümPaKén P nig P . EtebI P mantMélxusKñaq¶ayBI P eK
n1 n2 n1 n2 n1 n2
RtUvsnμt; c b¤ a fμI ehIyeFVIkarKNnaeLIgvijcab;epþImBICMhan $ rhUtdl; P ≈ P . ¬eKGacTTYlyk)an n1 n2
ebI P nig P xusKña 1% ¦.
n1 n2
eRKOgbgÁúMrgkarsgát; nigrgkarBt; 209
18. T.Chhay NPIC
f ( ao )
a1 = ao −
f ' ( ao )
$> edayeRbItMél a KNna a dUcsmIkarxagelI
1 2
f (a1 )
a2 = a1 −
f ' (a1 )
%> Gnuvtþn_nUvviFIenHrhUtdl;)antMélsuRkitmYy a ≅ a . kñúgkrNIviPaKssrenAeBl compression
n n −1
control tMél a EtgEtFMCag a . dUcenH eKcab;epþImCamYy a = a ehIyGnuvtþsmIkarxagelIBIrdgedIm,I
b o b
TTYl)ancMelIy.
]TahrN_5³ eFVI]TahrN_TI4eLIgvijedayeRbIviFI numerical analysis
dMeNaHRsay³
!> KNna A / B / C nig D nigkMNt; f (a)
0.85 f 'c b 0.85 × 27 × 350
A= = = 4016.25
2 2
B = 0.85 f 'c b(e'− d ) = 0.85 × 27 × 350(479 − 500) = −168682.5
C = A' s ( f y − 0.85 f 'c )(e'−d + d ' ) + 600 As e'
C = 282 π (400 − 0.85 × 27)(479 − 500 + 50) + 600 × 282 π × 479
C = 734800328.08
D = −600 As e' β1d = −600 × 282 π × 479 × 0.85 × 500 = −300844190383.4
f (a) = 4016.25a 3 − 168682.5a 2 + 734800328.08a − 300844190383.4
@> KNnaedrIevTI1
f ' (a) = 12048.75a 2 − 337365a + 734800328.08
#> eGay a o = ab = 255mm sMrab;muxkat; balanced section c b = 300mm nig a
b = 255mm
f (255)
a1 = 255 − = 295.39
f ' (255)
$> nigKNna a ³ 2
f (295.39)
a2 = 295.39 − = 292.4mm
f ' (295.39)
tMélrbs; a mantMélRsedognwg a enAkñúg]TahrN_TI3. CMnYstMél a eTAkñúgsmIkar (-10) b¤ (-11)
eKTTYl)an P = 2594.66kN
n
8>3> dMeNaHRsayRbEhl Approximate Solution
smIkar approximate RtUv)anesñIreLIgeday Whitney edIm,IedaHRsayrk nominal compressive
strength sMrab;ssrxøI enAeBl compression control.
eRKOgbgÁúMrgkarsgát; nigrgkarBt; 213
38. T.Chhay NPIC
[ (
Pu = φPn = φK 0.85 f 'c Ag + Ast f y − 0.85 f 'c )] Edl φ = 0.65 nig K = 0.80 sMrab;ssrEdl
man dkkgdac;² nig φ = 0.70 nig K = 0.85 sMrab;ssrEdlmanEdkvNн ¬sUmemIl]TahrN_kñúg
emeronssrrgkMlaMgcMGkS½¦. sMrab;krNIepSgBIenH GñkKNnaGacGnuvtþtamkrNITI2. krNIbnÞúk
enHRbRBwtþeTAsMrab;ssrGKarCan;eRkaménGKareRcInCan; Edlm:Um:g; M u )anmkBIRbBn§½mYyCan; nig
Pu )anmkBIbnÞúkRKb;Can;EdlmanGMeBIenABIelIva.
2> tMbn; compression failure KWtMbn;EdlsßitenAcenøaHGkS½QreTAbnÞat; balanced load dUcbgðaj
kñúgrUbTI 3 nigrUbTI11. kñúgkrNIenH muxkat; bh GacRtUv)ansnμt; ehIybnÞab;mkmuxkat;EdkRtUv)an
KNnasMrab; Pu nig M u EdleGay. CMhanénkarKNnaRtUv)ansegçbdUcxageRkam³
k> snμt;muxkat;kaer b¤ctuekaN bh rYckMNt; d / d ' nig e = M u
P u
A' s f y
x> edaysnμt; As = A's KNna A's BIsmIkar Pn = 3he 'c
bhf
+
e
edayeRbI
+ 1.18 + 0.5
d2 (d − d ' )
TMhMmuxkat;Edl)ansnμt; nig φ = 0.65 sMrab;ssrEdleRbIEdkkgFmμta. yk As = A's rYc
eRCIserIsmuxkat;RKb;RKan;. kMNt;muxkat;BitR)akdEdleRbIsMrab; As nig A's . mü:agvij
eToteKGaceRbIdüaRkam ACI.
+
K> epÞógpÞat;fa 1% ≤ ρ g = As bhA's ≤ 8% . RbsinebI ρ g mantMéltUc kat;bnßymuxkat;
snμt; b:uEnþBRgIkmuxkat;RbsinebIeKcg;)anmuxkat;EdktUc.
X> epÞógpÞat;PaBRKb;RKan;rbs;muxkat;cugeRkayedayKNna φPn BIsmIkarsþaTic
dUcBnül;kñúg]TahrN_xagedIm. φPn ≥ Pu .
g> kMNt;EdkkgcaM)ac;.
rUbmnþRbhak;RbEhl approximate formula y:agsamBaØ sMrab;kMNt;muxkat;ssrdMbUg bh b¤PaK
ryEdksrub total steel retio ρ g KW
Pn = K c bh 2 b¤ Pu = φPn = φK c bh 2 ¬-24¦
Edl K c mantMéldUcbgðajkñúgtaragTI2 nigbgðajkñúgrUbTI19 sMrab;Edk f y = 400MPa nig
As = A' s . xñatrbs; K c KW kN / m 3 .
taragTI2 tMélrbs; K ¬ f c y = 400MPa ¦
Kc
ρ g (% )
f 'c (28MPa) f 'c (35MPa) f 'c (42MPa)
1% 24817 30246 35286
4% 37574 43003 48044
eRKOgbgÁúMrgkarsgát; nigrgkarBt; 233
40. T.Chhay NPIC
mü:agvijeTot RbsinebIeKcg;)anPaKryEdksrubCak;lak; ]TahrN_ ρ g = 6% bnÞab;mkGnuvtþdUc
xageRkam³
1> snμt; ρ g dUcEdlTamTar nigbnÞab;mkKNna e = M u Pu
2> edayQrelI f 'c nig ρ g EdleGay/ kMNt; K c BItaragTI2
3> KNna bh 2 = φPu bnÞab;mkeRCIserIs b nig h . GnuvtþCMhan 4 nig 5 eLIgvij.
Kc
eKKYrEtepÞógpÞat;fa 1% ≤ ρ g ≤ 8% . dUcKña epÞógpÞat;fa c
Edl)anmkBIkarKNnatamsþaTicmantMélFMCag cb = 600 +dft sMrab; compression failure .
600
y
]TahrN_13³ kMNt;muxkat;EdkTaj nigmuxkat;Edksgát;sMrab;ssrEdleRbIEdkkgFmμtamanmuxkat;
400 × 600 edIm,IRTbnÞúk Pu = 3470kN nig M u = 530kN .m . edayeRbI f 'c = 28kN nig f y = 400MPa .
dMeNaHRsay³
1> KNna e = M u = 3470 = 152.74mm . eyIgman h = 600mm yk d = 550mm nig d ' = 50mm
P
530
u
edaysar e < 2 d = 366.67mm snμt;fa compression failure.
3
2> snμt; As = A's . kMNt;tMéldMbUgrbs; A's tamrUbmnþ
bhf 'c A' s f y
Pn = + (-17)
3he e
+ 1.18 + 0.5
d 2 (d − d ' )
sMrab; P 3470
Pn = u =
φ 0.65
= 5338.5kN
A' s = 4271.8mm 2 = As
eRKOgbgÁúMrgkarsgát; nigrgkarBt; 235
44. T.Chhay NPIC
enAeBlbnÞúk P mantMéltUcNas;ebIeRbobeFobCamYynwgm:Um:g; M TMhMrbs;muxkat;GacRtUv)ankM
u u
Nt;edayeRbIEt M EtmYy)anehIy edaysnμt;fa P = 0 . muxkat;cugeRkayKYrRtUv)anepÞógpÞat;eday
u u
smIkarsþaTic. krNIenHekIteLIgsMrab;eRKagGKarmYyCan; b¤BIrCan; EdlGKarenaHRtUv)aneKeRbIsMrab;eFVICa
saltaMgBiBN’ b¤k¾GKarTaMgLayNaEdlmanlkçN³dUcKñaenaH. sMrab;krNIenH A' GacRtUv)ansnμt;eGay s
mantMéltUcCag A . karKNnay:aglMGitsMrab;saltaMgBiBN’kMBs;mYyCan;Edlmansnøak;BIrRtUv)anBnül;
s
enAkñúgCMBUkTI 16 FñwmCab; nigeRKag.
]TahrN_16³ kMNt;sésrEdkcaM)ac;sMrab;ssrragctuekaNEkg 400 × 560 EdlmanEdkkg
FmμtaRTbnÞúk P = 1140kN nig M = 850kN .m . eRbI f ' = 28MPa nig f = 400MPa
u u c y
dMeNaHRsay³
1> KNna e = M
P
u
=
850
1140
= 0.7456m . yk d = 560 − 60 = 500mm . edaysar
u
Mu
Pu
= 745.6mm > 530mm b¤edaysar e > d snμt;fassrenH)ak;edaykrNI tension failure
enaH φ = 0.9 ¬RtUvepÞógpÞat;enAeBleRkay¦.
2> snμt; A = A' nig f ' = f nigeRbIsmIkar (-25) edIm,IkMnt; A nig A' . eday P = 1140kN /
s s s y s s u
e = 745.6mm / h = 560mm / d = 500mm / nig d ' = 60mm
1140 ⋅ 10 3 (745.6 − 0.5 × 560 + 0.2 × 500 )
As = A' s = = 4070.71mm 2
0.9 × 400(500 − 60 )
eRbI 5DB32 (4021.24mm ) sMrab; A nig A' . ¬rUbTI22¦
2
s s
3> epÞógpÞat; ρ = 2400 × 560) = 0.0359 EdltUcCag 0.08 nigFMCag 0.01 .
(4021.24
g
4> epÞógpÞat;kareRCIserIsmuxkat;edaysmIkarsþaTic EdlkarKNnaRsedogKñanwg]TahrN_TI3
eRKOgbgÁúMrgkarsgát; nigrgkarBt; 239