3.tension members

NPIC

III. eRKOgbgÁúMrgkarTaj
Tension Members
3>1> esckþIepþIm
eRKOgbgÁúMrgkarTaj CaeRKOgbgÁúMsMNg; EdlrgnUvkMlaMgTajtamGkS½. vaRtUv)aneKeRbIsMrab;
eRKOgbgÁúMeRcInRbePT nigrYmbBa©ÚlTaMgeRKOgbgÁúM truss ExSrkabsMrab; suspension bridge nig cable-
stayed bridge, RbBn§½BRgwgsMrab;GKar nigs<an ExSrkabsMrab;RbBn§½dMbUlBüÜrpgEdr. sMrab;Ggát;rg

karTaj RkLaépÞmuxkat;CaGñkkMNt;lT§PaBTb;eTAnwgkMlaMgxageRkA. EdkEdlmanmuxkat;mUl nig
EdkEkghUtekþA (rolled angle shape) RtUv)aneRbICaTUeTA. eBlxøH muxkat; built-up BImuxkat;hUtekþA
(rolled shape) b¤muxkat;pSMKñaBImuxkat;hUtekþACamYynwgEdkbnÞH (plate) RtUv)aneRbIR)as;kñúgkrNITb;

Tl;CamYybnÞúkFM. muxkat; built-up PaKeRcInCa double-angle section ¬rUbTI3>1¦ CamYynwg
muxkat;KMrUepSg²eTot. edaysarEtkareRbIR)as;muxkat;enHmanPaBTUlMTUlay taraglkçN³énbnSM
muxkat;Ekg (combinations of angles) epSg²k¾RtUv)anbB©ÚaleTAkñúg AISC Manual of steel
Construction.

Figure 3.1

kugRtaMgenAkñúgGgát;rgkarTajtamGkS½KW
P
f =
A
RbsinebIRkLaépÞmuxkat;énGgát;rgkarTajERbRbYltamRbEvg enaHkugRtaMgnwgERbRbYltam
muxkat;Edr. CaFmμtaeRKOgbgÁúMrgkarTajEdlP¢ab;edayb‘ULúg EtgEtmanRbehag. vtþmanrbs;Rb
ehagmanT§iBleTAelIkugRtaMg. enARtg;kEnøgenH muxkat;RtUvKitedayecalmuxkat;Rbehag. Net

28 Tension Members

T.chhay

area b¤ net section Camuxkat;suT§EdlminKitmuxkat;Rbehag É gross area Camuxkat;eBjEdlKitrYm
TaMgmuxkat;Rbehag. CaerOy² Ggát;rgkarTajEtgRtUvP¢ab;edayb‘ULúgenAxagcug ¬rUbTI3>2¦.
Figure 3.2

karKNnaeRKOgbgÁúMrgkarTaj CakareRCIserIsGgát;Edlmanmuxkat;RKb;RKan; edIm,ITb;nwgkug
RtaMgEdl)anBIbnÞúkemKuN. kñúgkrNIEdlsÁal;muxkat;Ggát; ersIusþg;KNna (design strength)
RtUv)anKNna nigeFVIkareRbobeFobCamYybnÞúkemKuN. CaTUeTA analysis CadMeNIrkarKNnaviPaK
ÉcMENk design CadMeNIrkarKNnasarcuHsareLIg ehIyRtUvkarkarsakl,g nigmankMhusecos
minput.

3>2> ersIusþg;KNna Design strength
eRKOgbgÁúMrgkarTajGacminCab;edaysßanPaBkMNt; (limit state) BIr³
- kMhUcRTg;RTayelIslb; (excessive deformation). edIm,IkarBarsßanPaBenH bnÞúkenAelI
gross section RtUvEtmantMéltUcRKb;RKan; EdlnaMeGaykugRtaMgenAelI gross section man

tMéltUcCagkugRtaMgyal (yield stress) F . y

Pn < Fy Ag

Edl Pn = nominal strength in yielding
Fy = yield strength
Ag = gross section area

29 eRKOgbgÁúMrgkarTaj

NPIC

- kardac; (fracture). edIm,IkarBarsßanPaBenH kugRtaMgenAelI net section RtUvEtmantMéltUc
CagersuIsþg;dac; (tensile strength) F . u

Pn < Fu Ae
Edl Pn = nominal strength in yielding
Fu = tensile strength
Ae = effective net area . kñúgkrNIxøH A mantMélesμI net section A EtkñúgkrNI
e n

xøHvamantMéltUcCag A . n

eTaHbICaenAelI net section ekItmanyalmunk¾eday EtkMhUcRTg;RTayenAelIRbEvg
éntMN mantMéltUcCagkMhUcRTg;RTayenAelIEpñkrgkarTajEdlenAsl;. mUlehtu KWsac;lUt
srub (total elongation) EdlCaplKuNRbEvgedIm nigsac;lUteFob (strain) ¬GnuKmn¾eTAnwgkug
RtaMg¦. sßanPaBkMNt; (limit state) sMerceGay gross section rgkugRtaMgyal (yield stress)
KWedaysarEtsac;lUtsrubmantMélFMCag minedaysarkaryalmuneT.
emKuNersIusþg; φ = 0.9 sMrab;karyal yielding
t

emKuNersIusþg; φ = 0.75 sMrab;kardac; fracture
t

BIsmIkar !># eyIgGacsresr
∑γ Q i i ≤ φt Pn

b¤ P ≤ φ P
u t n

Edl P CabnSMbnÞúkemKuNEdlmantMélFMCageK.
u

edaysareKman limit state BIr dUcenHsßanPaBTaMgBIrRtUvbMeBjlkçxNÐxageRkam³
uP ≤ 0.9 F A y sMrab;; gross section
g

uP ≤ 0.75F A sMrab;; net section
u e

tMéltUcCagkñúgcMeNamtMélTaMgBIrCa ersIusþg;KNnarbs;eRKOgbgÁúM.
RkLaépÞBitR)akdEdlRtUv)andkecjBI gross area edayvtþmanRbehagKWGaRs½yeTA
nwgdMeNIrkarplit. sMrab;karGnuvtþn_CaTUeTA rn§EdlecaHedaylkçN³bTdæan drill or punch
oversized holes eKRtUvbUkbEnßm 2mm eTAelIGgát;p©itrbs;b‘ULúg. sMrab; drill or punch standard

holes eKRtUvbUkbEnßm 4mm eTAelIGgát;p©itrbs;b‘ULúg EdleKeRbIR)as;. sMrab;rn§RTEvg slotted

30 Tension Members

T.chhay

holes 2mm RtUv)aneKbUkbEnßmeTAelIGgát;p©itrbs;b‘ULúg. xageRkamCataragbgðajBIGgát;p©itb‘ULúg
nigGgát;p©itrn§.
Nominal Hole Dimensions, mm
Ggát;p©itb‘ULúg xñatRbehag Hole Dimensions
Bolt Diameter Standard Oversize Short-Slot Long-Slot
(Dia.) (Dia.) (Width × Length) (Width × Length)
M16 18 20 18×22 18 ×40
M20 22 24 22×26 22×50
M22 24 28 24×30 24×55
M24 27 [a] 30 27×32 27×60
M27 30 35 30×37 30×67
M30 33 38 33×40 33×75
≥ M36 d+3 d+8 (d + 3)×(d + 10) (d + 3)× 2.5d
RtUvKña 25mm )
[a]Clearance provided allows the use of a 1-in. bolt if desirable. (

]TahrN_3>1³ r)aEdkm:ak A36 Edlmanmuxkat; 125 × 12.5mm RtUv)aneRbICaGgát;rgkarTaj.
2

vaRtUv)antP¢ab;eTAnwg gusset plate CamYynwgb‘ULúg M16 cMnYn 4 RKab; ¬rUbTI3>3¦. edaysnμt;fa
effective net area A esμInwg net area cUrkMNt;ersIusþg;KNna (design strength).
e

Figure 3.3

dMeNaHRsay³
EdkEdlmanm:ak A36 man F = 250MPa nig F
y u = 400MPa

sMrab; yielding én gross section

NPIC

Ag = 125 × 12.5 = 1562.5mm 2

ersIusþg; nominal
Pn = Fy Ag = 250 × 1562.5 = 390kN

ersIusþg;KNna (design strength)
φt Pn = 0.9 × 390 = 351kN
sMrab; fracture én net section
An = Ag − Aholes
= 1562.5 − 2 × (12.5 × 20) = 1062.5mm 2
Ae = An = 1062.5mm 2 ¬sMrab;Et]TahrN_enH¦
ersIusþg; nominal
Pn = Fu Ae = 400 × 1062.5 = 425kN
φt Pn = 0.75 × 425 = 348.75kN
dUcenH ersIusþg;KNna (design strength) φ P
t n = 348.75kN ¬tMéltUcCag CacMelIy¦

T§iBlénkugRtaMgpþúM (stress concentration) minRtUv)aneKBicarNakñúgkrNIenHeT EtFatuBit
kugRtaMgenARtg;rn§mantMélRbEhlbIdgkugRtaMgmFümEdlekItmanenAelI net area ehIykugRtaMgenA
Rtg; fillet énmuxkat;hUtekþA mantMélFMCagkugRtaMgmFümelIsBIrdg. edaysarEtPaBsVit b¤PaB
hUtlYs (ductile) rbs;EdkEdlTItaMgEdlman overstress RtUv)anecalsMrab;karKNnaTUeTA. eRkam
lkçxNÐCak;Esþg EdkGac)at;bg;PaBsVitrbs;va ehIy stress concentration GaceFVIeGayr)adac;
Pøam². sßanPaBenHrYmman fatigue loading nigeRkamsIutuNðPaBTabEmnETn.
Figure 3.4

]TahrN_3>2³ r)argkarTajmuxkat;EkgeTal L89 × 89 × 9.5 Rtv)anP¢ab;eTAnwg gusset plate
CamYynwgb‘ULúg M22 cMnYn 3 RKab; ¬rUbTI3>4¦. r)aEdkenH manm:ak A36 . bnÞúkefr DL = 155kN
32 Tension Members

T.chhay

nigbnÞúk LL = 67kN . viPaKmuxkat;enH edaysnμt; effective net area A esμIeTAnwg 85% rbs; net
e

area .

dMeNaHRsay³
bnSMbnÞúk (load combination)
(A4-1): 1.4 DL = 1.4 × 155 = 217 kN
(A4-2): 1.2 DL + 1.6 LL = 1.2 × 155 + 1.6 × 67 = 293.2kN > 217 kN
⇒ Pu = 293.2kN
gross section: Ag = 1610mm 2
φt Pn = φt Fy Ag = 0.9 × 250 × 1610 = 362.25kN
net section: An = 1610 − (9.5 × 26) = 1363mm 2
Ae = 0.85 × 1363 = 1158.55mm 2
φt Pn = φt F y u Ae = 0.75 × 400 × 1158.55 = 347.57kN < 362.25kN

eday P < φ P
u t n (293.2kN < 347.57kN ) dUcenH r)armansuvtßiPaBedaybMeBjlkçxNÐ.

enAkñúg]TahrN_xagelIenH eyIgeXIjfa bnSMMbnÞúk (A4-2) RtUv)anykmkeFVIkarKNna. enA
eBlmanEtbnÞúkefr nigbnÞúkGefreFVIGMeBIelIeRKOgbgÁúM enaHbnSMbnÞúk (A4-2) RtUv)anykmkeFVIkar
KNna enAeBlEdlbnÞúkefr tUcCagbnÞúkGefr *dg. sMrab;]TahrN_xagmux eyIgnwgmineFVIkarepÞóg
pÞat;bnSMbnÞúk 1.4D (A4-1) eT edaysarEtvaminGacFMCagbnSMbnÞúk (A4-2).

3>3> RkLaépÞmuxkat;RbsiT§PaBsuT§ Effective net area
kñúgcMeNamktþaCaeRcInEdlmanT§iBleTAelIkarRbRBwtþeTArbs;r)arrgkarTaj rebobénkart
Pa¢b;CaktþamYyEdlsMxan;CageK. tMNPaKeRcInEtgEteFVIeGayr)arcuHexSay karKNnanUvT§iBl
rbs;vaRtUv)aneKehAfa Joint efficiency . ktþaenHCaGnuKmn_eTAnwgPaBsVitrbs;sMPar³ (ductility of
material) KMlatrbs;eRKOgP¢ab; (fastener spacing) kugRtaMgpþúMenARtg;Rbehag (stress

concentration) TMrg;énkarplit rYmTaMg)atuPUtEdleKsÁal;fa shear leg. ktþaTaMgenHnaMeGaymankar

kat;bnßyRbsiT§PaBrbs;r)ar b:uEnþ shear lag CaktþamYyEdlsMxan;CageK.
Shear lag ekItmanenAeBlEdlmuxkat;r)arTaMgmUlminRtUv)antP¢ab; dUcCaenAeBlEdleCIg

mçagrbs;EdkEkgRtUv)anP¢ab;edaysarb‘ULúgeTAnwg gusset plate ¬rUbTI3>5¦. sar³sMxan;rbs;kart

NPIC

P¢ab;edayEpñk eFVIeGayEpñkrbs;r)arEdltP©ab;rgbnÞúkFM (overload) ehIyEpñkEdlmintP¢ab;minman
rgkugRtaMgeBjelj. karbnøayRbEvgtMbn;tP¢ab;CYykat;bnßyT§iBlenH. karRsavRCavEdleFVIeLIg
eday Munse nig Chesson (1963) )ansMNUmBreGayKit shear lag kñúgkarkat;bnßy net area.
edaysarEt Shear lag manT§iBleTAelITaMgkartP¢ab;edayb‘ULúg nigkarpSar enaH effective net area
RtUv)anGnuvtþcMeBaHtMNTaMgBIrRbePTenH.
Figure 3.5

Effective net area sMrab;tMNb‘ULúg
Ae = UAn
Effective net area sMrab;tMNpSar
Ae = UAg

U CaemKuNkat;bnßyRbsiT§PaB (reduction factor)
x
U = 1− ≤ 0.9 (AISC Equation B3-2)
L
x CacMgayBITIRbCMuTMgn;rbs;muxkat;eTAbøg;énkartP¢ab;.
L CaRbEvgénkartP¢ab;.

RbsinebIr)artP¢ab;edaymanlkçN³sIuemRTI x RtUveRCIserIsyktMéltUcCageK ¬rUbTI3>6¦.

Figure 3.6

34 Tension Members

T.chhay

L CaRbEvgtP¢ab;tamTisedAbnÞúkeFVIGMeBI ¬rUbTI3>7¦. sMrab;tMNb‘ULúg L RtUv)anvas;BIcug
mçagrbs;GkS½b‘ULúg eTAcugmçageTotrbs;GkS½b‘ULúg. sMrab;tMNpSar L RtUv)anvas;BIcugtMNmçageTA
tMNmçag. RbsinebI kMNat;EdlpSarmanRbEvgtamTisedAkMlaMg RbEvgkMNat;EdlmanRbEvgEvgCag
RtUv)anykmkKNna.
Figure 3.7


NPIC

tMélmFüm L sMrab;karP¢ab;edayb‘ULúgsMrab;Ggát;rgkarTajepSg² Commentary to AISC
x

B3 eGaytMél U CMnYseGaykarKNna 1 − . tMélmFüm U sMrab;tMNb‘ULúgmanBIrRbePT³ sM
x
L
rab;karP¢ab;eday fastener BIrkñúgmYyCYrtamTisedAbnÞúkeFVIkar nigsMrab;karP¢ab;eday fastener bIb¤
eRcInkñúgmYyCYr. eKeGaytMél U bIepSgKña EdleKaeBtamlkçxNÐxageRkam³
!> sMrab;EdkEdlmanmuxkat; W, M, S EdlmanpleFobTTwgelIkMBs;y:agtic ¬nigsMrab;
2
3

muxkat; T Edlkat;ecjBImuxkat;TaMgbIxagelI¦ ehIyRtUv)anP¢ab;enAnwgsøabCamYynwg fastener y:ag
ticbIkúñgmYyCYrtamTisedAbnÞúkeFVIGMeBI
U = 0 .9
@> sMrab;RKb;TMrg;muxkat;epSgeTot ¬rYmTaMgmuxkat; built-up¦ CamYynwg fastener y:agticbI
kúñgmYyCYr
U = 0.85
#> sMrab;RKb;Ggát;TaMgGs; CamYynwg fastener y:agticBIrkúñgmYyCYr
U = 0.75
rUbxageRkamnwgbgðajnUv bMerIbMras;c,ab;TaMgenH ¬rUbTI3>8¦.
eKk¾GaceRbIR)as;tMél U mFümsMrab;tMNpSarEdr. ebIeTaHCamin)anbriyaykñúg
Commentary k¾eday EtvaCaectnarbs; ¬AISC, 1989b¦. c,ab;enHdUcKña EtelIkElgsMrab;karpþl;

eGayEdleqøIytbeTAnwg fastener BIrminRtUv)anGnuvtþ. tMélmFüm U sMrab;tMNpSarmandUcxag
eRkam³
!> sMrab;EdkEdlmanmuxkat; W, M, S EdlmanpleFobTTwgelIkMBs;y:agtic ¬nigsMrab;
2
3

muxkat; T Edlkat;ecjBImuxkat;TaMgbIxagelI¦ ehIyRtUv)anP¢ab;enAnwgsøab
U = 0 .9
@> sMrab;RKb;TMrg;muxkat;epSgeTot
U = 0.85

36 Tension Members

T.chhay

Figure 3.8

krNIBiesssMrab;kartedaykarpSar
Ae mantMéltUcCag A enAeBlEdlmuxkat;rbs;Ggát;xøHb:ueNÑaHminRtUv)antP¢ab;. sMrab;Ggát;
n

rgkarTajdUcCa bnÞHEdk b¤r)ar ¬dUcbgðajkñúg]TahrN_3>1¦ effective net area RtUv)anykeBj
dUckarKNna net area. EteTaHCay:agNa vamankrNIelIkElgsMrab;c,ab;enH³ sMrab;bnÞHEdk b¤Edk
r)arEdltP¢ab;edaykarpSartambeNþay (longitudinal weld) Epñkxagcugrbs;va ¬rUbTI3>9¦ .

NPIC

Figure 3.9

Ae = UAn
Edl U =1 sMrab; l ≥ 2w
U = 0.87 sMrab; 1.5w ≤ l < 2w
U = 0.75 sMrab; w ≤ l < 1.5w
l = RbEvgkarpSar > w
w = cMgaycenøaHkarpSar ¬EdlGacykTTwgrbs; plate b¤ bar¦

AISC B3 k¾eGaynUvkrNIBiessmYysMrab;Ggát;edaykarpSarEt transverse weld b:ueNÑaH

A = RkLaépÞmuxkat;EdlpSar
e

¬rUbTI3>10¦ bgðajBIPaBxusKñarvagkarpSartambeNþay (longitudinal weld) nigtamTTwg
(transverse weld). karEdlpSarEt transverse weld CakarxusFmμta EdleKmineRbIkñúgplitkmμeT.

Figure 3.10

]TahrN_TI3>3³ kMNt; effective net area sMrab;Ggát;rgkarTaj ¬rUbTI3>11¦

38 Tension Members

T.chhay

Figure 3.11

dMeNaHRsay³ A n = Ag − Aholes

An = 3.72 × 10 −3 − (12.7 × 20) × 2 × 10 −6 = 3.212 × 10 −3 m 2
eCIgEtmçagb:ueNÑaHrbs;muxkat;RtUv)anP¢ab; dUcenH net area RtUvEtkat;bnßy. BItaraglkçN³
kñúgEpñkTI1 rbs; Manual cMgayBITIRbCMuTMgn;eTAépÞxageRkAéneCIgrbs; L152 × 152 × 12.7 KW
x = 4.25 × 10 −2 m
RbEvgtP¢ab;KW L = 75 × 2 = 150mm
42.5
U = 1− = 0.717 < 0.9
150
Ae = UAn = 0.717 × 3.212 ⋅ 10 −3 = 2.3 ⋅ 10 −3 m 2
eKGaceRbItMélmFüm U BI Commentary . edaysarEtmuxkat;minEmn W, M, S b¤ GkSr T
ehIymanb‘ULúgeRcInCagBIrkñúgmYyCYrtamTisbnÞúkeFVIGMeBI U = 0.85
Ae = 0.85 × 3.212 ⋅ 10 −3 = 2.73 ⋅ 10 −3 m 2
tMél U TaMgBIrGacTTYlyk)anTaMgBIr EttMél U Edl)anBIkarKNnatam AISC Equation
B3-2 mantMélsuRkitCag. EteTaHCay:agNak¾eday k¾tMélmFüm U manRbeyaCn_sMrab;karKNna

dMbUg (preliminary design) enAeBlEdlmuxkat;BitR)akd nigB½t’manlMGitGMBIkarpSarminTan;RtUv)an
dwgenaH.

]TahrN_TI3>4³ RbsinebIGgát;kñúg]TahrN_TI3 RtUv)anpSardUcbgðajkñúgrUbTI3>12 cUrkMNt;
effective net area


NPIC

Figure 3.12

dMeNaHRsay³ dUckñúg]TahrN_TI3>3 manEtEpñkmuxkat;tP¢ab; nig reduced effective net area
RtUv)aneRbI. karP¢ab;RtUv)aneFIVeLIgCamYynwgkarpSartambeNþay nigtamTTwg dUcenHvaminEmnCa
krNIBiesssMrab;Ggát;pSareT.
⎛x⎞ ⎛ 42.5 ⎞
U = 1− ⎜ ⎟ = 1− ⎜ ⎟ = 0.7 < 0.9
⎝L⎠ ⎝ 140 ⎠
cMeLIy³ A e = UAg = 0.7 × 3.72 ⋅ 10 −3 = 2.604 ⋅ 10 −3 m 2

3>4> kartMerobtamEbbqøas; Staggered fasteners
RbsinebIkartP¢ab;Ggát;eFIVeLIgCamYynwgb‘ULúg net area nwgmantMélGtibrmakñúgkrNIEdl
eRKOgP¢ab; (fastener) RtUv)andak;EtmYyCYr. eBlxøH edaysarEtKMlatRtUv)ankMNt; dUcCaTMhM a enA
kñúgrUbTI3>13 (a) caM)ac;eFVIeGayeKRtUvEteRbIeRKOgP¢ab;eRcInCagmYyCYr. RbsinebIdUcenH karkat;
bnßyRkLaépÞmuxkat;RtUv)ankat;bnßy RbsinebIeRKOgP¢ab;RtUv)antMerobtamEbbqøas; staggered
pattern dUcbgðaj. eBlxøH Staggered fasteners RtUv)antMrUveGayerobtamlkçN³FrNImaRtdUc

bgðajkñúgrUbTI13 (b). kñúgkrNIepSgeTot muxkat;xøHEdlkat;tamrn§nwgkat;tamrn§EdlmancMnYntic
CagRbsinebIeRKOgP¢ab;minRtUv)antMerobtamEbbqøas;eTenaH.
RbsinebIcMnYnén stagger mancMnYnticlμm enaHkarP¢ab;Gacdac;tamExSKenøag abcd dUckñúgrUbTI
3>13 (c). kñúgkrNIEbbenH eKminGacGnuvtþTMnak;TMng f = P A )aneT ehIykugRtaMgenAkñúgmuxkat;
tamExSeRTt bc KWCabnSMénkugRtaMgTaj nigkugRtaMgkMlaMgkat;. viFIsaRsþ approximate CaeRcIn
RtUv)anesñIeLIgedIm,IBnül;GMBIRbsiT§PaBrbs; staggered hole. elak Cochran (1922) )anesñInUvkar
40 Tension Members

T.chhay

eRbIR)as;RkLaépÞsuT§ net area EdlesμInwgplKuNrvagkMras;bnÞH nigTTwgsuT§ net width. karKNna
RkLaépÞRtUv)aneFVIeLIgdUcteTA³ kMNt;nUvExSdac;EdlGacekIteLIg)anedIm,IeFVIkarGegát nigeGay
TTwgsuT§ net width esμInwgTTwgdkeGay
s2
d'= d − (2-1)
4g
sMrab;muxkat;dac;tam staggered hole b¤dk d sMrab;muxkat;dac;tam unstaggered hole. d CaGgát;
p©itRbehag s (pitch) CaRbEvgKMlatrvagrn§BIr CitKñatamTisedARsbnwgbnÞúk nig g (gage) CaRbEvgKM
latRbehagtamTTwg. AISC specification k¾eRbInUvnUvviFIsaRsþdUcKñaenHEdr b:uEnþkñúgTMrg;xusKñabnþic.
Epñk B2 tMrUvfa TTwgsuT§RtUv)anKNnaeday dkplbUkGgát;p©itRbehagBITTwg ehIybUkbEnßmExSeRTt
2
tamCYrmYy²EdlmantMél 4 g . s

Figure 3.13

s2
wn = w g − ∑ d + ∑
4g
enAeBlEdlkardac;GacekIteLIgCaTMrg;eRcIn eKRtUveFVIkarGegátRKb;lT§PaBénkardac;TaMgGs;
ehIy net width EdlmantMéltUcCageKbMputRtUv)anykmkeRbI. cMNaMfa viFIsaRsþenHmin)anpþl;nUv
TMrg;nwgkardac;CamYyExSRsbeTAnwgTisedAbnÞúkeFVIGMeBIenaHeT.


NPIC

]TahrN_TI3>5³ KNna net area EdltUcbMputsMrab;bnÞHEdlbgðajkñúgrUbTI3>14 . RbehagTaMg
Gs;sMrab;b‘ULúgGgát;p©it 25mm .
Figure 3.14

dMeNaHRsay³ Ggát;p©itRbehagRbsiT§PaB effective hole diameter KW 30mm
sMrab;ExSbnÞat; abcd
wn = 410 − 2(30) = 350mm
sMrab;ExSbnÞat; abcde
2(75) 2
wn = 410 − 3(30) + = 341.6mm < 350mm
4(130)
cMeLIy³ A n = twn = 20 × 341.6 = 6832mm 2

edaysarEteRKOgP¢ab; (fastener) nImYy²Tb;Tl;nUvkMlaMgesμI²Kña ¬karsnμt;EdleRbIenAkñúg
karKNnatMNsamBaØ kñúgCMBUkTI 7¦ sñamExSdac;EdlmanlkçN³epSgKña GaceFVIeGaymuxkat;Rtg;
kEnøgdac;rgnUvkMlaMgepSgKña. ]TahrN_ ExS abcde kñúgrUbTI3>14 muxkat;rbs;Ggát;Rtg;kEnøgdac;rg
nUvkMlaMgeBj 100% EdlExS ijfh eFVIeGaymuxkat;rbs;Ggát;Rtg;kEnøgdac;Tb;Tl;Et 8 / 11 énkMlaMg
EdlGnuvtþ. mUlehtuKW kMlaMg 3 / 11 EdlbBa¢ÚnBIGgát;RtUv)anTb;edayeRKOgP¢ab; munnwg ijfh TTYlnUv
bnÞúk.
enAeBlEdl eRKOgP¢ab; (fastener) RtUv)anP¢ab;CaCUrenAelIeCIgTaMgBIrrbs;EdkEkg ehIykar
P¢ab;manlkçN³qøas; staggered KñaeTAvijTAmk enaHedIm,ITTYl)anRkLaépÞ net area dMbUgeKRtUvBnøat
42 Tension Members

T.chhay

EdkEkgedIm,ITTYl)anbnÞHEdksmmUl. bnÞHEdkenHRtUv)anviPaKdUcbnÞHEdkdéTeTotEdr. karBnøat
RtUv)aneFVIeLIgtamRTnugEdkEkg Edlpþl;eGaynUvTTwgEdkbnÞHesμIeTAnwgplbUkRbEvgeCIgrbs;vadk
nwgkMras;EdkEkg. AISC B2 kMnt;faRbEvg g Edlkat;tamRTnugEkgrbs;EdkEkg RtUv)andkedaykM
ras;EdkEkg. dUcenH RbEvg g enAkñúgrUbTI3>15 EdlRtUv)anykeTAeRbIkñúgtY s 2 / 4 g nwgmantMél
esμInwg 75 + 50 − 12 = 113mm .
Figure 3.15

]TahrN_TI3>6³ cUrrkPaBFn; design tensile strength rbs;EdkEkgdUcbgðajkñúgrUbTI 3>16. Edk
A36 RtUv)aneKykmkeRbIEdlmanRbehagsMrab;b‘ULúg 22mm.

dMeNaHRsay³ KNna net width
wg = 203 + 152 − 12.7 = 342.3mm

Ggát;p©itRbehagRbsiT§PaB effective hole diameter esμI 28mm
sMrab;ExSbnÞat; abdf w = 342.3 − (2 × 28) = 286.3mm
n
2
sMrab;ExSbnÞat; abceg w = 342.3 − (3 × 28) + 4(× 63.5 = 263.98mm
n
38)

Figure 3.16


NPIC

edaysarEt bnÞúk 1 / 10 RtUv)anepÞrBIGgát;edayeRKOgP¢ab;enAcMnuc d enaHExSrdac; potential
failure line enHRtUvEtTb;nwgbnÞúkEt 9 / 10 . dUcenH net width 263.98mm RtUvEtKuNnwg 10 / 9

edIm,ITTYl)an net width EdlGaceRbobeFobCamYynwgExSbnÞat;EdlTb;nwgbnÞúkeBj 100% .
dUcenHExSbnÞat; abceg man w = 263.98 ×10 / 9 = 293.31mm
n

sMrab;ExSbnÞat; abcdeg
g cd = 76 + 57 − 12.7 = 120.3mm
(38) 2 (38) 2 (38) 2
wn = 342.3 − (4 × 28) + + + = 243.74mm
4 × 63.5 4 × 120 4 × 76
eday net width Edldac;tamExS abcdeg mantMéltUcCageK dUcenHkrNIenHRtUv)anykmk
KNna net area
An = 12.7 × 243.74 = 3095.5mm 2
edaysarEteCIgTaMgBIrrbs;EdkEkgRtUv)anP¢ab; dUcenH
Ae = An = 3095.5mm 2
ersIusþg;KNnaKW
φt Pn = 0.75Fu Ae = 0.75 × 400 × 3095.5 = 928.65kN
φt Pn = 0.5Fy An = 0.9 × 250 × 4390 = 987.75kN
cMeLIy³ ersIusþg;KNnaKW 928.65kN

cMNaMfa plKuNrvag gross width nwgkMras;EdkEkgKWCa gross area krNIRtwmRtUvRbsinebI
eCIgrbs; EdkEkgmanragctuekaNEkg. mUlehtuKWfa eKGacTTYl)anragctuekaNEkgeday dképÞ
enARtg;rbt;Ekg nigbUkbEnßmépÞenARtg;cugEdkEkg.
AISC Specification min)anpþl;nUvkarENnaMsMrab;karerobeRKOgP¢ab;tamEbbqøas;enAelI

rolled shape eRkABI EdkEkg. bnÞHEdksmmUlmanPaBsμúKsμajedaysarkMras;Ggát;manPaBxusKña

dUckrNIEdk channel nig wide flange . enAkñúgkrNIEbbenH eKesñIeGayeRbIRkLaépÞ ¬RbesIrCag
TTWg¦ nigdkGgát;p©itrn§ EdleGayedaysmIkar (2-1).
enAkñúg]TahrN_TI3>7 RKb;rn§RbehagTaMgGs;sßitenAEtmYyEpñkénmuxkat;.

44 Tension Members

T.chhay

]TahrN_TI3>7³ kMNt;RkLaépÞmuxkat;suT§Gb,brma (smallest net area) sMrab;Edk American
Standard Channel dUcbgðajenAkñúgrUbTI3>17. RbehagsMrab;b‘ULúgEdlmanGgát;p©it 16mm.

dMeNaHRsay³ A n = Ag − ∑ t w × (d b¤ d')

d = 20mm
ExSbnÞat; abc
An = Ag − t w d = 2460 − 11.1 × 20 = 2238mm 2

ExSbnÞat; abcd
An = Ag − t w (d sMrab;RbehagRtg; b) − t w (d ' sMrab;RbehagRtg; c)
⎡ 50 2 ⎤
= 2460 − 11.1 × 22 − 11.1 × ⎢22 − ⎥ = 2064.1mm
2
⎢
⎣ 4 × 75 ⎥
⎦
cMelIy³ RkLaépÞmuxkat;Gb,brma (smallest net area) KW 2064.1mm 2

Figure 3.18


NPIC

enAeBlEdlEpñkCaeRcInrbs;muxkat;manRbehag eKeRbIviFIsaRsþedaHRsayxusKñabnþic. eTaH
bICaEdkEdlmanrUbragepSgBIEdkEkgminGacBnøattamviFIEdlEdkEkgBnøatk¾eday k¾eKmanviFIsaRsþ
epSgeTotkñúgkarBnøatrUbragEdkTaMgenaHEdr. viFIsaRsþkñúgkarBnøatEdkTaMgenaHRtUv)anbgðajkñúgrUbTI
3>18 nigkñúg]TahrN_TI3>8.

]TahrN_TI3>8³ kMNt;ersIusþg;KNnarbs;Edk S-Shape dUcbgðajkñúgrUbTI3>19. RbehagKWsMrab;b‘U
LúgEdlmanGgát;p©it 20mm . eRbIEdk A36 .

Figure 3.19

dMeNaHRsay³ KNnaRkLaépÞ net area
A = A − ∑ (t × Ggát;p©itRbehag )
n g

Ggát;p©itRbehagRbsiT§PaB = 24mm
sMrab;ExS ad
An = 9470 − 4 × 24 × 15.8 = 7953.2mm 2
2
sMrab;ExS abcd RbEvg g sMrab;eRbIenAkñúgtY 4 g KW
s

g t 89 14
+ g1 − w = + 70 − = 107.5mm
2 2 2 2
edayKitRbehagRtg; b nigRtg; c CaRbehagEdlerobqøas; eKTTYl)an
⎛ 382 ⎞
An = 9470 − 4 × 15.8 × 24 − 2 × 14 × ⎜ 24 − ⎟ = 7375.23mm 2
⎜ 4 × 107.5 ⎟
⎝ ⎠
kardac;tamExS abcd mantMéltUcCageK. edaysarRKb;EpñkTaMgGs;rbs;muxkat;RtUv)anP¢ab; dUcenH
Ae = An = 7375.23mm 2
sMrab; net section
46 Tension Members

T.chhay

φt Pn = 0.75Fu Ae = 0.75 × 400 × 7375.23 = 2212.57kN
φt Pn = 0.5Fy An = 0.9 × 250 × 9470 = 2130.75kN
cMeLIy³ ersIusþg;KNnaKW 2130.75kN

3>5> Block shear
sMrab;rUbsNæanénkartP¢ab;xøH kMNat; b¤bøúkénsMPar³enAxagcugénGgát;GacrEhk. ]TahrN_
kartP¢ab;rbs;Ggát;ragEkgeTalrgkarTaj dUcbgðajkñúgrUbTI3>20 gayrgnUv)atuPUtEbenH EdleK
eGayeQμaHfa block shear ¬kardac;TaMgbøúk¦. sMrab;krNIEdl)anbgðajkñúgrUb épÞEdlqUtGacdac;
edaykMlaMgkat;TTwg (shear) tammuxkat;beNþay ab nigkMlaMgTaj (tension) tammuxkat;TTwg bc.
RbFanbT enHmin)anbgðajy:agc,as;kñúg AISC Chapter D (“Tension Members”) eT b:uEnþkfaxN½Ð
epþImdMbUg )anENnaMeyIgeTAkan; Chapter J (“Connections, Joints, and Fasteners”), Section J4.3
(“Block Shear Rupture Strength”).

nitiviFIKWQrenAelIkarsnμt;fa muxkat;dac;mYyKWdac;eday fractures nigmYyeTotdac;eday
yielding. enaHmann½yfa muxkat;EdlrgkugRtaMgTaj yield naMeGaymuxkat;EdlrgkugRtaMgkMlaMg

kat;TTwg fracture b¤pÞúymkvij. muxkat;TaMgBIrenH naMmknUvPaBFn;srub ehIyersIusþg;rbs; block
shear KWCaplbUkénPaBFn;énmuxkat;TaMgBIr.

Figure 3.20

PaBFn;Fmμta (nominal strength) enAkñúgGgát;rgkarTajKW Fu Ant sMrab; fracture nig Fy Agt
sMrab; yield Edl Ant KWCa net area nig Agt KWCa gross area tambeNþaymuxkat;rgkarTaj ¬ bc
enAkñúgrUbTI3>20¦. edayykkugRtaMg yield kMlaMgkat; nigkugRtaMg ultimate kMlaMgkat;esμI 60%

NPIC

énkugRtaMgkMlaMgTaj enaHersIusþg;Fmμta (nominal strength) sMrab;kMlaMgkat; fracture KW 0.6Fu Anv
nigersIusþg;sMrab;kMlaMgkat; yield KW 0.6Fy Agv Edl Anv KWCa net area nig Agv KWCa gross area
tambeNþaymuxkat;rgkMlaMgkat; ¬ ab enAkñúgrUbTI20¦.
eKGacmanTMrg;énkardac;Ca2rebob.
sMrab;kMlaMgkat; yield nigkMlaMgTaj fracture ersIusþg;KNnaKW
φRn = φ[0.6 Fy Agv + Fu Ant ] (AISC Equation J4-3a)

sMrab;kMlaMgTaj yield nigkMlaMgkat; fracture ersIusþg;KNnaKW
φRn = φ[0.6 Fu Anv + Fy Agt ] (AISC Equation J4-3a)

sMrab;krNITaMgBIr φ = 0.75 . BIeRBaH sßanPaBkNt; limit state KW fracture smIkarEdlman
lub KWsmIkarNaEdlmantY fracture FMCag.
]TahrN_TI3>9³ kMNt;ersIusþg; block shear rbs;Ggát;rgkarTajdUcbgðajenAkñúgrUbTI3>21.
rn§RbehagRtUv)aneRbIsMrab;Ggát;p©it 22mm nigEdkRbePT A36RtUv)aneRbI.
Figure 3.21

dMeNaHRsay³
RkLaépÞkMlaMgkat;KW
Agv = 9.5 × 190 = 1805mm 2

edaysarEtman 2.5 Ggát;p©itrn§
Anv = 9.5 × [190 − 2.5 × 28] = 1140mm 2
RkLaépÞmuxkat;kMlaMgTaj
Agt = 9.5 × 39 = 370.5mm 2

Ant = 9.5 × [39 − 0.5 × 28] = 237.5mm 2
edayeRbI AISC Equation J4-3a eKTTYl)an
48 Tension Members

T.chhay

φRn = φ[0.6 Fy Agv + Fu Ant ]

= 0.75 × [0.6(250 )(1805) + 400 × 237.5]

= 0.75 × [270750 + 95000] = 274.3kN
edayeRbI AISC Equation J4-3b eKTTYl)an
φRn = φ[0.6 Fu Anv + Fy Agt ]

= 0.75 × [0.6(400 )(1140 ) + 250 × 370.5]

= 0.75 × [273600 + 92625] = 274.7 kN
smIkarTI 2 mantY fracture FM ¬tYEdlman F ¦ dUcenHsmIkarTI 2 lub.
u

cMeLIy³ ersIusþg;KNnasMrab; block shearKW 274.7kN

3>6> karKNnaGgát;rgkarTaj Design of tension members
karKNnaGgát;rgkarTaj KWkarKNnark gross area nig net area RKb;RKan;sMrab;Ggát;Edlrg
karTaj. RbsinebIGgát;enaHRtUv)anP¢ab;edaytMNb‘ULúg enaHeKRtUvkarnUvmuxkat;smRsbsMrab;RkLa
épÞEdl)an)at;bg;edaysarrn§tMN. sMrab;Ggát;Edlmanmuxkat;ctuekaNEkg karKNnamanlkçN³
RsYlCag. RbsinebImuxkat; rolled shape RtUv)aneRbImuxkat;EdlRtUvkat;bnßyminGacRtUv)an
BüakrN_TukCamun)an BIeRBaHkMras;rbs;muxkat;enARtg;cMnucrn§minRtUv)andwg.
karBicarNabnÞab;kñúgkarKNnaGgát;rgkarTajKW PaBrlas; (slenderness). RbsinebIGgát;
rbs;eRKagbgÁúMmanmuxkat;tUceFobeTAnwgRbEvgrbs;va enaHGgát;enaHmanlkçN³Rsav (slender). kar
KNnaEdlmanlkçN³suRkit KWpleFobrlas; (slenderness ration) R Edl L CaRbEvgrbs;Ggát;
L

nig r Ca kaMniclPaB (radius of gyration) énRkLaépÞmuxkat;Gb,brma. kaMniclPaB (radius of
gyration) Gb,brma KWRtUvKñanwgGkS½ minor principal énmuxkat;. tMélrbs; radius of gyration

RtUv)anerobCataragsMrab;muxkat; rolled shape TaMgGs;enAkñúg properties tables enAkñúgEpñkTI1 én
Manual.

sMrab;Ggát;rgkarsgát; slenderness mansar³sMxan;sMrab;ersIusþg; (strength) b:uEnþ
slenderness minsUvCasMxan;sMrab;Ggát;rgkarTajb:unμaneT. eTaHCay:agnwgk¾eday enAkñúgsßanPaBxøH

vaCakarRbesI sMrab;karkMNt;nUv slenderness sMrab;Ggát;rgkarTaj. RbsinebIbnÞúkcMGkS½enAkñúg


NPIC

Ggát;rgkarTajRsav (slender tension member) RtUv)anCMnYsedaybnÞúktamTTwg transverse load
tUc enaHrMjr½EdleKminR)afñacg;)an b¤PaBdabnwgekItmaneLIg. Ca]TahrN_ krNIenHGacekIteLIg
sMrab;EdkBRgwg (bracing rod) EdlmanlkçN³mintwgRbQmnwgkMlaMgxül;. sMrab;krNIenH AISC
B7 )anesñInUv slenderness ratio GtibrmaesμInwg 300. tMélenHRKan;EtCatMélesñI (commended

value) BIeRBaH slanderness minmanPaBsMxan;sMrab;Ggát;rgkarTajeT ehIytMélenHGacRtUv)anykFM

CagenHenAeBl Edlkal³eTs³BiessGnuBaØteGay. EdntMélenHminRtUv)anGnuvtþeTAelIExSkabeT
ehIy specification k¾)anelIkElgcMeBaHEdksrésEdr.
bBaðasMxan;kñúgkarKNnaRKb;muxkat;TaMgGs; rYmbBa©ÚlTaMgkarKNnaGgát;rgkarTaj KWkarrk
nUvmuxkat; EdlplbUkbnÞúkemKuNTaMgGs;minRtUvelIsersIusþg;rbs;Ggát;. Edl
∑ γQ ≤ φRn
sMrab;Ggát;rgkarTaj smIkarenHmanrag
Pu ≤ φt Pn b¤ φt Pn ≥ Pu
Edl Pu KWCaplbUkbnÞúkemKuN. edIm,IKNna yielding
0.9 Fy Ag ≥ Pu b¤
Pu
Ag ≥
0.90 F y

edIm,IeCosvag fracture
0.75Fu Ae ≥ Pu b¤ Ae ≥ 0.75uFP
u

Slenderness ratio RtUv)anbMeBjRbsinebI
L
r≥
300
Edl r Ca radius of gyration Gb,brma nig L CaRbEvgGgát;.

]TahrN_TI3>10³ Ggát;rgkarTajEdlmanRbEvg 1750mm RtUvTb;nwgbnÞúkefresvakmμ (service
dead load) 80kN nigbnÞúkGefresvakmμ (service live load) 233kN . eRCIserIsGgát;Edlmanmux

kat;ctuekaNEkg. eRbIEdk A36 nigtMNRtUv)ansnμt;eRbIb‘ULúgEdlmanGgát;p©it 22mm mYyCYr.
dMeNaHRsay³
Pu = 1.2 × 80 + 1.6 × 233 = 468.8kN

50 Tension Members

T.chhay

468.8 ⋅ 103
muxkat;caM)ac; Ag =
Pu
0.9 Fy
=
0.9 × 250
= 2083.6mm 2

muxkat;caM)ac; A = 0.75F = 468.8×⋅400 = 1562.7mm
3
P u 10 2
e
0.75 u

edaysarEt A = A sMrab;Ggát;enH gross area EdlRtUvKñanwg muxkat;caM)ac; net area enHKW
e n

Ag = An + Ahole

= 1562.7 + 28 × t
sakl,g t = 25mm
Ag = 1562.7 + 28 × 25 = 2262.7mm 2

edaysarEt 2262.7 > 2083.6 dUcenHmuxkat;caM)ac;KW 2262.7mm 2

Ag 2262.7
wg = = = 90.5mm
t 25
sakl,gmuxkat; 25 × 92
epÞógpÞat; slenderness ratio
92 × 253
I min = = 119791.7mm 4
12
A = 25 × 92 = 2300
BI I = Ar eyIgTTYl)an
2

I min 119791.7
rmin = = = 7.22mm
A 2300
L 1750
= = 242.4 < 300 (OK)
r 7.22
cMeLIy³ eRbIEdlEdlmanmuxkat; 25 × 92 .

Ggát;enAkñúg]TahrN_TI3>10 manTTwgtUcCag 203mm EdlRtUv)aneKcat;fñak;vaCar)arEdk
bar CaCagEdkbnÞH plate. r)arEdkKYrRtUv)ankMNt;edayeGayTTwgrbs;vaERbRbYlmþg 5mm nigkM

ras;rbs;vaERbRbYlmþg 2mm ¬RbBn§½cMNat;fñak;Cak;lak;RtUv)anpþl;eGaykñúgEpñkTI1 én Manual
eRkamcMNgeCIg “Bars and Plates”.


NPIC

Figure 3.22

KMlatRbehagtamTTWgsMrab;EdkEkg (mm)
Leg 203 178 152 127 102 89 76 64 51 44 38 35 32 25
g1 114 102 89 76 64 51 44 35 26 25 22 22 19 16
g2 76 64 57 51
g3 76 76 64 44

(b)

RbsinebIEdkEkgRtUv)aneRbICaGgát;rgkarTaj ehIykartP¢ab;RtUv)aneFVIeLIgedayeRbIb‘ULúg
enaHvacM)ac;RtUvmanépÞ ¬TMhM¦ RKb;RKan;sMrab;bLúg. vaGacekItmanbBaðaenAeBlEdl eKeRbIb‘ULúgBIr
‘U
CYrenAelIeCIgmYy. rn§RbehagRtUv)anecaHenATItaMgdUcbgðajenAkñúgrUbTI3>22 (a) sMrab;karplitTUeTA
eday)andkecjBIrUbTI 9-5 enAkñúgEpñkTI9 én Manual (VOL. II). cMgayKMlatRbehagtamTTwg
gage g1 RtUv)aneRbIenAeBlEdleKmanb‘ULúgmYyCYr ehIy g 2 nig g 3 RtUv)anenAeBlEdleKmanb‘U

LúgBIrCYr. rUbTI3>22 (b)bgðajfaeCIgEdkEkgRtUvmanRbEvgy:agxøIbMput 127mm edIm,IGnuBaØateGay
eRbIb‘ULúgBIrCYr)an.

]TahrN_TI3>11³ KNnaGgát;rgkarTajEdlmanmuxkat;EdkEkgeCIgminesμIKña (unequal-leg angle)
RbEvg 4.6m Tb;nUv service dead load 155kN nig service live load 310kN . eRbIEdkRbePT
A36 . kartRtUv)anbgðajenAkñúgrUbTI23.

52 Tension Members

T.chhay

Figure 3.23

dMeNaHRsay³
bnÞúkemKuN (factored load) P = 1.2D + 1.6L = 1.2(155) + 1.6(310) = 682kN
u

nig muxkat;caM)ac; A = φPF = 0.9682 ) = 3031.1mm
g
u
(250
2
t y

ehIy muxkat;caM)ac; A = φPF = 0.75(400) = 2273.3mm
e
682
u 2
t u

kaMniclPaB (radius of gyration) KYrmantMély:agtUcbMput
L 4600
r= = = 15.33mm
300 300
edIm,IrknUvmuxkat;RsalbMputsMrab;bMeBjlkçxNÐTaMgenH eyIgrkEdk (unequal-leg angle) Edlman
RkLaépÞeBj (gross area) EdlGacTTYlyk)anmantMélrUcbMput rYcehIyepÞógpÞat; effective net
area. kaMniclPaB (radius of gyration) k¾GacRtUv)anepÞógpÞat;edaykarRtYtBinitüpg Edr. eday

sarkarteFVIeLIgedaymanb‘ULúgBIrCYr enaHeCIgEdlRtUv)aneFVIkartP¢ab;RtUvmanTTwgtUc bMput 127mm
¬emIlkñúgtaragKMlatRbehagtamTTWgsMrab;EdkEkg rUbTI3>22¦. eyIgcaMepþImBItaraglkçN³sMrab;
EdkEkgeTal table of properties for single angle enAkñúgEpñkTI1 én Manual nigerobnUvmuxkat;
EdkRsalCageKtamlMdab;BItUceTAFM ¬minEmnlMdab;dUcKñaenAkñúgtarageT¦.
muxkat;xageRkamGacRtUv)anerob.
L152 × 102 × 12.7 : A = 3060mm nig r = 22.1mm
g
2
min

L127 × 89 × 15.9 : A = 3180mm nig r = 20mm
g
2
min

L 203 × 102 × 11.1 : A = 3300mm nig r = 22.1mm
g
2
min

L178 × 102 × 12.7 : A = 3400mm nig r = 22.15mm
g
2
min

¬cMNaMfa sMrab;EdkEkg GkS½ X nig Y Edl)anbgðajenAkñúgtaragminEmnCaGkS½em r(principal
axes)eT EtGkS½ Z eTIbCaGkS½em (principle axis) r = r . EtsMrab;EdkEkgDub (double-angle
min z

shape) GkS½ X nig Y KWCaGkS½em.¦


NPIC

sakl,g L152 × 102 ×12.7 . muxkat;enHman gross area EdlRtUvKñaBitR)akdeTAnwgRkLaépÞcaM)ac;
¬RbesIrCagmuxkat;bIeTot RkLaépÞrbs;vaRtUv)aneGayenAkñúgtarag¦.
An = Ag − Aholes = 3060 − 2(24)(12.7 ) = 2450.4mm 2

edaysarRbEvgtminRtUv)andwg AISC Eq. B3-2 minGacRtUv)aneRbIedIm,IKNna shear lag factor U .
dUcenH eyIgeRbI U = 0.85 / tMélmFüm)anBI Commentary. ¬]TahrN_TI8 kñúgCMBUkTI 7 tMNsamBaØ
bgðajlMGitGMBItMN nigtMél U mFüm GacRtUv)aneRbIedIm,ITTYl)annUvmuxkat;sakl,g bnÞab;tMél
U BI AISC Eq. B3-2 GacRtUv)anKNna¦.

A = UA = 0.85 × 2450.4 = 2082.84mm < 2273.3mm
e n
2
¬minl¥ N.G.¦
2

sakl,g L127 × 89 × 15.9
An = 3180 − 2(24)(15.9 ) = 2416.8mm 2
Ae = 0.85 × 2416.8 = 2054.28mm 2 < 2273.3mm 2 ¬minl¥ N.G.¦
eTaHbICamuxkat;enHman gross area FMCagmuxkat;munk¾eday Etvamin)anbegáIn net area eT. mUlehtu
KWRkLaépÞEdlRtUvdksMrab;rn§mantMélFM edaysarEtkMras;eCIg.
sakl,g L203 ×102 ×11.1
An = 3300 − 2(24)(11.1) = 2767.2mm 2
Ae = 0.85 × 2767.2 = 2352.12mm 2 > 2273.3mm 2 (OK)
cMeLIy³ muxkat;enHbMeBjRKb;lkçxNÐtMrUvkar dUcenHeRbI L203 ×102 ×11.1 ttameCIgEdlmanRbEvg
203mm .

enAeBlEdlEdkrag (structural shape) b¤EdkbnÞHRtUv)aneRbIedIm,IpÁúMCa built-up shape vamin
RtwmEtRtUv)anpÁúMenAEtxagcugGgát;b:ueNÑaHeT b:uEnþvak¾RtUv)anpÁúMenAcenøaHtamRbEvgbeNþayrbs;vapg
Edr. eKminRtUvkarkarpÁúMEdlmanlkçN³Cab;rhUteT. karpÁúMEbbenHRtUv)aneKehAfa stitching ehIy
eRKOgP¢ab;rbs;vaRtUv)aneKehAfa stitch bolts. karGnuvtþTUeTAKWkMNt;TItaMg stitching Edl L / r sM
rab;EpñkpÁúMnImYy² minelIs L / r sMrab;muxkat; built-up. AISC D2 ENnaMfa Edkrag built-up Edl
EpñkpÁúMrbs;vaRtUv)anEckeday filler EdlRtUv)aneRbIsMrab;P¢ab;enAcenøaH filler enaHtMélGtib,rma
L / r sMrab;EpñkmYy²minRtUvelIs 300. Edkrag built-up EdlekItelIgedayEdkbnÞH b¤edaykarpÁúM

rvagEdkbnÞHnigEdkragRtUv)aneBalenAkñúg AISC Section J3.5 of Chapter J (“Connections joints,
54 Tension Members

T.chhay

and Fasteners”). CaTUeTA KMlatrbs;eRKOgP¢ab; b¤karpSarminKYrelIs 24dg énkMras;EpñkesþIgbMput
rbs;bnÞHEdk b¤ 300mm . RbsinebIGgát;CaEdk weathering EdlsßitenAkñúgbriyakasgayrgERcHsIu
enaHKMlatGtibrmaKW 24dg énkMras; b¤ 175mm .

3>7> EdksrésEdlmaneFμj nigExSkab Threaded rods and Cables
enAeBl slenderness minRtUv)anBicarNa Edksrés rod Edlmanmuxkat;mUl nigExSkab
(cable) RtUv)aneRbIR)as; CaTUeTACaGgát;rgkarTaj. Edksrés nigExSkabxusKñaRtg; Edksréstan;

EtExSkabekItBIExSlYs kabCaeRcInvNÐ½bBa©ÚlKñaehIymanrUbragdUcExSBYr. Edksrés nigExSkab
RtUv)aneKeRbICaerOy²sMrab;RbBn§½dMbUlBüÜr k¾dUcCa hanger nig suspension member sMrab;s<an.
Edksrésk¾RtUv)aneRbIenAkñúgRbBn§½ bracing enAkñúgkrNIxøH vaRtUv)aneKeFVIeRbkugRtaMg edIm,IkarBar
vaBIPaBrlg; (slack) enAeBlEdlbnÞúkxageRkARtUv)andk. rUbTI3>24 bgðajBIviFItEdksrés nigExS
kabKMrU.
enAeBlcugmçagrbs;EdksrésRtUv)aneFVIeGaymaneFμj (thread) eBlenaH upset end RtUv)an
eRbI. EpñkEdlmaneFμjRtUv)ankat;ecjedIm,IBRgIkmuxkat;. enAkEnøgeFμj muxkat;EdkRtUv)ankat;
bnßy EtkareFVI upset end )anbegáInmuxkat;EdkeGayFM. EdkbTdæan upset end EdlmaneFμj CaTUeTA
man net area enARtg;kEnøgeFμj eRcInCagRtg;EpñkEdlKμaneFμj. eTaHCa upset end mantMéléføk¾
eday EtvamincaM)ac;eRbIRKb;krNIeT.
RkLaépÞmuxkat;RbsiT§PaB (effective cross-sectional area) enARtg;EpñkeFμjRtUv)aneKeGay
eQμaHfa stress area ehIyvaCaGnuKmn_eTAnwgGgát;p©it unthreaded nwgcMnYneFμjkñúg 1inch . pleFob
rvag stress area nig nominal area ERbRbYlb:uEnþvamantMéltUcbMputRbEhl 0.75 . dUcenHersIusþg;rg
karTaj nomial rbs;Edk threaded GacRtUv)ansresrdUcxageRkam³
Pn = As Fu

= 0.75 Ab Fu
Edl As = stress area
Ab = nominal (unthreaded) area
smIkarenHpþl;nUv nominal strength EdlRtUv)anbgðajenAkñúgtarag Table J3.2 enAkñúg
Section J3.6 én AISC Specification. emKuNersIusþg; resistance factor enAkñúgkrNIenH φt = 0.75 .


NPIC

RbsinebI upset end RtUv)aneRbI enaHlT§PaBrgkarTajenAGgát;eFμjEdlFMRtUvFMCag Fy KuNnwg
unthreaded body area (AISC Table J3.2, footnote c).

Figure 3.24

]TahrN_TI3>12³ Edk threaded RtUv)aneKeRbICaGgát;sMrab;BRgwgEdlRtUvEtTb;Tl;nwg
service tensile load. EdlbnÞúkefr 9kN nigbnÞúkefr 26.5kN . etIGgát;p©itEdkTMhMb:uNÑaRtUv)aneRbI

RbsinebI A36RtUv)aneRbI?
dMeNaHRsay³ bnÞúkemKuN (factored load)
Pu = 1.2(9) + 1.6(26.5) = 53.2kN
Edaysar φ P ≥ P
t n u

φt (0.75Fu )Ag ≥ Pu

muxkat;caM)ac; A g =
Pu
=
53.2
φt (0.75)Fu 0.75(0.75)400
= 236.44mm 2

BI A = πd
2
g
4

Ggát;p©itcaM)ac; d = 4 × 236.44 = 17.35mm
π
cMeLIy³ eRbIEdk threaded EdlmanGgát;p©it 18mm (A g = 254.47mm 2 ).

56 Tension Members

T.chhay

edIm,IkarBarkarxUcxatkñúgeBlsagsg; EdksrésminRtUvRsav b¤rlas; (slender) eBkeT.
eTaHbIminmankarTamTarBI specification k¾eday EtsMrab;karGnuvtþn_TUeTA Ggát;p©itGb,brmaEdlRtUv
eRbI RtUvmantMél 16mm .
ExSkabkñúgrUbragCa strands b¤ wire rope RtUv)aneRbIenAkñúgkarGnuvtþn_EdlTamTar high
strength EtPaBrwg (rigidity) minmanlkçN³sMxan;eT. bEnßmBIelIkareRbIR)as;vaenAkñúgRbBn§½s<anBüÜr

nigdMbUl vak¾RtUv)aneKeRbIenAkñúgeRKOgelIkdak;dUcCa hoist nig derrick EdleKeRbIvadUcCaExSeyag
sMrab;GKarx<s;² nigsMrab;BRgwgtambeNþayenAkñúgGKarEdleFVIBIEdk. PaBxusKñarvag strand nig
wire rope KWbgðajenAkñúgrUbTI3>25. Strand CakarrYmpSMKñaénsréslYsCaeRcInrMuvN½ÐKña ehIy wire

rope CakarrYmpSMKñaén strand CaeRcInrMuvN½ÐKña.

kareRCIserIsExSkabEdlRtwmRtUvsMrab;bnÞúkEdleGayCaTUeTAQrenAelIkarBicarNaGMBI ersIu
sþg; (strength) nigkMhUcRTg;RTay (deformation). bEnßmBIelIsac;lUteGLasÞicFmμta karlUtdMbUg
EdlbNþalmkBI seating b¤ shifting énsréslYsmYy² EdlCalT§plvaeFVIeGayExSkabmankarlUt
Gcié®nþy_. sMrab;mUlehtuenH CaTUeTAExSkabRtUv)aneKTajBnøÚtmun (prestretched). Wire rope nig
strand RtUv)anpliteLIgBIEdkEdlmanesIusþg;x<s;CagEdksMNg;Fmμta ehIyminmanEcgenAkñúg AISC

Specification eT. ersIusþg;dac;rbs;ExSkabnImYy² k¾dUcCakarlMGitBIkarttMNr GacTTYl)anBI

manufacturer’s literature. Tinñn½ymanRbeyaCn_sMrab;RbePTenHmanenAkñúg Cable Roof structures

(Bethlehem Steel, 1968).

3>8> Ggát;rgkarTajenAkñúgdMbUl Tension members in roof trusses
Ggát;rgkarTajCaeRcInEdlvisVkrKNnaCaeRKOgbgÁúM trusses. enAeBleRKOgbgÁúM trusses
RtUv)aneRbIR)as;enAkñúgsMNg; CaTUeTAvamannaTIcMbgkñúgkarRTRbBn§½dMbUlEdleKRtUvkarElVgEvg. va
RtUv)aneKykmkeRbIenAeBlEdléfø nigTMgn;FñwmmantMélx<s;. ¬eRKOgbgÁúM trusses RtUv)anKitCaFñwmCM

NPIC

erA (deep beam) EdlykecjnUvEpñénRTnugy:ageRcIn¦. dMbUl trusses RtUv)aneRbICaerOy²enAkñúg
sMNg;shRKas eTaHbICasMNg;RbePTenHRtUvkareRKagrwg (rigid frame) k¾eday. dMbUl trusses KMrU
EdlRTeday load-bearing wallRtUv)anbgðajenAkñúgrUbTI 3>26. sMNg;RbePTenH CaTUeTAcugmçag
rbs; trusses EdlP¢ab;eTAnwgCBa¢aMgRtUv)aneKKitCaTMr pinned nigTMrmçageTotRtUv)aneKKitfaCaTMr
roller. dUcenH trusses GacRtUv)anviPaKCaeRKOgbgÁúMsþaTickMNt;. CBa¢aMgEdlCaTMrGaceFVIBIebtug

BRgwgedayEdk bøúkebtug dæ b¤bnSMénsMPar³TaMgenH.
CaFmμta dMbUl trusses EtmanKMlatesμIKñatambeNþayGKar nigcgP¢ab;KñaeTAvijeTAmkeday
sarFñwmbeNþayEdleKehAfa édrENg (purlin) nigedayEdkExVg (X-bracing). tYnaTIcMbgrbs;éd
rENgKWbBa¢ÚnbnÞúkeTAGgát;xagelI (top chord) rbs; trusses b:uEnþvak¾GaccUlrYmedayEpñkxøHkñúgkar
BRgwgRbBn§½. CaTUeTAEdkBRgwg (bracing) RtUv)andak;enAkñúgbøg;énGgát;xagelI nigGgát;xageRkam
b:uEnþvamuncaM)ac;enARKb;ElVg (bay)TaMgGs;eT edaysarkMlaMgxag (lateral forces) GacRtUv)anbBa¢ÚnBI
ElVgEdlTb;mYyeTAElVgEdlTb;mYyeTot edaysarédrENg.
vaCakarRbesIrbMputEdlédrENgRtUv)andak;enAelItMNrbs; trusses. dUenH trusses Gac
RtUv)anKitCaeRKOgbgÁúMtMNsnøak; (pin-connected structure)EdlRTbnÞúkEtRtg;tMN. EteBlxøHkM
raldMbUlminGaclatsn§WgelIcMgayrvagtMN dUcenHeKRtUvkarédrENgkNþal (intermediate purlin).
enAkñμúgkrNIEbbenHGgát;xagelInwgrgnUvm:Um:g;Bt;FM k¾dUcCakMlaMgsgát;Ekg (axial compression)ehIy
vaRtUv)anKNnaedayKitCa Fñwm-ssr (beam-column)EdlmanBnül;kñúgCMBUkTI6.
Sag rod CaGgát;rgkarTajEdlRtUv)aneRbIedIm,Ipþl;TMrxagsMrab;édrENg. bnÞúkPaKeRcInEdl

GnuvtþmkelIédrENgmanTisQr dUcenHvanwgmanbgÁúMkMlaMgRsbeTAnwgmMuCMraldMbUl EdlnwgeFVIeGay
édrENgekagenAkñúgTisedAenaH ¬rUbTI 3>27¦.
Sag rod GacRtUv)andak;enAcMnuckNþal b¤cMnucmYyPaKbI b¤GacjwkenAtambeNþayédrENg

GaRs½yeTAnwgcMnYnTMrEdlRtUvkar. KMlatrbs; sag rodCaGnuKmn_eTAnwgKMlat trusses, mMuCMralrbs;
Ggát;xagelI/ ersuIsþg;rbs;édrENgTb;nwgkarBt;RbePTenH ¬rUbragPaKeRcInrbs;EdkEdleRbICaédr
ENgmanlkçN³exSayNas;sMrab;karBt;tamTisenH¦ nigcMnYnTMrEdlpþl;edaydMbUl. RbsinebIeKeRbI
bnÞHEdk CaTUeTAvaRtUv)aneKP¢ab;y:agrwgCamYyédrENg dUcenHeKmincaM)ac;RtUvkar sag rod eT. Et
eBlxøH EtTMgn;pÞal;rbs;édrENgKWvaRKb;RKan;kñúgkarbgábBaðaenH dUcenHeKcaM)ac;dak; sag rod edIm,IRT
kñúgGMLúgeBlsagsg;muneBldak;kMraldMbUl.
58 Tension Members

T.chhay

RbsinebIeKeRbI sag rod eKcaM)ac;KNnavaedIm,IRTbgÁMúbnÞúkdMbUlEdlRsbeTAnwgdMbUl. Ggát;
nImYy²cenøaHédrENgRtUv)ansnμt;eGayRTGVI²TaMgGs;BIxageRkamva dUcenHGgát;xagelIRtUv)anKNna
sMrab;bnÞúkenAelIépÞdMbUlEdlmanGMeBIelIGgát;enaH BIcugdMbUldl;kMBUldMbUldUcbgðajenAkñúg rUbTI 3>

NPIC

28. eTaHbICakMlaMgenAkñúgGgát;nImYy²xusKñak¾eday EtCakarGnuvtþn_TUeTAeKeRbITMhMEtmYysMrab;RKb;
Ggát; sag rod enaH. kareRbIR)as;nUvmuxkat;dUcKñasMrYldl;kargarsagsg; ÉbrimaNEdkelIsminCaFM
b:unμaneT.

rUbTI 3>29 a bgðajBIkarcgP¢ab;édrENgenARtg;RBMdMbUl. Tie rod cenøaHédrENgxagRtUvTb;
nwgbnÞúkBIRKb; sag rod TaMgGs;EdlenAsgçagsøabdMbUl. kMlaMgTajenAkñúgGgát;edkmYyCabgÁúMkMlaMg
rbs;Ggát; sag rod EdlenAxagelI. düaRkamGgÁesrI (free-body diagram) rbs;édrENgkMBUl
RtUv)anbgðajenAkñúgrUbTI 3>29 b .

]TahrN_TI3>13³ Fink trusses EdlmanKMlat 6m KitBIGkS½eTAGkS½nigRTédrENg W 150 × 0.18
dUcbgðajenAkñúg rUbTI 3>30 a. édrENgRtUv)anRTeday sag rod enAcMnuckNþal. edayeRbIEdk
A36 KNna sag rod nig tie rod enAédrENgkMBUlsMrab;bnÞúk service load dUcxageRkam³

kMraldMbUlEdk (metal deck)³ 0.1kN / m 2

Built-up roof: 0.25kN / m 2
RBwl³ 0.85kN / m elIbøg;edk
2

TMgn;édrENg³ 0.18kN kñúgmYyEm:RtRbEvg

60 Tension Members

T.chhay

dMeNaHRsay³
KNnabnÞúk³
TTwgrgbnÞúksMrab; sag rod nImYy² = 6m / 2 = 3m
RkLaépÞrgbnÞúksMrab;kMraldMbUl nig Built-up roof = 3 ×14 = 42m
2

bnÞúkefr ¬kMraldMbUl nig Built-up roof¦ = (0.1 + 0.25) × 42 = 14.7kN
TMgn;édrENgsrub = 0.18 × 3 × 9 = 4.86kN
bnÞúkefrsrub = 14.7 + 4.86 = 19.56kN
épÞrgbnÞúkRBwl = 3 ×13.6 = 40.8m
2

bnÞúkRBwlsrub = 34.68kN
RtYtBinitübnSMbnÞúk³
(A4-2)³ 1.2 D + 0.5S = 1.2 × 19.56 + 0.5 × 34.68 = 40.8kN

(A4-3)³ 1.2 D + 1.6 S = 1.2 × 19.56 + 1.6 × 34.68 = 79kN

bnSMbnÞúk A4-3 lub. ¬tamkarGegát A4-1, A4-4 nig A4-5 nwgminmantMélFMeT¦.
sMrab;bgÁMkMlaMgRsbeTAnwgpÞdMbUl ¬rUbTI 3>30 b¦
3.6
T = 79 = 20.3kN
14

NPIC

20.3 ⋅ 103
muxkat;EdkEdlRtUvkar Ag =
T
=
φt (0.75Fu ) 0.75(0.75 × 400)
= 90.2mm 2

cMeLIy eRbIEdk threaded rod Ggát;p©it 16mm ¬ A = 201mm ¦
g
2

Edk tie rod EdlP¢ab;drENgenARBMdMbUl ¬rUbTI 3>30 c¦
14
P = 20.3 = 20.9kN
13.6
⋅ 3
muxkat;EdkEdlRtUvkar A = φ (0.T F ) = 0.75200..37510 400) = 90.2mm
g
75 ( ×
2
t u

cMeLIy eRbIEdk threaded rod Ggát;p©it 16mm ¬ A = 201mm ¦
g
2

sMrab;ragFrNImaRtrbs; truss nigkardak;bnÞúk Ggát;xageRkam (bottom chord) nigrgkugRtaMg
Taj ehIyGgát;xagelI (top chord) nigrgkugRtaMgsgát;. Ggát;RTnugxøHrgkugRtaMgTaj nigxøHeTot
rgkugRtaMgsgát;. enAeBleKbBa¢ÚlT§iBlxül;kñúgkarviPaK Tisxül;epSgKñaRtUv)aneKykmkBicarNa
eBlenaHkMlaMgenAkñúgGgát;RTnug (web member) xøHGacnwgERbRbYlcenøaHkugRtaMgsgát; nigkugRtaMg
Taj. kñúgkrNIEbbenH Ggát;EdlrgGMeBIRtUv)anKNnaedayeGaymannaTICaGgát;rgkarsgát;pg nig
rgkarTajpg.
sMrab; truss Edlcab;b‘ULúg (bolted truss) muxkat;EdkEkgDub (double-angle section)
RtUv)aneRbICajwkjab;sMeb;Ggát;xagelI (top chord) nigGgát;RTnug (web member) . karKNnaenH
sMrYldl;karP¢ab;Ggát;EdlCYbKñaenARtg;dMNedayGnuBaØatnUvkareRbIR)as;bnÞHEdkeTal (single gusset
plate) dUcbgðajenAkñúgrUbTI 3>31. enAeBlGgát;xagelIrbs;eRKOgbgÁúM truss EdlpSareRbIEdkmuxkat;

GkSret EdkRTnugEdlmanmuxkat;EdkEkgGacpSarP¢ab;CamYyeCIg (stem) rbs;Edkmuxkat;GkSret.
RbsinebI kMlaMgenAkñúgGgát;RTnug (web member) mantMéltUc eKGaceRbIEdkEkgeTal (single
angle) ebIeTaHbIkareFVIEbbenaH)ankat;bnßybøg;sIuemRTIBI truss ehIybNþaleGayGgát;RTnugrgnUv

bnÞúkcakp©itk¾eday. CaTUeTAGgát;xagelI nigxageRkam (chord member) CaGgát;Cab; ehIyeKGac
kat;vaCakMNat;²RbsinebIcaM)ac;.

62 Tension Members

T.chhay

CakarBitEdlfa chord member CaGgát;Cab; ehIytMNRtUv)ancab;b‘ULúg b¤pSarEdleKmin
Gacsnμt;fa truss CaeRKOgbgÁúMtMN pin-connected )aneT. Pabrwgrbs;tMNBitCanaMmknUvm:Um:g;Bt;enA
kñúgGgát; b:uEnþCaTUeTAvamantMéltUc ehIyRtUv)anBicarNavaCakMlaMgrg (secondary effect) dUcenH
kñúgkarGnuvtþTUeTAeK)anecalva. EtkarBt;EdlbNþaledaysarbnÞúkxageRkAEdlGnuvtþedaypÞal;
eTAelIGgát;cenøaHtMN RtUvEtykmkKitBicarNadac;xat. eyIgKitkrNIenHenAkñúgemeronTI 6.
ExSeFVIkar (working line) Ggát;rbs;eRKOgbgÁúM truss TaMgGs;RtUvkat;KñaRtg;tMNnImYy². sM
rab; truss EdlP¢ab;edayb‘ULúg CYrrbs;b‘ULúg (bolt line) Ca working line ehIysMrab; truss pSar
GkS½TIRbCMuTMgn;rbs;TwkbnSarCa working line. karsnμt;kñúgdMeNIrkarviPaK truss RbEvgGgát;RtUv)an
vas;BIcMnuceFVIkar (working point) eTA working point.
]TahrN_TI3>14³ eRCIserIsmuxkat;GkSretsMrab;Ggát;xageRkam (bottom chord) rbs;eRKOgbgÁúM
dMbUl Warren truss dUcbgðajenAkñúgrUbTI 3>32 a. Truss RtUv)anpSar nigmanKMlatcMgay 6m .
snμt;fakarP¢ab;rbs;Ggát;xageRkamRtUv)aneFVIeLIgdaykarpSarbuitkaMtambeNþay (longitudinal fillet
weld) enAnwgsøabRbEvg 230mm . edayeRbIEdk A36 CamYynwgTinñn½ybnÞúkxageRkam ¬xül;min

RtUv)anBicarNaenAkñúg]TahrN_enHeT¦.
édrENg (purlin)³ M 200 × 0.097
RBwl³ 0.95kN / m elIbøg;edk
2

kMraldMbUlEdk (metal deck): 0.1kN / m 2

dMbUl³ 0.2kN / m2

kMralGIusULg;³ 0.15kN / m2


NPIC

dMeNaHRsay³
KNnabnÞúk³
RBwl = 0.95 × 6 ×12 = 68.4kN
bnÞúkefr ¬elIkElgédrENg¦ = kMraldMbUlEdk 0.1kN / m 2
dMbUl 0.2kN / m 2
kMralGIusULg; 0.15kN / m 2
srub 0.45kN / m 2

bnÞúkefrsrub = 0.45 × 6 × 12 = 32.4kN
TMgn;édrENgsrub = 0.097 × 6 ×12 = 7kN
64 Tension Members

T.chhay

snμt;faTMgn; truss esμI 10% énbnÞúkepSg²
0.1(68.4 + 32.4 + 7 ) = 10.78kN
bnÞúkenAelItMNxagkñúgKW
32.4 10.78
D= + + 0.097 × 6 = 6kN
8 8
68.4
S= = 8.55kN
8
enAelItMNxageRkA RkLaépÞrgbnÞúkKWesμInwgBak;kNþalRkLaépÞrgbnÞúkrbs;tMNxagkñúg. bnÞúkenAelI
tMNxageRkAKW
32.4 10.78
D= + + 0.097 × 6 = 3.28kN
2×8 2×8
68.4
S= = 4.3kN
2×8
karbnSMbnÞúk A4-3 nwgTTYl)antMélFMCageK³
Pu = 1.2 D + 1.6S
enAelItMNxagkñúg P = 1.2 × 6 + 1.6 × 8.55 = 20.88kN
u

enAelItMNxageRkA P = 1.2 × 3.28 + 1.6 × 4.3 = 10.82kN
u

Truss EdlrgbnÞúkRtUv)anbgðajenAkñúg rUbTI 3>32 b.

Ggát;xageRkamRtUv)anKNnaedaykMNt;kMlaMgkñgGgát;nImYy²rbs;Ggát;xageRkam nigeFVIkar
ú
eRCIserIsmuxkat;smrmüedIm,ITb;nwgkMlaMgEdlFMCageK. enAkñúg]TahrN_enH kMlaMgenAkñúgGgát; IJ
mantMélFMCageK. GgÁesrI (free body) enAxageqVgmuxkat; a-a RtUv)anbgðajenAkñúg rUbTI 3>32 c.
∑ M E = 83.9(6) − 10.82(6) − 20.88(4.5 + 3.0 + 1.5) − 1.2 FIJ = 0
FIJ = 208.8kN
sMrab;muxkat;eBj (gross section)
8 ⋅ 10 3
muxkat;EdlRtUvkar A = 0.F F = 208.× 250 = 928mm
g
9
IJ
0.9
2
y

sMrab; net section
muxkat;EdlRtUvkar A = 0.75F = 208.8×⋅400 = 696mm
3
F IJ 10 2
e
0.75
u

sakl,g WT125 × 0.09
Ag = 1140mm 2 > 928mm 2


NPIC

kartP¢ab;eFVIeLIgedaykarpSartambeNþay ehIyGgát;minEmnCaEdkbnÞHEdksrés dUcenHkartP¢ab;
enHminsßitenAkñúgkrNIBiessNamYysMrab;Ggát;EdlpSarEdlrg shear leg.
⎛x⎞ ⎛ 34.5 ⎞
U =1− ⎜ ⎟ =1− ⎜ ⎟ = 0.85 < 0.9
⎝L⎠ ⎝ 230 ⎠
Ae = CAg = 0.85 × 1140 = 969mm 2 > 696mm 2 (OK)

RbsinebIGgát;xageRkamRtUv)anBRgwgenA panel point
L 1500
= = 75.4 < 300 (OK)
r 19.9
cMeLIy eRbIEdk WT125 × 0.09

3>9> Ggát;EdltPa¢b;edayknøas; Pin-Connection Members
enAeBlGgát;RtUv)antP¢ab;edayknøas; rn§RbehagRtUv)aneFVIeLIgenAcugTaMgsgçagrbs;Ggát;
nigEpñkEdlvaRtUvP¢ab; ehIyknøas;RtUv)ans‘ktamrn§enaH. kareFVIEbbenHedIm,IkMueGayGgát;rgm:Um:g;Bt;.
Ggát;rgkarTajEdltP©ab;tamTMrg;EbbenHRbQmnwgkar)ak;eRcInRbePT EdlRtUv)aneRobrab;enAkñúg
AISC D3 nigRtUv)anBnül;dUcxageRkam.

Eyebar CaRbePTBiessrbs;Ggát;EdlP¢ab;edayknøas; (pin-connected member) EdlenA

xagcugrbs;vamanrn§knøas; dUcbgðajkñúgrUbTI 3>33. ersIusþg;KNnaKWQrelIersIusþg;yalrbs;mux
kat;eBj. k,ÜnlMGitsMrab;KNnaTMhM eyebar manenAkñúg AISC D3 EtminRtUv)anykmkerobrab;enATI
enHeT. Eyebar RtUv)aneRbIy:agTUlMTUlayenAeBlmunCaGgát;rgkarTajEdleRbIenAkñúg truss s<an
b¤enAkñúgs<anBüÜr. vaminRtUv)aneKeRbIeTenAeBlbc©úb,nñ.
Ggát;EdltP¢ab;edayknøas;KYrRtUv)anKNnasMrab;sßanPaBkMNt;dUcxageRkam ¬rUbTI 3>34¦
!> kugRtaMgTajenAelI net effective area ¬rUbTI 3>34 a ¦
φt = 0.75, Pn = 2tbeff Fu (ASIC Equation D3.1)

@> kugRtaMgkMlaMgkat;enAelI net effective area ¬rUbTI 3>34 b¦
φsf = 0.75, Pn = 0.6 Asf Fu (ASIC Equation D3.21)

#> kugRtaMg bearing . tMrUvkarenHmanenAkñúg chapter J (“Connections, Joints and

fastener”) ¬rUbTI 3>34 c¦
φ = 0.75, Pn = 1.8Fy Apb (ASIC Equation J8-1)

$> kugRtaMgTajenAelI gross area
66 Tension Members

T.chhay

φ = 0.9, Pn = Fy Ag (ASIC Equation D1-1)

Edl t= kMras;rbs;EpñkEdltP¢ab;
beff = 2t + 16 ≤ b ¬KitCa mm ¦
b = cMgayBIépÞxagrbs;rn§knøas;eTAépÞxagrbs;Ggát; EdlEkgeTAnwgTisrbs;kMlaMg

Asf = 2t (a + d / 2)

a= cMgayBIépÞxagrbs;rn§knøas;eTAépÞxagrbs;Ggát; EdlRsbeTAnwgTisrbs;kMlaMg
d = Ggát;p©itknøas;
Apb = projected bearing area = dt

tMrUkarbEnßmsMrab;karkMNt;TMhMrbs;knøas; nigGgát;manbkRsayenAkñúg AISC D3.


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