The Moment Distribution Method2

8/9/2019 The Moment Distribution Method2

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DISPLACEMENTDISPLACEMENT

MEDTHOD OF ANALYSIS:MEDTHOD OF ANALYSIS:

MOMENT DISTRIBUTIONMOMENT DISTRIBUTION

Member Stiffness Factor (Member Stiffness Factor (KK))Distribution Factor (DF)Distribution Factor (DF)Carry-Over FactorCarry-Over FactorDistribution of Couple at NodeDistribution of Couple at Node

Moment Distribution for BeamsMoment Distribution for BeamsGeneral BeamsGeneral BeamsSymmetric BeamsSymmetric BeamsMoment Distribution for Frames No Sides!ayMoment Distribution for Frames No Sides!ay

Moment Distribution for Frames Sides!ayMoment Distribution for Frames Sides!ay


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General "rinciples and DefinitionsGeneral "rinciples and Definitions

#$us t$e Moment Distribution Met$od (also %no!n as t$e Cross Met$od) became#$us t$e Moment Distribution Met$od (also %no!n as t$e Cross Met$od) became

t$e preferred calculation tec$ni&ue for reinforced concrete structures't$e preferred calculation tec$ni&ue for reinforced concrete structures'#$e description of t$e moment distribution met$od by ardy Cross is a little#$e description of t$e moment distribution met$od by ardy Cross is a little

masterpiece' e !rote Moment Distribution' #$e met$od of momentmasterpiece' e !rote Moment Distribution' #$e met$od of momentdistribution is t$isdistribution is t$is

*ma+ine all ,oints in t$e structure $eld so t$at t$ey cannot rotate and compute*ma+ine all ,oints in t$e structure $eld so t$at t$ey cannot rotate and computet$e moments at t$e ends of t$e members for t$is conditiont$e moments at t$e ends of t$e members for t$is condition

at eac$ ,oint distribute t$e unbalanced fi.ed-end moment amon+ t$e connectin+at eac$ ,oint distribute t$e unbalanced fi.ed-end moment amon+ t$e connectin+members in proportion to t$e constant for eac$ member defined as stiffnessmembers in proportion to t$e constant for eac$ member defined as stiffness multiply t$e moment distributed to eac$ member at a ,oint by t$e carry-overmultiply t$e moment distributed to eac$ member at a ,oint by t$e carry-over

factor at t$e end of t$e member and set t$is product at t$e ot$er end of t$efactor at t$e end of t$e member and set t$is product at t$e ot$er end of t$emembermember

distribute t$ese moments ,ust carried overdistribute t$ese moments ,ust carried over repeat t$e process until t$e moments to be carried over are small enou+$ to berepeat t$e process until t$e moments to be carried over are small enou+$ to be

ne+lected andne+lected and add all moments - fi.ed-end moments/ distributed moments/ moments carriedadd all moments - fi.ed-end moments/ distributed moments/ moments carried

over - at eac$ end of eac$ member to obtain t$e true moment at t$e end'over - at eac$ end of eac$ member to obtain t$e true moment at t$e end'0Cross 1232450Cross 123245


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1. Restrain all pssi!le "ispla#e$ents.

%. Cal#&late Distri!&tin Fa#trs:

#$e distribution factor DFi of a member connected to any ,oint 6 is

!$ere S is t$e rotational stiffness / and is +iven by


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'. Deter$ine #arr()*er +a#trs

#$e carry-over factor to a fi.ed end is al!ays 7'8/ ot$er!ise it is 7'7'

,. Cal#&late Fi-e" En" M$ents. Ta!le '.1/.

#$ese could be due to in-span loads/ temperature variation and9or:relative displacement bet!een t$e ends of a member'

0. D "istri!&tin #(#les +r all ints si$&ltane&sl(

;ac$ cycle consists of t!o steps

1' Distribution of out of balance moments Mo/

4'Calculation of t$e carry over moment at t$e far end of eac$ member'

#$e procedure is stopped !$en/ at all ,oints/ t$e out of balance moment is a

ne+li+ible value' *n t$is case/ t$e ,oints s$ould be balanced and no carry-over

moments are calculated'


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2. Cal#&late t3e +inal $$ent at eit3er en" + ea#3 $e$!er.

#$is is t$e sum of all moments (includin+ F;M) computed durin+ t$e

distribution cycles'


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;.ample;.ample


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;.ample


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Symmetric Beam and


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Symmetric Beam !it$Symmetric Beam !it$

=ntisymmetric


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Moment Distribution for framesMoment Distribution for frames

No sides!ayNo sides!ay


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The Moment Distribution Method2

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