## Problems Moment Distribution Continuous Beams

A series of continuous beams are indicated in Problems 4.28 to 4.32 in which the relative EI values and the applied loading are given. In each case:

i) determine the support reactions, ii) sketch the shear force diagram and iii) sketch the bending moment diagram.

Problem 4.28

Problem 4.29

Problem 4.30

Problem 4.31

Problem 4.32

4.7.12 Solutions: Moment Distribution—Continuous Beams

Solution

Lirpir: Moment Dislrilfuliuit - Cunlinuous lk-;tins

PI^IIItki No whir; iJI Putt Sc. J

(i) Filed vertical rcaclions:

Consider span AC: = 0

- 13,9 + M.6 - (J,0 x P« hkj) = 0 ffA ^ - + 2.(58 kN

Consider th( verticil equilibrium of the beam: +vc | = 0

Consider jjpon CD: Wc = 0

Consider th< vertical cquil ibrium of tin beam: +ve f = 0 + FaMhri+rSlcfc4j-fl ffufcjj- + 2,12kN

Consider apfln DF: XAfe " 0

- 1L9+ 12-0-(4J0 x Vm ii«j) - 0 A P™ = + 0.03 kN

Consider (he vertiuil equilibrium of [he beam: +ve | EFy:n 0 + V„ ^ t Vib m " 0 Pw M - - 0.03 kN

Consider [hi vertital equilibrium uflhe beam: +ve t ilPy-O + ' >o m + Vim m - & ¡to m = + 6-0 kN |

The lotat vertiesi read ion st eflih. siippon due lo the cominiii^ momc-jits is c^qital to die algebnie sum of [he ioimibuiioiis from cadi beam M die support,

FlXtad - Puc hd + I'm M -(-2.12 - 0.01) - - 2.15 KN Vtm = Pnntod+ fro Arid ={+ 0,03 + i.0) = + 6,03 kN kN

Sol ul io 11

Tupie: Moment MtfribHtfon- Oflili*moui Itemiis I'mMrm Nuntlwr; 4J2

Pain No, 5

Free bending manicnli:

+2 0