Drawing sfd and bmd of udl & moment load

sfd and bmd of a structure is drawn to analyze the structure for stability by calculating different loads acting on that particular structure to ensure the structure is safe to be constructed.

here we will solve the given beam problem by the method of slope and deflection, below we will know the steps to analyze this beam.

draw sfd and bmd diagram by slope and deflection method

SIGN CONVENTION

steps of slope and deflection method

fixed end moment

slope and deflection equation

equilibrium equation

final moments

REACTIONS AT EACH SPAN

SPAN AB

∑MB=0

-5.317+3RA-(10*3*1.5)+11.865=0

RA=12.817KN

∑FY=0

RA-(10*3)+RB1=0

12.817-30+RB1=0

RB1=17.183KN

SPAN BC

∑MC=0

-11.865+5RB2-(15*3)+1.141=0

RB2=11.145KN

∑FY=0

RB2-15+RC1=0

11.145-15+RC1=0

RC1=3.855KN

SPAN CD

∑MD=0

-1.141+6RC2+20+1.93=0

RC2=-3.465KN

∑FY=0

RC2+RD=0

-3.465+RD=0

RD=3.465KN

FINAL REACTIONS

RA= 12.817KN

RB=RB1+RB2=17.183+11.145= 28.328KN

RC=RC1+RC2=3.885-3.465= 0.39KN RD= 3.465KN

END SHEAR FORCE

FA= 12.817KN

FBL=12.817-(10*3)= -17.183KN

FBR=12.817-(10*3)+28.328= 11.145KN

FCL=12.817-(10*3)+28.328-15= -3.855KN

FC=12.817-(10*3)+28.328-15+0.39= -3.465KN

FD=12.817-(10*3)+28.328-15+0.39+3.465= 0

To Calculate The Mid Shear Force

Take Summation of forces acting on node or member.

MID SHEAR FORCE

F(A-B)= 12.817-(10*1.5)= -2.183KN

F(B-C)= 12.817-(10*3)+28.328-15= -3.855KN

F(C-D)= 12.817-(10*3)+28.328-15+0.39= -3.465KN

FINAL MOMENT VALUE WILL BE THE END BENDING MOMENTS

END BENDING MOMENTS

MAB= -5.317KNm

MBA= 11.865KNm

MBC= -11.865KNm

MCB= 1.141KNm

MCD= -1.141KNm

MDC= 1.93KNm

To Calculate The Mid Bending Moment

Calculate moments acting on each node or member and add the remaining distance up to which node you want to calculate the moment

MID BENDING MOMENTS

M(A-B)= -5.317+(12.817*1.5)-(10*1.5*0.75)= 2.659KNm

M(B-C)= -5.317+(12.817*5.5)-(10*3*4)+(28.328*2.5)+11.865-11.865

-(15*0.5)= 8.497KNm

M(C-D)=-5.317+(12.817*11)-(10*3*9.5)+(28.328*8)+11.865-11.865

-(15*6)+(0.39*3)+1.141-1.141= -11.536KNm

note

To Draw the bending moment diagram first we have to draw free moment diagram, and then we have to mark all the values of final moments which we got by solving the slope deflection equation. join all the marked points to get the net bending moment diagram.

SFD AND BMD DIAGRAM MANUAL

SFD AND BMD DIAGRAM MANUAL

staad output

Result Summary

FX = FORCE IN HORIZONTAL DIRECTION

FY = FORCE IN VERTICAL DIRECTION

MZ = BENDING MOMENT

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