easy sfd and bmd by slope and deflection method

draw shear force and bending moment diagram by slope and deflection method

SIGN CONVENTION

steps of slope and deflection method

WE WILL ASSUME DEFLECTION VALUE TO BE ZERO, i.e., (∂=0).

SO, WE ARE NOT GOING TO CONSIDE DEFLECTION HERE.

slope and deflection method

fixed end moment

slope and deflection equation

∑M at joints will be zero

applying condition of equilibrium

final moments

SUPPORT REACTIONS BY SEPARATING EACH SPAN

SPAN AB

∑MB=0

30-4.806+6RA=0

RA= -4.2KN

∑FY=0

RA+RB1=0

-4.2+RB1=0 RB1= 4.2KN

SPAN BC

∑MC=0

4.805+6.53+10+4RB2=0

RB2=-5.333KN

∑FY=0

-5.333+RC1=0

RC1= 5.333KN

SPAN CD

∑MD=0

-6.53-(20*2)+15.934+5RC2=0

RC2=6.119KN

∑FY=0

6.119-20+RD=0

RD= 13.881KN

FINAL SUPPORT REACTIONS

RA= -4.2KN

RB= RB1+RB2= 4.2-5.333= -1.133KN

RC= RC1+RC2= 5.333+6.119= 11.449KN RD= 13.881KN

END SHEAR FORCE

FA= -4.2KN

FB= -4.2-1.133= -5.333KN

FC= -4.2-1.133+11.449= 6.116KN

FDL= -4.2-1.133+11.449-20= -13.884KN

FDR= -4.2-1.133+11.449-20+13.881= 0

To Calculate The Mid Shear Force

 Take Summation of forces acting on node or member.

MID SHEAR FORCE

F(A-B)= -4.2KN

F(B-C)= -4.2-1.133= -5.33KN

F(C-D)= -4.2-1.133+11.449= 6.116KN

FINAL MOMENT VALUE WILL BE THE END BENDING MOMENTS

END BENDING MOMENTS

MAB= 0

MBA= -4.807KNm

MBC= 4.807KNm

MCB= 6.53KNm

MCD= -6.53KNm MDC= 15.934KNm

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)= (-4.2*3)= -12.6KNm

M(B-C)= (-4.2*8)+30+(-1.133*2)+10= 4.134KNm M(C-D)= (-4.2*12.5)+30+(-1.133*6.5)+10+(11.449*2.5)= 8.785KNm

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

shear force and bending moment diagram manual

shear force and bending moment

In the case of fixed beams we will not get the accurate values, we will get approximate values

staad output

BENDING MOMENT DIAGRAM IN STAAD IS SHOWING DOWNWARD DUE TO NEGATIVE VALUE BECAUSE OF SIGN CONVENTION, WE HAVE TAKEN CLOCK WISE MOMENT AS POSITIVE BUT IN STAAD PRO  CLOCK WISE MOMENT IS TAKEN AS NEGATIVE AND VICE VERSA SO DON’T GET CONFUSE WITH DIAGRAM.

YOU CAN DRAW BMD SAME AS STAAD BY TAKING CLOCKWISE MOMENT AS NEGATIVE AND ANTI CLOCK WISE MOMENT AS POSITIVE.

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