know about sfd and bmd of cantilever fixed beam

sfd and bmd diagram of a structure is essential in different engineering feilds like civil engineering, mechanical engineering, etc., to calculate the load acting on the structure and how the structure behaves due to different loadings.

fixed beam cant be solved directly by three equilibrium equation there are many other methods to solve it, here we will use slope and deflection method to solve the given fixed beam problem.

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

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 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.

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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