learn sfd and bmd of simple frame structure

The process of drawing sfd and bmd diagram of frame structure is same as that of horizontal beam, in this example also we are going to use slope and deflection method to calculate the load on the structure and draw the required diagram.

draw sfd and bmd diagram of frame structure having udl load of 10KN/m

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

SUM OF MA=0

10-6FB+20=0

FB=5KN

SUM OF FX=0

FA-FB=0

FA-5=0

FA= 5KN

SPAN BC

SUM OF MC=0

-(10*6*3)+6RB=0

RB=30KN

SUM OF FY=0

RB-(10*6)+RC=0

30-60+RC=0

RC= 30KN

SPAN CD

SUM OF MC=0

20+10-6FD=0

FD=5KN

SUM OF FX=0

FD-FC=0

5-FC=0

FC= 5KN

FINAL REACTIONS

HORIZONTAL FORCE

FA= 5KN

FB= 5KN

FC= 5KN

FD= 5KN

VERTICAL FORCE

RB= 30KN

RC= 30KN

RC=RC1+RC2=8.1+10.715= 18.815KN

RD= 16.285KN

END SHEAR FORCE

FA= 9.308KN

FBL=9.308-(0.5*6*9)= -17.692KN

FBR=9.308-(0.5*6*9)+27.592= 9.9KN

FCL=9.308-(0.5*6*9)+27.592-(0.5*1.5*12)-(0.5*1.5*12)= -8.1KN

FCR=9.308-(0.5*6*9)+27.592-(0.5*1.5*12)-(0.5*1.5*12)+18.815= 10.715KN

FDL=9.308-(0.5*6*9)+27.592-(0.5*1.5*12)-(0.5*1.5*12)+18.815-(6*3)-(0.5*6*3)= -16.285KN

FDR=9.308-(0.5*6*9)+27.592-(0.5*1.5*12)-(0.5*1.5*12)+18.815-(6*3)-(0.5*6*3)+16.285= 0

To Calculate The Mid Shear Force

Take Summation of forces acting on node or member.

MID SHEAR FORCE

F(A-B)=5= 5KN 

F(C-D)=-5= -5KN 

F(B-C)=30-(10*3)= 0 

FINAL MOMENT VALUE WILL BE THE END BENDING MOMENTS

END BENDING MOMENTS

MA= -13.22KNm

MB= -11.362KNm

MC=-8.662KNm MD= -16.369KNm

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)=10-(5*3)= 5KNm 

M(B-C)=-20+(10*3*1.5)= 25KNm 

M(C-D)=-20-(-5*3)= -5KNm 

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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