shear force and bending moment diagram of overhang beam

draw shear force and bending moment diagram of given figure. 

SIGN CONVENTION

STEPS FOR FINDING REACTIONS

Here, In The Above Figure We Have Two Unknown Reaction Force RA And RD.

1.   Apply First Equilibrium Equation

∑FY( Summation Of Vertical Forces)= 0

Here, TWO Vertical Reaction Forces Are Acting Upward. They Are +RA And +RD and Three Vertical Loads are acting downward

i.e., -5KN of nodal load, -4KN/m of UDL &  Nodal load of -3KN.

Take The Summation Of All Vertical Forces Acting On The Beam (Both Upward And Downward)

2.   Apply Second Equilibrium Equation

∑M(Summation Of Moments)= 0

Formula Of Moment= Force*Distance.

e.g. ∑MC= +(RA*3)-(5*1)

Here We Have Taken ∑M At C.

Take The Summation Of All Moments Acting On The Beam (Both Clock Wise And Anti clock Wise)

(Better See The Sign Convention For Positive And Negative Moment Or Clockwise And Anticlockwise Moment).

By Solving The Two Equations We Can Calculate Both The Support Reaction.

Once We Got The Values Of Reaction We Can Calculate Shear Force And Bending Moment.

FINDING THE REACTION

∑FY=0

RA-5-(4*2)-3+RD=0

RA+RD= 16KN

∑MA=0

(RA*0)+(5*2)+(4*2*4)-5RD+(3*6)= 0

RD= 12KN

RA= 16-12= 4KN

To Calculate The End Shear Force

 Take summation of forces acting on node or member.

In the below calculation L indicates left and R indicates right.

CALCULATION OF END SHEAR FORCE

FA= 4KN

FB= 4-5= -1KN

FC= 4-5= -1KN

FDL= 4-5-(4*2)+12= -9KN

FDR= 4-5-(4*2)+12= 3KN

FE= 4-5-(4*2)+12-3= 0

FF= 4-5-(4*2)+12-3= 0

To Calculate The Mid Shear Force

 Take Summation of forces acting at the mid span of the member.

CALCULATION OF MID SHEAR FORCE

F(A-B)=  4KN

F(B-C)= 4-5= -1KN

F(C-D)= 4-5-(4*1)= -5KN

F(D-E)= 4-5-(4*2)+12= 3KN

F(E-F)= 4-5-(4*2)+12-3= 0

To Calculate The End Bending Moment

 Calculate moments acting at the mid span of the member and add the remaining distance up to which node/member you want to calculate the moment.

CALCULATION OF END BENDING MOMENTS

MA= (4*0)= 0

MB= (4*2)= 8KNm

MC= (4*3)-(5*1)= 7KNm

MD= (4*5)-(5*3)-(4*2*1)= -3KNm

ME= (4*6)-(5*4)-(4*2*2)+(12*1)= 0

MF= (4*7)-(5*5)-(4*2*3)+(12*2)-(3*1)= 0

To Calculate The Mid Bending Moment

 Calculate moments acting at the mid span of the member and add the remaining distance up to which node/member you want to calculate the moment.

CALCULATION OF MID BENDING MOMENTS

M(A-B)= (4*1)= 4KNm

M(B-C)= (4*2.5)-(5*0.5)= 7.5KNm

M(C-D)= (4*4)-(5*2)-(4*1*0.5)= 4KNm

M(D-E)= (4*5.5)-(5*3.5)-(4*2*1.5)-(12*0.5)= -1.5KNm

M(E-F)= (4*6.5)-(5-*4.5)-(4*2*2.5)+(12*1.5)-(3*0.5)= 0

shear force and bending moment diagram manual
shear force and bending moment diagram manual
Staad output

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