shear force and bending moment diagram of triangular load

figure

draw shear force and bending moment diagram of given figure. 

SIGN CONVENTION  

sign convention

STEPS FOR FINDING REACTIONS 

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

To Solve Two Unknowns We Need Two Equations. 

1.   Apply First Equilibrium Equation 

∑FY( Summation Of Vertical Forces)= 0 

Here, TWO Vertical Reaction Forces Are Acting Upward.

Convert The UVL into Force by Calculating The Area Of the Triangle. (0.5*3*6)=9KN

Here, Base of Triangle = 3m 

Height Of  Triangle= 6KN/m

2.   Apply Second Equilibrium Equation 

∑M(Summation Of Moments)= 0 

Formula Of Moment= Force*Distance. 

Force= Area of Triangle= 0.5*3*6=9KN 

if we are taking moment at the perpendicular side of triangle 

= F*(b/3) (Node B

if we are taking moment at the vertex side of triangle=  

F*(2b/3) (Node A) 

bending moment distance

(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. 

FINDING THE REACTIONS 

∑FY=0, 

RA-(0.5*3*6) +RB =0 

RA+RB=9KN    (EQN-1) 

LET US USE ∑M=0,  

∑MA=0 

(RA*0)+ (0.5*3*6*3*(2/3))-3RB=0 

RB= (18/3) =6KN

FROM (Eqn-1), 

RA+6=9KN 

RA=3KN

Or, 

If  we take moment at B. 

∑MB=0 

(RB*0)-(0.5*3*6*(3/3))+3RA=0 

RA=9/3=3KN

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=RA= 3KN 

FBL=3-(0.5*3*6) = -6KN 

FBR=3-(0.5*3*6) +6= 0 

To Calculate The Mid Shear Force 

 Take Summation of forces acting on node or member. 

CALCULATION OF MID SHEAR FORCE

F (A-B) =3-(0.5*1.5*(6/2))= 0.75KN

To Calculate The End Bending Moment 

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

CALCULATION OF END BENDING MOMENTS

MA= (3*0) = 0        (AS, THE DISTANCE IS ZERO) 

MB= (3*3)-(0.5*3*6*(3*(1/3))) = 0 

To Calculate The Mid Bending Moment  

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

CALCULATION OF MID – MOMENTS

          M (A-B) = (3*1.5)-(0.5*1.5*(6/2)*(1.5*(1/3))) = 3.375KNm 

shear force and bending moment diagram manual

shear force and bending moment diagram

STAAD OUTPUT

reaction staad
 shear force staad
bending moment staad

STAAD RESULT SUMMARY

FX = FORCE IN HORIZONTAL DIRECTION

FY = FORCE IN VERTICAL DIRECTION

MZ = BENDING MOMENT

result staad

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