shear force and bending moment of point load

Shear force and bending moment are two important concepts in structural engineering and mechanics.

Shear force, in simple terms, is a pushing or pulling force that acts parallel to the surface of an object.

Bending moment denotes the internal moment within a structure that initiates a bend in a beam. The calculation involves multiplying the applied force on the beam by the perpendicular distance from the point of force application to the axis of rotation.

diagram

DRAW SHEAR FORCE AND BENDING MOMENT DIAGRAM OF GIVEN FIGURE

  • WE KNOW, THERE ARE THREE EQUILIBRIUM EQUATION

∑FX=0, (SUMMATION OF HORIZONTAL FORCE) 

∑FY=0, (SUMMATION OF VERTICAL FORCE) 

∑M=0, (SUMMATION OF MOMENTS) 

LET US FIRST UNDERSTAND THE SIGN CONVENTION

AS THERE ARE NO HORIZONTAL FORCE IN THE GIVEN  FIGURE,  

NO NEED TO USE ∑FX=0,  

STEPS FOR FINDING REACTIONS 

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

1.   Apply First Equilibrium Equation 

∑FY( Summation Of Vertical Forces)= 0 

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

2.   Apply Second Equilibrium Equation 

∑M(Summation Of Moments)= 0 

Formula Of Moment= Force*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

LET US USE ∑FY=0,  

THERE ARE THREE VERTICAL FORCES GIVEN IN THE FIGURE, 

∑FY=0, 

RA-6 +RC =0 

RA+RC=6Kn     (Eqn-1) 

LET US USE ∑M=0,  

∑MA=0 

(RA*0)+ (6*1) -4RC=0 

RC= (6/4) = 1.5KN

FROM (Eqn-1), 

RA+1.5=6 

RA= 4.5KN. 

Or, 

∑MC=0 

(RC*0)- (6*3) +4RA=0 

RA= (18/4) =4.5KN. 

CALCULATION OF SHEAR FORCE

FA=RA= 4.5KN

FB=4.5-6= -1.5KN

FC=-1.5+1.5= 0 

CALCULATION OF BENDING MOMENTS

MA= (4.5*0) = 0        (AS, THE DISTANCE IS ZERO) 

MB= (4.5*1) = 4.5KNm 

MC= (4.5*4)-(6*3) = 0 

MID – MOMENTS

MB= 0 

MC= (4.5*0.5) = 2.25KNm 

MD= (4.5*2.5)-(6*1.5) = 2.25KNm 

shear forceand bending moment manual

shear forceand bending moment manual
reaction staad
end shear force staad
end bending moment staad
mid bending moment staad

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