Question

explain how to draw the shear and moment diagrams in details , please use computer font and organize your work.

Answer 1

Shear Force Diagram(SFD)

Shear force occurs when a perpendicular force is applied to a beam or any static material.It occurs at along different points of the beam,so we need to find at which point the shear force is greater and the beam fails at this point.Let us consider one simple beam(Refer the drawing below) to calculate the shear forces and develop the shear force diagram

Step:1

If there is an upward force then the SFD will start at this point as positive ie., above the x axis.If there is an downward point load and no support then the shear force diagram will start as negative .First we need to calculate the reactions at A and B.Now shear force diagram should start at the first value of the force ie., +10 KN.ie., it starts above the x-axis

Step:2

Now the line should be kept moving across the beam and it should be stopped at every load which is acting on the beam.when we get a load it should be added to the shear force .Next here we have downward load -20 KN.So when this value is added, the shear force becomes -10KN.So the SFD should be brought below the X-axis at this point.

Step:3

We need to repeat the same procedure of moving across the beam and at the end we encounter another force +10KN reaction at support B.When this value is added, the shear force becomes zero.So SFD should end at B exactly on the X-axis.

Bending Moment

Moment is a rotational force that occurs when a force is applied perpendicularly to a point at a given distance.Moment is equal to force multiplied by distance

Step:1

First we need to calculate the reactions at supports,then we need to draw the free body diagram.next we need to work in the same way we did for the shear force diagram.Starting at X=0 we need to move and calculate bending moment at each point

Step:2

To have better understanding we need to make a cut immeddiately after the first reaction ,then we need to consider the forces to the left of the cut to start with the bending moment.So here we have the force +10KN .Let us consider the distance as x.So the bending moment equation will be as follows

-Mx=10(-x)

Mx=10x

Step:3

Now another cut should be made just before the downward force.Since there are no other forces between the first and the second cut,the equation remains the same.So let us substitute the x value as 5(just for understanding)which is the midpoint to the same equation to calculate the maximum bending moment.

So M=10 x 5 =50 KN

Step:4

Now another cut should be made after the second force.Now there are two forces to the left of the cut.10KN reaction force and -20 KN downward load.So considering this for every metre we move across the beam,there will be a 10KNm moment added from the first forceand -20KNm from the second .So after x=5,the equation becomes

M(x)=50 +10(x-5)-20(x-5)

M(x)=50-10(x-5)

Step:4

Now another cut to be made just before the next support.Since there are no other forces between the support and our last cut,the equation is same.

M(x)=50-10(x-5)

Now let us substitute x=10 to find the bending moment at the end,

M(x)=50-50 =0Knm