This article will clear your concepts of bending moment diagrams (BMD). You will know the important five steps required to draw the BMD.
For the ease of understanding we will discuss the same example what we have discussed in the shear force diagram tutorial
The shear force diagram of the above example looks like below:
Now, for creating the bending moment diagram of the simply supported beam you have to follow the five steps:
Step-1: Get the Reaction Forces: While creating shear force diagram of the beam you already have calculated the vertical reaction forces at different points as below:
Rc = 60 KN
Re = -20 KN
These reaction forces will be useful for calculating the bending moments at different points on the beam.
Step-2: Sign Convention: The bending moment, which will cause “sagging” to the beam, will be considered positive and the bending moment, which cause “hogging” to the beam, will be considered negative. We will consider this sign convention for the rest of this article.
Step-3: Calculate the Bending Moments: You need to calculate the bending moments at the different points on the beam. For calculating that you need to start from the extreme left (point A) and gradually you have to approach toward right hand side support (point A). You will use the following formula :
Bending moment (M) = (Force) X (Distance between the point of application of the force and the point at which you need to calculate the bending moment (BM))
BM @ A:
Ma = -20 * 0
BM @ B:
Mb = -20 * 1
= – 20 KN-M
BM @ C:
Mc = bending moment due to the 20KN force + bending moment due to the 10KN\M UDL
= – 20 * (1+1) – (10*1*0.5)
= – 45 KN-M
BM @ D:
Md = BM due to the 20KN force + BM due to the 10KN \ M UDL + BM due to the reaction force Rc
= – 20 * (1+1+1) – (10*2X1) + (60*1)
= -20 KN-M
BM @ E:
Me = BM due to the 20KN force + BM due to the 10KN \ M UDL + BM due to the reaction force Rc
= – 20 * (1+1+1+1) – (10*2X2) + (60*2)
Step-4: Plot the Bending Moments: Just now you have calculated the BM values at different points of the beam, now plot the values and you will get the bending moment diagram like below:
In the above BMD you might have observed for the point load bending moment diagram is a straight line and for UDL bending moment is a curve. But how to decide whether the curve should be a convex or concave one? We will discuss in the next article.
So, as of now you are ready to calculate bending moments and create BM diagram of a simply supported beam. Creating the BMD is the important first step toward design of structural member