How is BMD calculated?

Answered by Michael Wilson

The calculation of Bending Moment Diagram (BMD) involves an understanding of the forces acting on a beam and their respective distances from a specific point along the beam. To calculate the BMD, we need to consider the external forces and the internal forces within the beam.

1. External Forces:
The external forces acting on a beam can include point loads, distributed loads, and moments. Point loads are forces applied at specific points along the beam, while distributed loads are forces spread over a certain length of the beam. Moments, on the other hand, create a rotational effect on the beam.

2. Internal Forces:
Internal forces within a beam arise due to the external forces acting on it. These internal forces include shear forces and bending moments. Shear force is the force that tends to shear or cut the beam, while bending moment is the force that tries to bend the beam.

3. Calculation Method:
To calculate the BMD, we follow a step-by-step process:

A) Determine the external loads: Identify and quantify all the external forces acting on the beam, including point loads, distributed loads, and moments.

B) Calculate the reactions: Determine the reactions at the supports of the beam using the principles of equilibrium. This step ensures that the beam is in a state of balance.

C) Cut the beam: Choose a section along the beam where you want to calculate the BMD. Cut the beam at this section and isolate it from the rest of the beam.

D) Draw the free body diagram: Draw a diagram of the isolated section, showing all the external forces acting on it. Include the reactions at the supports.

E) Calculate the shear force: Calculate the shear force at the section by summing up all the vertical forces acting on one side of the cut section. This can be done by taking moments about a point on the other side of the cut section.

F) Calculate the bending moment: Determine the bending moment at the section using the shear force and the distance from the section to the point where the bending moment is to be calculated. The bending moment is calculated by multiplying the shear force by the perpendicular distance.

G) Repeat steps c) to f) for different sections: Move along the beam and repeat steps c) to f) to calculate the bending moment at different sections. This will enable you to plot the complete BMD.

H) Plot the Bending Moment Diagram: Plot the calculated bending moments on a graph with the distance along the beam as the x-axis and the bending moment as the y-axis. Connect the points to obtain the BMD.

The BMD is calculated by considering the external loads, determining the reactions, cutting the beam to isolate a section, calculating the shear force and bending moment at that section, repeating the process for different sections, and plotting the BMD using the calculated bending moments.