This video explains how to draw the shear force SFD and bending moment diagram BMD for a beam under a distributed load.
Here are the steps you should follow when drawing a shear force and bending moment diagram for a beam.
Step 1: Determine the support reactions from the free body diagram of entire beam.
Step 2: Divide the beam into segments so that the loading within each segment is continuous.
Perform the following steps for each segment of the beam.
Step 3: Introduce an imaginary cutting plane within the segment, locating at a distance x from the left end of the beam, that cuts the beam into two parts.
Step 4: Draw free body diagram for the segment of the beam. Show the shear force and bending moment on the cut section.
Step 5: Write the equilibrium equation, obtainable from the free body diagram.
Step 6: Solve the equilibrium equation for the shear force and the bending moment.
Step 7: Plot the curves for shear force and bending moment. It is desirable to draw the shear force diagram below the entire beam and then draw the bending moment diagram below the shear force diagram.
Shear force and bending moment diagrams are graphical representations used in structural engineering to analyze and understand the internal forces and moments that act on a beam or a structural member. These diagrams are essential in designing and assessing the structural integrity of various systems, such as bridges, buildings, and other load-bearing structures.
1. Shear Force Diagram (SFD): The shear force diagram represents the variation of the internal vertical forces acting on the beam along its length. It shows the magnitude and direction of the shear force at any given point along the beam. The shear force at a specific location is calculated by summing the vertical forces on one side of that point.
Key points to remember:
• The shear force at any support is usually equal to the external applied load acting on the beam at that point.
• The shear force will change abruptly at point loads and will vary linearly between concentrated loads.
• The shear force is zero at the supports for beams in equilibrium.
2. Bending Moment Diagram (BMD): The bending moment diagram shows the variation of the internal bending moments along the length of the beam. It illustrates the magnitude and type (positive or negative) of the bending moment at any given point along the beam.
Key points to remember:
• The bending moment is the algebraic sum of moments about a point on the beam section.
• The bending moment is zero at points where there are no external loads or supports.
• The bending moment changes sharply at concentrated loads and varies linearly between concentrated loads.
To construct the shear force and bending moment diagrams for a given beam, follow these steps:
Step 1: Calculate the reactions at the supports (if necessary) using equilibrium equations. Step 2: Identify all the external loads and their distances from the left end of the beam. Step 3: Start from the left end of the beam and move towards the right, calculating the shear force and bending moment at each point. Step 4: Plot the shear force and bending moment values on a graph against the distance from the left end of the beam. Step 5: Connect the plotted points to obtain the shear force diagram and bending moment diagram.
Remember to consider the sign conventions for shear force and bending moment. Upward forces and clockwise moments are considered positive, while downward forces and counterclockwise moments are considered negative.
These diagrams are useful for engineers to determine critical sections of a beam, assess its strength and stability, and ensure that the design can withstand the applied loads without failure or excessive deflection.