Beam diagrams are an easy way to understand how loading of a beam translates into bending stress. If you add a deflection diagram, there is even more information that is readily available. MEboost has a tool that can create shear, moment and deflection diagrams.
Assumptions and Load Types
The tool requires that the beam is simply supported. A simply supported beam has one of these conditions:
- One fixed support on one end of the beam.
- Two simple supports.
The following load types are supported:
- Concentrated load
- Uniformly distributed load
- Increasing distributed load
- Decreasing distributed load
To illustrate the types of loads, consider the simply supported beam shown below. The beam is loaded with each type.
The loads are:
- A uniformly distributed load of 20 lb/inch from x = 5 to 19 inches.
- A point load of 200 lb at x = 26.
- A counter-clockwise couple of 300 in-lb at x = 35.
- An increasing distributed load from x = 44 to 54 inches. The load starts with 20 lb/inch and ends with 30 lb/inch. An increasing load is defined as increasing from left to right.
- A decreasing distributed load from x = 65 to 75 inches. The load starts with 24 lb/inch and ends with 8 lb/inch. A decreasing load is defined as decreasing from left to right.
Creating Beam Diagrams with MEboost
To start the beam diagram tool, click on Beam Diagrams in the MEboost ribbon.
The beam diagrams form will appear. This is where we define loads, supports, and beam properties. We'll use the example beam loading from earlier to illustrate how to create the beam diagrams.
Loads, Couples, and Supports
The beam loading and support is defined in this frame. Loads are defined in the up or down direction and their values are entered as a positive number. Couples are defined in the clockwise and counter-clockwise directions. Couple magnitudes are entered as positive numbers.
We also need to introduce the concept of beam ends. In our example, the left end of the beam (x = 0) has no load or support. It just overhangs unloaded beyond the left support. The software will by default start the diagrams at the first load or support, and end at the last load or support.
For shear and moment diagrams, this is not a big deal since there is no shear or moment present at the unloaded beam ends. However, if we want to know the deflection at x = 0 of our example beam, we need to define where the diagrams start. We do this by specifying the location of the left end of the beam. In the image below, we have added the left beam end by selecting "Beam end - left" and specifying the x location. Note that we do not need to add a right beam end, since the decreasing load ends at the right end of the beam.
To enter the uniform load, select "Distributed load - down" from the type drop-down box. The x start, x end, start magnitude, and end magnitude boxes will appear. For the example, the load starts at x = 5 and ends at x = 19. Since it's a uniformly distributed load, the start and end magnitudes are both 20. When the parameters are entered, click the Add button and the load will appear in the list box.
Continuing to add the supports, couple, and remaining loads, we get the following.
Now we've defined the beam ends, supports, and loads.
You can select the diagrams to include in the report by checking/unchecking the boxes in the diagrams frame.
X increment is the minimum number of data points per unit of length. For non-linear portions of the diagrams, a smaller increment will result in a more precise curve. The default is .05 and will generally be sufficient for most applications. In our example, x location is in inches, so an increment of .05 will result in 20 data points per inch.
When a deflection diagram will be created, the area moment of inertia and the modulus of elasticity must be specified. Otherwise, for shear and moment diagrams, these properties are not needed.
The properties of the example beam are entered below. Also note that US units are selected.
The Beam Diagrams Report
Once the report is created, the diagrams will appear on a new worksheet. The report includes +/- max values for shear, moment and deflection. The data used to create each diagram is also included.
The shear, moment and deflection diagrams are shown below.
As you can see, we can take a complex loading situation and create beam diagrams in just a couple of minutes. In addition, we can determine deflections of unloaded portions of the beam. While our example was a simply supported beam, the beam diagrams tool works equally well for beams with a fixed support.