Beam Under Transverse Loads



The purpose of this Java Application  is to study shear, moment, and deflection distribution over the length of a beam which is under various transverse load.

Click on Beam View button above to start the program and adjust the frame to desired size  by clicking and dragging on the edge of the frame.

Pay attention to how shear and moment distribution changes under each load added to the beam keeping in mind that the slope of the moment diagram at any point is equal to the shear at that section and the slope of the shear is equal to the load density at that section.
 

Input

On the right input panel,  choose type of beam to be analyzed and put in beam property values in the lower input field.
Next choose type of loading and fill in the corresponding values for the location and scale of the load. Click Add button to apply this load to the beam.
To add additional loading to former loads, fill in the load input filed and click on Add button. To start over, click Initialize button.

You can choose from 4 types of beams.

  1. Cantilever Beam.
  2. Both end pinned Beam (Simply supported beam).
  3. Both ends clamped beam.
  4. One end pinned and the other end clamped (Propped cantilever Beam)
When the selection of beam type is changed and add button is pressed, the program is initialized and the corresponding supports for each ends will be shown.

Also there are 3 kind of loading to choose from.

  1. Concentrated Force (P).
  2. Linearly Distributed Load (W1 to W2).
  3. Moment (M).
In case of Concentrated Force (P), the load is in lb unit and for Moment (M) the unit is in lb in. In these cases, Start Point (x=a) is the distance of the loading from the left end of the beam. The Values of End Point (x=b) and right end load density (w2) in the load input panel are ignored in these two loading cases. The Force and load density are positive when downward and the moment is positive when clockwise. When put in counterclockwise moment, enter negative value.

In case of Linearly Distributed Load, the load density varies from left end load density (w1) to right end load density (w2), from the start point (a) to the end point (b) which are measured from the left end of the Beam. The unit of load density is lb/in.
When applying uniform load, put same value for w1 and w2 input fields.
When applying triangular load, put zero for one of w1 or w2 and the maximum for the other.

Linearly Distributed Load can be put in by Table Input in Option of the Menu bar. In each line, first put in the location of the point measured from the left and next the load density of that section separated by space, tab, or comma and press enter for each line. Press ADD button to add these loading to the beam.

After each load is added, this load will be shown in black color around the beam diagram with previously added loads. The total sum of the distributed load is shown on the top of the frame.

For the properties of the beam, there are input fields for the length of the Beam (L), Young's modulus (E), and moment inertia (I). When the values of these fields are changed and the add or initialize button is pressed, the program will be initialized. This program assumes constant cross section properties over the whole length of the beam.
 

OutPut

After each load is added, the effect of this load to the deflection, shear, and moment distribution over the length of the beam will be shown in blue colored diagram.

The exaggerated deflection of the beam is displayed in blue line over the beam diagram. The scale of the deflection line is set after initialization or the boundary of the diagram is reached and then the deflection line shows the relative change under added loads.
The scale of the deflection diagram relative to the length of the beam is shown on the bottom of the panel.

The shear diagram V, and the moment diagram M are shown under the beam diagram. The sign conventions are shown in the help of the program.

The reaction forces and moments are shown in red color. The calculated value of reactions are in red colored text under the moment diagram.

When the mouse is clicked over the diagram, the location, shear, moment and deflection of that section of the beam will be displayed in blue color text under the moment diagram.

Table output window shows current results for shear, moment, and deflections. Choose the number of data points desired and click update to get the results.
 

Calculation

The exact equations for the shear force, bending moment and deflection along the length of a beam with given support conditions are used from the reference. The principle of superposition is used to obtain the combined effects of various multiple loads. Since the equations are in separate classes, these classes can be used in any programs for the further use of the calculation routine.
 

Reference

Roark, Raymond J. and Young, Warren C. Formulas for Stress and Strain, McGraw Hill, 1975, p104-113.

The applet button source file.
The main source file.
The calculation source file.


Please send any comment on this program.