The Uniform Beam Analysis module calculates the vertical shears, moments, slopes, and displacements of a transversely loaded uniform beam with various end supports. The module also calculates the natural frequencies and mode shapes of the beam. The module's closed-form equations are based on the following assumptions:

• The cross section is uniform.
• The beam is of homogeneous material with the same elastic modulus in tension and compression.
• The beam is straight.
• The beam is long in proportion to its depth.
• The maximum stress does not exceed the proportional limit.

Figure 1. Module input form

Beam End Constraints
Each end of the beam can be fixed (i.e., cantilevered), guided, pinned (i.e., simply supported), or free. The module will verify that the beam is adequately constrained for the static analysis. Any combination of end constraints is valid for a natural frequency analysis.

Static Load Conditions
A list of static loads is displayed in the upper right hand corner of the main input form. The loads applied to the beam in a static analysis are dependent on the solution type specified:

• Static Analysis (Selected Load) - Only the selected load is applied.
• Static Analysis (All Loads) - All loads in the list of static load conditions are applied.
• Natural Frequency Analysis - The list of static load conditions is not used.

New loads can be added to the list of static load conditions by by clicking the 'Add' button and entering the load type, location, and magnitude using the Beam Static Loads input form shown in Figure 2.  Load types currently supported are concentrated forces, concentrated moments, and distributed forces. Existing loads can be removed from the list of static load conditions by clicking the 'Remove' button.

Figure 2. Input form for applied static loads.

Beam Geometric and Material Properties
The following six input fields are used to define the beam length, cross section, and material type:

• Elastic Modulus - The material modulus of elasticity.
• Mass Density - The material mass density.
• Moment of Inertia - The section moment of inertia in the vertical plane.
• Area - The section area.
• Dist to Outer Fiber - The distance from the neutral axis to the point where bending stress is to be calculated.
• Length - The length of the beam

Links to the Section Properties module and Materials Database module are provided for automatic input of beam section properties and material data.

• Scatter plots
• Tabular output
• Beam graphics and animation.

Scatter Plots
Calculated deflections, slopes, moments, shears, and mode shapes can be plotted using the standard ETB plot utility shown in Figure 3.

Figure 3. Module plotted results.

Tabular Output
The Uniform Beam Analysis module follows the standard ETB convention for tabular output by providing the following header information:

• Module name and version

• Analysis time and date

• Input data

Calculated deflections, slopes, moments, shears, stresses, natural frequencies, and mode shapes can be output in tabular format. An example is shown in Figure 4 below.

Figure 4. Module tabulated results.

Beam Graphics and Animation

The Uniform Beam Analysis module provides a simple graphics post-processor, shown in Figure 5, for visualization of the analyzed beam problem, including loads and boundary conditions. The utility has the capability to display and animate beam deflections (static analysis) or mode shapes (natural frequency analysis).

Figure 5. Beam deflected shape.