Overview

This program provides analysis of single span beams with a variety of loading and support conditions. Maximum moments, shears, reactions, and deflections are given. The basic ability of this program is also contained in the various beam design programs in the steel, concrete, and timber divisions. This program performs a more detailed analysis and offers more loading options than most of the design programs.

 

A single span beam with optional cantilevers can be analyzed, and the end supports can be modified to give almost any configuration.....simple supports, propped cantilever, fixed at both ends, pure cantilever, or double cantilever.

 

Loads that can be applied are extensive. Uniform, partial length, trapezoidal, concentrated, and moment type load can be entered. For partial length and trapezoidal loads, entry is very simple by just entering the start and end magnitudes and locations. The program uses the locations to determine how the load is applied to center and cantilever spans.

 

NOTE! All load locations are in reference to the LEFT support. Distances are positive toward the right support, and negative over the left cantilever. The program also provides a QUERY section, allowing you to enter locations along the span where you would like to investigate the conditions.

 

 

Assumptions and Limitations

 

 

Example

The data entry for this example is shown in the screen captures that accompany the Data Entry Tabs and Results & Graphics Tabs sections to follow. The example is for a double-cantilevered beam with loads applied to center span and cantilever. Because this program does not do automatic calculations for multiple locations of live load only one set of results are given.  Here is a basic sketch of the geometry and loading:

 

 

               

Data Entry Tabs

This set of tabs provides entries for all input in this calculation. While you are entering data and switching between these tabs you can view the desired resulting information on the tabs on the right-hand side of the screen (calculated values, sketches, diagrams, etc.). A recalculation is performed after any entry data is changed. After each data entry you can view the results on the right-hand set of tabs.

 

General Tab

 

 

Center Span, Left Cantilever, Right Cantilever

Enter the span lengths for center span and cantilevers. When an end fixity is specified as Fixed, any entry for cantilever length or loads that extend past the fixed support will be ignored. Distributed loads that extend past the fixed support will simply be truncated.

 

End Fixity

This entry enable you to specify the end fixity combination for the beam. The order of the words is refers to the left-right ends of the beam.

 

Inertia & Elastic Modulus

Entry of both these items is required to for the program to calculate deflections. If one or both of these entries is zero deflections will be "0.0".

 

Uniform Tab

This tab provides entries for you to apply full-length uniform loads to the center span and cantilevers. Positive values act with the force of gravity and deflect a beam downward resulting in compression on the top fiber.

 

Point Tab

This tab provides entries so you can enter up to 14 point loads. The "Location" is the distance from the left support to the location of the point load. If the "Location" value is negative then it is on the left cantilever. If the value exceeds the center span length then it is on the right cantilever. Cases where negative Locations are entered with no left cantilever or a "Fixed" left support are ignored. Similar behavior happens for Location values that are longer than the Center Span distance. Positive values act with the force of gravity and deflect a beam downward resulting in compression on the top fiber.

 

Trapezoidal Tab

Up to 8 full or partial length uniform loads with varying start & end magnitudes can be specified on this tab. The "Left/Start" magnitude refers to the left hand side of the load. Magnitudes can be positive or negative values at both or either ends. The "Location" is the distance from the left support to the location of the Startpoint or Endpoint of the load. If the "Location" value is negative then it is on the left cantilever. If the value exceeds the center span length then it is on the right cantilever. Cases where negative Locations are entered with no left cantilever or a "Fixed" left support are ignored. Similar behavior happens for Location values that are longer than the Center Span distance. Positive values act with the force of gravity and deflect a beam downward resulting in compression on the top fiber.

 

Moment Tab

This tab provides entries so you can enter up to 8 moments. The "Location" is the distance from the left support to the location of the point load. If the "Location" value is negative then it is on the left cantilever. If the value exceeds the center span length then it is on the right cantilever. Cases where negative Locations are entered with no left cantilever or a "Fixed" left support are ignored. Similar behavior happens for Location values that are longer than the Center Span distance. Positive values act with the force of gravity and deflect a beam downward resulting in compression on the top fiber.

 

 

Query Tab

This tab enables you to enter specific locations on the beam span and have the moment, shear, and deflection given.  The accuracy of these values is to the nearest 1/500th of the span.

 

 

 

Results & Graphics Tabs

This set of tabs provides the calculated values resulting from your input on the "Data Entry Tabs". Because a recalculation is performed with each data entry, the information on these tabs always reflects the accurate and current results, problem sketch, or stress/deflection diagram.

 

Results Tab

This tab contains the resulting calculated values for the beam analysis.

 

     

 

Maximum Moment & Location

The maximum moments at location is shown with it's location measured from the left support. This is an absolute value maximum with the sigh intact. The actual span lengths increments used to determine the accuracy depend upon the center span and cantilever lengths. A beam with no cantilevers will be divided up unto 500 increments. When cantilevers are used, each span is divided into a portion of the 500 increments according to its percentage of the total beam length.

This is the maximum positive moment (compression at top of beam) between the supports. The entire length of the beam is scanned, and if compression occurs over a support due to a cantilever this will be included also.

 

Moments....Max.+, Max. -, Left & Right End Support

These values are the maximum and minimum values for the center span and the actual moment at the end support. M The entire length of the beam is scanned, and if compression occurs over a support due to a cantilever this will be included also.

 

Shears

These values are the maximum shear at each support. This value is determined by checking two items:

 

Reactions

These are the calculated vertical reactions at each support from the given loads.

 

Maximum Deflections

When both moment of inertia and elastic modulus are non-zero, this area displays the beam deflections for center and cantilever spans (as applicable). All 250 span locations are checked for maximum deflection and both the location and deflection are given.

 

Sketch Tab

This tab provides a sketch of the beam with loads and resulting values shown.

 

Diagrams Tab

This displays a moment, shear, and deflection diagram for the beam with the applied loads and end conditions. Note the two tabs...."Graphic Diagram" and "Data Table". The Data Table tab provides the entire internal analysis at the 1/500th points within the beam.

 

 

Printing Tab

This tab allows you to control which areas of the calculation to print. Checking a box will signal that the information described by the item will be printed. However, if there is no information in for a particular selection it will not be printed. So these checkboxes are best described as "If this particular area of the calculations contains data then print it".

 

 

 

Sample Printout