Understanding Shear Force and Bending Moment diagrams


   
Applies To    
   
Product(s): STAAD.Pro  
Version(s): ALL  
Environment: ALL  
Area: Postprocessing workflow  
Subarea:    
Original Author: Sye Chakraborty, Bentley Technical Support Group  
   

 

I have a concentrated load acting on a simply supported beam. I am plotting a shear force diagram and it does not look right. The shear force diagram does not change sign at the point where the load is applied but instead shows a slope.

 

Diagram that I get

 

 

Diagram that I expect to get

 

 

 

This is due to a limitation in the way in which shear force diagrams ( and bending moment diagrams ) are plotted in STAAD.Pro.
 
For any member/beam, the program uses the values of bending moments ( shear forces, torsions and axial forces ) determined from the global analysis at the start node and end node of the member/beam. Using this information, and the loads on the member, it calculates the values at 11 more equally spaced intermediate positions along the member span (1/12th point, 2/12th point, 3/12th point, etc. upto 11/12th of the member length). 
 
So, it now knows the values at a total of 13 points along the member span. These are drawn perpendicular to the line of the member at the locations they were determined and
connects these adjacent values by drawing a straight line from the end of one line to the next. That is how you see the diagram.
 
There are some limitations in this approach.
 
a) If there is a concentrated load on the member, and it is located at a point that is not one of these 13 points, the shear force diagram will fail to capture the sudden change in shape of the diagram under that load. Since this point is not one of the 13 equidistant points, the value is not calculated at that location and the program. The program knows the value at a location before and at a location after the load location and joins the data points to generate the diagram which results in a slope in the diagram.
 
b) Similarly if the load happens to be a concentrated moment, the sudden change in value of the moment at that location will also not be captured by the Bending Moment Diagram.
 
Hence, the diagram plotted is accurate if there are no concentrated forces or moments on the span, but approximate if such loads are present at locations which does not correspond to the 1/12 th points.
 
The best thing to do when concentrated loads/moments are present at such locations, is to split the member at that location to create a node and then apply the member load as a joint load.

 

This same logic is employed in the other locations where result diagrams are produced, namely the Member Properties dialog> Shear Bending tab (also known as the Member Query dialog) and the graph windows displayed in the Layouts>Beam Results>Graphs layout.