Lecture 16:
Multiple Force Members
The term, three-force member, is often incorrectly applied to members with more than three forces. Any member which is subjected to more than three single concentrated loads should be identified as a Multiple Force Member. The "extra" forces acting upon a multiple force member can be replaced until the total number of forces is reduced to three; the resultant force of the loading and the two reactions. This means that distributed loads must always be replaced so that only one resultant force is applied to the member. Then, all of the other forces must be replaced so that there is only one resultant representing the external loading. The three non-parallel forces must be concurrent so that the three-force principle then applies.
The illustrations are two examples of multiple force members:
The loading of the first image would be resolved in the following manner. The resultant of the distributed load would be determined. This would act at the mid-point of the width of the load. The resultant of this force and the concentrated load acting at the cantilevered end of the beam would be combined into one load by summing moments about the right-hand support. This system would then be reduced from multiple force member to a three force member.
The second system could represent an entrance canopy to a hotel that also has four large spot lights sitting upon it. These six loads must also be combined into one load resultant before the member can be considered a three force member.
System Reactions
Copyright © 1995, 1996 by Chris H. Luebkeman and Donald Peting