Title | ME256Equivalen Force Systemsfor Distributed Loads |
---|---|
Course | Statics |
Institution | Western Michigan University |
Pages | 1 |
File Size | 90 KB |
File Type | |
Total Downloads | 65 |
Total Views | 139 |
Download ME256Equivalen Force Systemsfor Distributed Loads PDF
ME 2560 Statics Equivalent Force Systems for Distributed Loads o It is common for structural members to experience loads that are distributed along parts or all of their length. o The diagram shows a simply-supported beam with a distributed load w( x) . The units of w( x) are lb/ft or N/m. o To find the external forces acting on the beam at its supports at A and B, it is helpful to replace the distributed load by an equivalent force system. o In this case, the equivalent force system is simply a single resultant force F R acting at the centroid of the area under the load diagram. L
FR F w( x) dx 0
o Because the resultant force can be moved along its line of action, we only need to find x the X-coordinate of the centroid of the load area. L
x w( x) dx x
0 L
w(x ) dx
L
1 FR
x w( x) dx 0
L
or x FR x w( x) dx 0
0
o Here, the term x FR represents the moment of the resultant force about point A, and L
the term
x w( x) dx represents the sum of the moments of the distributed load about 0
point A. o As mentioned in previous notes, if we are studying the internal forces within a body, we cannot use equivalent force systems. We must use the forces and couple moments as applied.
Kamman – ME 2560: page 1/1...