Find the reactions at the beam ends 'A' and 'B'. The beam is 6ft in length and the distributed load ends midway across the beam. The applied load shown represents the intensity of a distributed load. The intensity at point 'A' is 0 lb/ft while the intensity at x-3ft is 400lb/ft. The general approach to dealing with a distributed load is to replace the distribution with a concentrated force with magnitude equal to the resultant of the distributed load. The concentrated force must be positioned so that it has the same net external effect on the system as the distributed load. It turns out that this is accomplished by having the concentrated load act through the centroid of the distributed load. 400 lb/ft A a. Calculate the magnitude of the resultant load as the area under the distributed load curve. (Consider what you would expect the units of the resultant force to be.) b. Calculate the x-coordinate of the centroid of the triangular load distribution relative to point 'A'. Draw the beam FBD with the distributed load replaced by a concentrated force acting с. through the distribution centroid. d. Apply the equilibrium equations F, = 0 and E M, = 0 to solve for the reactions at 'A' %3D and 'B'.
Find the reactions at the beam ends 'A' and 'B'. The beam is 6ft in length and the distributed load ends midway across the beam. The applied load shown represents the intensity of a distributed load. The intensity at point 'A' is 0 lb/ft while the intensity at x-3ft is 400lb/ft. The general approach to dealing with a distributed load is to replace the distribution with a concentrated force with magnitude equal to the resultant of the distributed load. The concentrated force must be positioned so that it has the same net external effect on the system as the distributed load. It turns out that this is accomplished by having the concentrated load act through the centroid of the distributed load. 400 lb/ft A a. Calculate the magnitude of the resultant load as the area under the distributed load curve. (Consider what you would expect the units of the resultant force to be.) b. Calculate the x-coordinate of the centroid of the triangular load distribution relative to point 'A'. Draw the beam FBD with the distributed load replaced by a concentrated force acting с. through the distribution centroid. d. Apply the equilibrium equations F, = 0 and E M, = 0 to solve for the reactions at 'A' %3D and 'B'.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Problem 6
Find the reactions at the beam ends 'A' and 'B'. The beam is 6ft in length and the distributed load ends
midway across the beam. The applied load shown represents the intensity of a distributed load. The
intensity at point 'A' is 0 lb/ft while the intensity at x-3ft is 400lb/ft.
The general approach to dealing with a distributed load is to replace the distribution with a
concentrated force with magnitude equal to the resultant of the distributed load. The
concentrated force must be positioned so that it has the same net external effect on the system
as the distributed load. It turns out that this is accomplished by having the concentrated load act
through the centroid of the distributed load.
400 lb/ft
A
a. Calculate the magnitude of the resultant load as the area under the distributed load
curve. (Consider what you would expect the units of the resultant force to be.)
b. Calculate the x-coordinate of the centroid of the triangular load distribution relative to
point 'A'.
С.
Draw the beam FBD with the distributed load replaced by a concentrated force acting
through the distribution centroid.
d. Apply the equilibrium equations F, = 0 and Mp
= 0 to solve for the reactions at 'A'
and 'B'.
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