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The task
The task
The cantilever beam is loaded with concentrated force F and moment m, as well as a uniformly distributed load q. Determine the magnitude and direction of the support reactions in a rigid fixed end.
An example of the calculation of support reactions in a rigid fixed end of a cantilever beam loaded with concentrated force, moment and distributed load.
Solution example
Solution example
In this case, there is a case of plane transverse bending, so the reactions will obviously also be located exclusively in the plane of the drawing.
For convenience, we denote the characteristic sections of the beam by points A, B, C, and D and establish a coordinate system with a origin at point A
As is known, fixed end prevents the beam from moving and rotating at the same time, therefore, a force R and a moment M arise in pinching.
For more information about reactions in terminations, see our video:
Without knowing the true direction, we direct them arbitrarily, for example: we direct the reaction R up, and the reference moment M counterclockwise.
To determine the unknown forces, we write the equations of equilibrium of the system (static equations):
Rules of signs for forces and moments.
From the first equation we determine the support force
from the second – a moment in closing
A positive sign of the reactions found indicates that their arbitrarily chosen direction turned out to be correct.
As a check of the obtained data, we write the equation of the sum of moments with respect to any other point of the beam, for example, point D:
Zero indicates that support reactions are defined correctly.
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