Engineering Statics

C-11


Consider the beam resting upon two supports with the loading shown. Neglecting the weight of the beam, determine the minimum value of P for which the beam is in equilibrium, hence safe.

If the minimum value of P is applied there will be no reaction at the support on the left side.  We will be looking at the problem 
the instant before the beam will start to rotate in the clockwise direction.
Notice that by taking moments about the right hand support we are 
eliminating the unknown of the the right side reaction, and P is 
the only unknown in the moment equilibrium equation.
If a force of 3.5 kN is applied, the beam will just be in equilibrium.
If the maximum value of P is applied there will be no reaction 
at the support on the right side.  We will be looking at the problem 
the instant before the beam will start to rotate in the counterclockwise 
direction.
Notice that by taking moments about the left hand support we are 
eliminating the unknown of the the left side reaction, and P is 
the only unknown in the moment equilibrium equation.
Arithmetic yields the answer for the maximum value of P.
Hence, if P is any value between 3.5 and 86 kN the beam will remain 
in equilibrium and not rotate.