How Do I Calculate Reactions for a Fixed Cantilever with Uneven Loads?

[EQ]

I need help finding reactions for a fixed cantilever. total length is 16ft and its fixed on the right side. The loads on it going from left to right. 2000 lbs at the end of the left. 1000 lbs 10ft from left. There is one support for the cantilever and its where A is at which is 6 ft from left. The dimension for the 1000 lb load is 6ft from B which is the fixed point of the cantilever.

I've been summing the moments at A and B and my numbers are 3800 at A and 800 at B with a zero torque moment at B which is not right, it has to have a torque moment doesn't it?

Please help if you can.


2000...10ft...1000...6ft...
|
|_______________|_________ B Fixed End
...6ft... A .....10ft...


Thanks

 

[Pyrrhus]

This is a hyperstatic system solved by differential equation of the deflexion curve. So what you should do is express reactionary moment in terms of the reaction at support A, and the reactionary force in B in terms of the reaction at support A, then start making your sections (bending moment equations).

 

[piercas]

for reaching out for help with your cantilever problem. I am happy to assist you in finding the reactions for your fixed cantilever.

First, let's review the concept of moments and torque. Moments are the product of a force and its distance from a reference point. In this case, we are summing the moments at points A and B to find the reactions. Torque, on the other hand, is the measure of a force's ability to cause rotational motion around an axis. It is calculated by multiplying the force by the distance from the axis of rotation.

Based on the information provided, it appears that you have correctly summed the moments at point A to be 3800 lbs. However, the moment at point B is not correct. Since point B is the fixed end of the cantilever, it cannot rotate and therefore has no torque moment. The moment at point B should be zero, as you have correctly noted.

To find the reaction at point A, we can use the equation: ΣM=0, where ΣM is the sum of the moments and must equal zero for a static equilibrium. Plugging in our known values, we can solve for the reaction at point A:

(2000 lbs)(10 ft) + (1000 lbs)(6 ft) - RA(6 ft) = 0
20000 ft-lbs + 6000 ft-lbs - 6 ft x RA = 0
26000 ft-lbs = 6 ft x RA
RA = 26000 ft-lbs / 6 ft
RA = 4333.33 lbs

The reaction at point A is therefore 4333.33 lbs, which is the upward force needed to balance the downward forces of the loads on the cantilever.

I hope this helps you find the correct reactions for your fixed cantilever. Remember to always carefully consider the concepts of moments and torque when analyzing a structure. If you continue to have trouble, it may be helpful to consult a structural engineer or seek additional resources for support. Good luck!