Two free standing pillars holding beam, moment of inertia problems.

[bigandy008]

Hi, I'm new here and didn't really know where to put this so decided to put it here as it is to do with my course work. I'm currently doing my Final year project on a lifter for lifting fertilizer bags its going okay and do know how to calculate moment of inertia but the problem is that I have two pillars standing beside other and I don't know weather I add the two moments of inertia or weather i multiply the depth and breath by 2 first?

Homework Statement

two free standing pillars connected at the bottom each pillar is 100mm x 50mm with a wall thickness of 5mm. These are holding a beam out like the way a crane looks i am assuming that it is a ridged body with no supports. to find the moment of inertia i know i have to include both pillars but i am not sure if i am writing the equation correctly.

Homework Equations

I={bd³}/{12}

The Attempt at a Solution

Ive tried
{(0.05x2)x((0.1³)x2)}/{12}
and
({0.05x0.1³}/{12})x2
and got two completely different answers
ino i have to take the inside moment of inertia away as well but i need to get my head round this first
any help would be greatly appreciated cheers Andy.

 

[SteamKing]

It's not clear from your description what you are trying to do. A picture of your lifting apparatus would be a big help. Are you trying to calculate the stresses in the apparatus when it is loaded?

 

[bigandy008]

yes basically that what I am trying to do I am just wondering what why to go about getting the moment of inertia for the two pillars together.

i think that a picture of it now. basically I am trying to find the stress exerted on the two green pillars.

 

[FireStorm000]

If you're trying to find the force exerted, or find stress, you need to find torque. You have a force m*g being exerted on a lever arm of length r. That creates a torque at the joint. If this contraption stays fixed, then the sum of the torques is 0 (taking into account direction). So each green pillar produces a restoring torque half the magnitude of the red bar.

Though honestly, I doubt this would hold together with a 500kg load and no extra supports.

I'm not sure what relevance moment of inertial has if you're trying to find the stress on the joint.

 

[Nickie]

First of all, it's great that you are working on your final year project and trying to understand the concept of moment of inertia. I would suggest approaching this problem by breaking it down into smaller parts and then combining them to get the overall moment of inertia.

In this case, you have two pillars connected at the bottom, each with their own moment of inertia. To find the total moment of inertia, you can first find the moment of inertia for each individual pillar using the equation I={bd^3}/{12}. Here, b represents the base (breadth) of the pillar and d represents the depth. Since the pillars are identical, you can use the same values for b and d for both pillars.

Once you have the moment of inertia for each pillar, you can then add them together to get the total moment of inertia for the entire system. This is because the pillars are connected at the bottom and act as one unit when it comes to resisting rotational motion.

So, to answer your question, you do not need to multiply the depth and breadth by 2 before calculating the moment of inertia. You can simply use the dimensions of one pillar and add the two individual moments of inertia to get the total moment of inertia for the system.

I hope this helps and good luck with your project!