What is the Moment of Inertia for a Rectangular Beam under Uniform Force?

In summary, the relevant moment of inertia is a measure of an object's resistance to rotational motion, taking into account the distribution of mass and the distance from the axis of rotation. It is different from the moment of inertia, which considers all of an object's mass and distance from the axis. The relevant moment of inertia is calculated using the formula I = ∫r²dm and is important in engineering and physics for accurately predicting an object's rotational motion. It directly affects an object's rotational motion by determining the amount of torque needed to rotate it.
  • #1
Savage32
1
0
Rectangular Beam-

Cross section
h - dimension in y direction
b - dimension in x direction

If with a uniform force acting on the beam in the negative y-dir, what is the relevant moment of inertia when modeling the deflection u(z): E I (d4/dz4)u =w?

I believe it is bh^3/12, but I am not positive

Thanks in advance for any help.
 
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  • #2
Yes, you are correct. You are listing the Second Moment of Inertia (Area), which deals with bending stress.
 

FAQ: What is the Moment of Inertia for a Rectangular Beam under Uniform Force?

What is the relevant moment of inertia?

The relevant moment of inertia, also known as the effective moment of inertia, is a measure of an object's resistance to rotational motion. It takes into account the distribution of mass and the distance from the axis of rotation.

How is the relevant moment of inertia different from the moment of inertia?

The moment of inertia is a measure of an object's rotational inertia, taking into account all of its mass and its distance from the axis of rotation. The relevant moment of inertia, on the other hand, only considers the mass and distance of specific components or sections of an object that are relevant to the rotation being studied.

How is the relevant moment of inertia calculated?

The relevant moment of inertia is calculated using the formula I = ∫r²dm, where I is the relevant moment of inertia, r is the distance from the axis of rotation, and dm is the differential mass of the relevant component or section being considered.

Why is the relevant moment of inertia important in engineering and physics?

The relevant moment of inertia is important because it allows engineers and physicists to accurately calculate and predict an object's rotational motion. It is used in various applications such as designing machines, analyzing the performance of rotating objects, and understanding the behavior of rotating systems.

How does the relevant moment of inertia affect an object's rotational motion?

The relevant moment of inertia directly affects an object's rotational motion, as it determines the amount of torque required to rotate an object. Objects with a higher relevant moment of inertia will require more torque to rotate, while objects with a lower relevant moment of inertia will require less torque. This concept is crucial in engineering and designing efficient and effective systems.

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