# Beam bending and moment of inertia

• ttlg
In summary, to find the first moment of area and moment inertia of two beams placed on top of each other in 3 point bending simply supported, assuming they will always stay in contact, the parallel axis theorem can be used. However, if there is no transverse shear between the beams, the loads can be split equally between the two beams, but the parallel axis theorem can still be applied to find the overall area MOI of the composite section.

#### ttlg

If you have two beams, not attatched to each other, placed on top of each other in 3 point bending simply supported, what do you do to find the first moment of area and moment inertia of the two beams.
Thanks

Hi Fred,
I think what ttlg is asking is if the two beams are simply sitting on top of each other such that there can be no transverse shear between the two (like a leaf spring on a car). The two beams, stacked one on top of the other, are then simply supported at the ends and loaded in the center with a verticle force. In that case, since there's no transverse shear between the two (ie: the beams act independantly) the parallel axis theorem doesn't apply to the beams as a set. In this case, the load acting on the beams can simply be split 50/50 between the two beams (each beam supports 1/2 the load).

Q,
The loads can be split the way you mention, but to find the area MOI of the assembly, i.e. the composite section, one needs to use the parallel axis theorem. I am using the interface between the two beams as the neutral axis (with no shear between the two as you mentioned). From there take the two individual beams' respective area MOIs and use the parallel axis theorem to calculate the overall area MOI.

ok, thanks for your help

FredGarvin said:
Q,
The loads can be split the way you mention, but to find the area MOI of the assembly, i.e. the composite section, one needs to use the parallel axis theorem. I am using the interface between the two beams as the neutral axis (with no shear between the two as you mentioned). From there take the two individual beams' respective area MOIs and use the parallel axis theorem to calculate the overall area MOI.

QGoest said:
since there's no transverse shear between the two (ie: the beams act independantly) the parallel axis theorem doesn't apply to the beams as a set.

Looking at Q's comments about the shear stress...he's right on that. The MOI is simply two times the individual MOIs.

## What is beam bending?

Beam bending is a phenomenon that occurs when a beam or structural element is subjected to external forces, causing it to bend or deform. This can happen in various engineering applications such as buildings, bridges, and machinery.

## What is the moment of inertia of a beam?

The moment of inertia of a beam is a measure of its resistance to bending or deformation. It is a mathematical property that describes how the mass of the beam is distributed around its axis of rotation. A higher moment of inertia indicates a stiffer and stronger beam.

## How is moment of inertia calculated?

The moment of inertia of a beam can be calculated using the beam's cross-sectional area and shape. The formula for moment of inertia varies depending on the shape of the cross-section, such as rectangular, circular, or I-shaped. It is an important consideration in structural design and can be calculated using various mathematical methods.

## What factors affect beam bending and moment of inertia?

The factors that affect beam bending and moment of inertia include the material properties of the beam, the external forces acting on it, and its cross-sectional shape and dimensions. The type of support and boundary conditions also play a significant role in determining the bending and moment of inertia of a beam.

## Why is understanding beam bending and moment of inertia important?

Understanding beam bending and moment of inertia is crucial in the design and analysis of structures and mechanical systems. It helps engineers and scientists determine the strength and stiffness of a beam, which is essential in ensuring the safety and reliability of a structure. Additionally, knowledge of beam bending and moment of inertia can aid in optimizing designs and reducing material costs.