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.
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.
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.
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.
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.
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.
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.