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chandran
- 139
- 1
how do we say that in a beam bending problem the bean cross section bends(rotates)around the centroidal axis. Why not about any other axis?
Beam bending is the process by which a beam is subjected to an external load and its shape changes as a result. This change in shape is known as deflection. It is important because it helps us analyze the strength and stability of a beam, as well as its ability to withstand external forces.
The centroidal axis is an imaginary line that runs through the centroid (geometric center) of a beam. It is important in beam bending because it is the axis about which the beam rotates when subjected to an external load. The rotation of the beam is known as centroidal axis rotation.
The shape of a beam plays a critical role in its centroidal axis rotation. Beams with different cross-sectional shapes (e.g. rectangular, circular, I-beam) have different moments of inertia, which determine how much the beam will deflect when subjected to an external load. The higher the moment of inertia, the less the beam will rotate.
There are several factors that can affect a beam's centroidal axis rotation. These include the type of material the beam is made of, the shape and size of the beam, the magnitude and direction of the external load, and the beam's support conditions (e.g. fixed, pinned, cantilever).
Centroidal axis rotation can be calculated using the principles of mechanics, specifically the equations for bending moment and deflection. The exact calculation will depend on the specific beam and loading conditions, but it typically involves determining the beam's moment of inertia and using it to calculate the deflection at various points along the beam's length.