Bending Stress in a Curved Beam

Bending stress is a type of stress that occurs in a beam when it is subjected to a bending moment. In a curved beam, the bending stress can be quite complex as the beam is not straight, and its cross-section changes along its length. The bending stress in a curved beam is affected by several factors, including the radius of curvature, the cross-section of the beam, and the material properties.

Zero at the Centroidal Axis

The centroidal axis is a line that passes through the centroid of the cross-section of the beam. In a curved beam, the centroidal axis is the axis of symmetry. At the centroidal axis, the bending stress is zero because the neutral axis coincides with the centroidal axis, and the moment arm is zero. The neutral axis is the line that divides the cross-section of the beam into two equal parts. Therefore, the bending stress is zero at the centroidal axis.

Maximum at the Point Other than Centroidal Axis

The bending stress is maximum at the point other than the centroidal axis because the moment arm is maximum at this point. The moment arm is the perpendicular distance between the centroidal axis and the point where the bending stress is being calculated. As the moment arm increases, the bending stress also increases, and it reaches a maximum value at the point farthest from the centroidal axis.

Conclusion

In conclusion, the bending stress in a curved beam is zero at the centroidal axis and maximum at the point other than the centroidal axis. The bending stress is affected by several factors, including the radius of curvature, the cross-section of the beam, and the material properties. It is important to consider these factors when designing and analyzing curved beams to ensure that they can withstand the bending stress and remain structurally sound.