If there is tensile stress perpendicular to the beam cross sections in the upper half of the beam, and compressive stress in the bottom half of the beam, the upper half of the beam will get longer and the bottom half of the beam will get shorter. This geometrically means that the beam is bent.chetzread said:
I agreed, but, it only means the beam is sheared , but not bent like U shape, right?Chestermiller said:
why you said that it's bent?chetzread said:
The key assumption involved here is the flat cross sections of the beam remain flat after the deformation has occurred. Can you tell me how the cross sections can remain flat while the upper part of the beam gets longer and the bottom part of the beam gets shorter without the beam developing curvature (i.e., bending)?chetzread said:
Yes.chetzread said:
Bending stress is the stress that occurs when a beam is subjected to a bending moment, causing it to bend or deform. Normal stress, also known as axial stress, is the stress that occurs when a beam is subjected to a force that is perpendicular to its cross-sectional area.
Bending stress is calculated using the formula σ = Mc/I, where σ is the bending stress, M is the bending moment, c is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia. Normal stress is calculated using the formula σ = F/A, where σ is the normal stress, F is the applied force, and A is the cross-sectional area.
Bending stress can cause a beam to bend or deform, while normal stress can cause a beam to elongate or compress. Both types of stress can lead to failure if they exceed the beam's strength. Bending stress can also cause shear stress in beams, which can lead to shear failure.
In bending stress, the stress is highest at the outermost fibers of the beam and decreases towards the neutral axis. In normal stress, the stress is uniform throughout the cross-sectional area of the beam.
The magnitude of bending stress is affected by the magnitude of the bending moment, the distance from the neutral axis, and the moment of inertia. The magnitude of normal stress is affected by the magnitude of the applied force and the cross-sectional area of the beam.
