Distribution of Stresses in a Narrow Rectangular Beam

In studying beam stress distribution, examining an elemental section is essential. To determine the average shearing stress on this face, the calculated shear is divided by the surface area. Importantly, shearing stresses on the beam's transverse and horizontal planes mirror each other, indicating a consistent stress distribution along the upper region of the beam. Notably, shearing stresses are absent at the beam's upper and lower surfaces due to the absence of applied forces in these areas.

For beams with a narrow rectangular cross-section, the variation in shearing stress across the width is minimal, less than 0.8% of the average stress. This minor variation is attributed to the beam's width being significantly smaller than its depth, making the average shearing stress equation a reliable method for assessing stress across any point of the beam's cross-section. In the rectangular beam's transverse section, shearing stresses are distributed parabolically. This distribution features zero stress at the beam's top and bottom edges, with stress increasing toward the center. This parabolic stress profile is essential for understanding how beams manage stress, ensuring their structural integrity and the capacity to bear loads without compromising stability.