22.2 : 狭い長方形の梁における応力の分布

An elemental section of a beam is considered to analyze the distribution of the stresses. The magnitude of the shearing force exerted on the horizontal face of the element is obtained from the horizontal shear expression.

The average shearing stress on that face is determined by dividing horizontal shear by the area of the face.

Shearing stresses on the transverse and horizontal planes of the beam section are equal, representing the average stress along the line on the upper part of the beam. Shear stresses are zero at the upper and lower faces as no forces are being exerted.

In a narrow rectangular beam, shearing stress along the width of the beam section varies less than 0.8% of the average shearing stress as the width is less than a quarter of its depth.

So, the average shearing stress equation is used to determine shearing stress at any point across its cross-section.

In the transverse section of the rectangular beam, the shearing stresses are distributed parabolically, with zero stress at the top and bottom.