19.11 : 非圆形杆件的扭转

During torsional loading, the cross-sections of the circular shafts remain plane and undistorted since they are axis-symmetric.

However, due to the lack of axisymmetry in a square bar, any line in its cross-section, apart from its diagonals and the lines joining the midpoints of that cross-section, will distort when the bar is twisted.

Consider a small cubic element at a corner of a square bar's cross-section in torsion. The element's face perpendicular to each axis is part of the bar's free surface, so all stresses on these faces and the cross-section's corners are zero. 

As a result, here, it cannot be assumed that shearing stress varies linearly with distance from the axis.

The maximum shearing stress occurs along the center line of the wider face of the bar and can be expressed in terms of the width of its wider and narrower faces. Similarly, the angle of twist is also defined in terms of these two widths.

Here, the coefficients, c1 and c2, depend solely on the ratio of dimensions of the two faces.