Structural Analysis II Section A6.10

### Section I.9 Shear Stress Distribution and Angle of Twist for Multiple-Cell Thin-Wall Closed Sections

In the figure above the area outside of the cross section will be designated as cell (0). Thus to designate the exterior walls of cell (1), we use the notation 1-0. Similarly for cell (2) we use 2-0 and for cell (3) we use 3-0. The interior walls will be designated by the names of adjacent cells.

From section A6.9, the torque of this multi-cell member can be related to the shear flows in exterior walls as follows

For elastic continuity, the angles of twist in all cells must be equal

The direction of twist chosen to be positive is clockwise.

NOTE: Since the exterior walls in each cell have equal shear flows, we can factor the shear flow out and multiply it by the sum of the quotient S/t of the exterior walls.

The above equations for angle of twist together with the torque equation provide a total of 4 linear equations which can be solved simultaneously for the 3 unknown shear flows (i.e., q1, q2, and q3) and 1 unkown angle of twist.

EXAMPLE PROBLEMS

• Example 1 Shear flow distribution, Maximum shear stress, and angle of twist in a two-cell section

To Index Page of Pure Torsion To Section I.8 To Section I.10