Weldments frequently are subject to torsional loading.

Unfortunately, designers often overlook such loading.

Even when torsional loading is recognized, the conscientious engineer is sometimes left wondering how to deal with it.

The situation is further complicated by the fact that the engineering equations that work well when designing circular shafts are meaningless when applied to more complex weldment configurations.

In this two-part series, we’ll examine several design rules that will permit weldments to be optimized for torsional loading.

A shaft that connects a motor to a driven component provides a simple example of a member subject to torsional loading.

The torsional load often is referred to as torque, which is expressed mathematically as the externally supplied force multiplied by the moment arm, the distance from the point of load application to the axis of the shaft. When the term torque is used, it is natural for the designer to begin to think of torsional loading.

The shaft shown in Figure 1 is subject to torsional loading, and the forces involved could be used to calculate the applied torque. Perhaps a bit more subtle is the torsional loading associated with the earthmoving scraper bucket illustrated in Figure 2.

Calculations
The designer should consider two parameters when dealing with torsional loading:
The stresses created by the torque.
And, the amount of twist that will result.

While one always must consider the stresses, the importance of twist depends upon the application: Where it is essential to maintain the alignment of components in the machine, limits on the permissible angular twist may be an important design parameter.

Various mechanical design handbooks show that we may compute the shear stresses in a round shaft subject to torsional loading as follows:

We can determine the angular twist of a round shaft with this formula:

These two formulas are true and accurate for round shafts, whether solid or tubular.

For non-circular members that are subject to torsional loading, the stresses are not uniform on the outer surface and these equations do not apply.

Since most weldments subject to torsional loading fit into the category of non-circular members, they require another approach.

The torsional resistance (R), a stiffness factor, provides much more reliable solutions to torsional rigidity problems. It is simple to use: Just replace J with R in the angular twist equation shown earlier. Tables 1 and 2 summarize the torsional properties of various sections.

Five torsional members were made and used to compare the predictions of the conventional polar moment of inertia (J) approach and the torsional resistance (R) method. The results are summarized in Table 3. The members all began as a 3 in. strip of 16 gage sheet steel, 12 in. long. For the first three configurations, the conventional method of calculation provides meaningless results, but the torsional resistance method predicts a rotation that is verified experimentally.

Table 3 provides an opportunity for two other observations, one of which will become a design rule.

Notice that for the first two examples shown in the table, the actual twist is essentially the same, whether the member was a flat plate, as in the first example, or a C-shaped channel, as in the second.

The third example in Table 3 is that of a tube, but the seam of the tube is not welded. It too provides essentially the same resistance to twist. All three are examples of “open sections.”

When the open shape is made into a “closed section” as is the case in the fourth and fifth examples (shown in Table 3), the resistance to angular twist is significantly increased. The difference between the third section and the fourth is that the seam has been welded; the weld has changed the assembly from an open section to a closed section, and the measured angular twist has gone from 11 degrees to essentially nil.

The circular closed shape (example 4) and the square closed shape (example 5) provide similar excellent resistance to twist.

This brings us to an important design rule: When tors ional resistance is required, use closed sections where possible.

In Part II of “Designing for Torsional Loading,” we’ll examine the design rules for situations where closed sections are not possible.

Omer W. Blodgett, Sc.D., P.E., senior design consultant with The Lincoln Electric Co., struck his first arc on his grandfather’s welder at the age of ten. He is the author of Design of Welded Structures and Design of Weldments, and an internationally recognized expert in the field of weld design. In 1999, Blodgett was named one of the “Top 125 People of the Past 125 Years” by Engineering News Record. Blodgett may be reached at (216) 383-2225.