What is the required bend radius for a simple L-shaped bracket that will require the most material?

In sheet metal design, the required bend radius is primarily determined by the material type, thickness, and the specific properties of the material being used. For a simple L-shaped bracket, a larger bend radius generally helps in minimizing the risk of cracking or deforming the material at the bend.

The correct choice reflects the fact that a smaller bend radius, such as 1/8 inch, can lead to increased material stretching and potential failure points in thinner materials. Although a smaller radius can seem to require less material initially, in practical applications, it isn't conducive to producing a durable and robust bracket.

Conversely, a larger bend radius, typically 1/4 inch or more, tends to distribute the stresses more evenly across the material, enhancing the structural integrity of the bracket. Therefore, the required bend radius should be selected to not only maintain material economy but also to assure mechanical performance, leading to the conclusion that a larger radius would be favored in most applications, particularly in load-bearing scenarios.

In this context, the largest bend radius being considered (which appears to be associated with maximum material usage) plays a significant role in achieving a balance between function, durability, and manufacturability.