Diesel Darryl is right
Darryl has it right, I use 1. 375" stock for the bar itself, that is . 125" smaller, or 1/8" smaller diameter. The ID of the tube is the same. With the Heim joints on each end all the forces on the tube are right down the center of the tube and the ultimate strength of the bar setup is not different because of the bar diameter. If anything were to let go it would have to be several of the attachment bolts that are in shear. This is why I use grade 8 fasteners and frame stiffener plates. The only way that a bar [the tube] could buckle would be if it was damaged [bent] and then it would just bend more when the axle forces were applied.
The design concept is the same as Darryl said. The idea is to keep the axle from rotating around the flexible leaf spring. When the traction of the tires lets go, [the 'Hop'] the leaf spring tries to return it's original shape and the axle rotates back to it's original location, then the tires gets traction again and the axle starts to flex [wrap-up] the leaf spring again. The bar locates the bottom of the axle a fixed distance to a frame mount and this keeps the axle from moving either forward or backwards while pushing or pulling on the truck and it's load. . wheel 'hop' is virtually eliminated. Tire sidewall flex still allows some axle hop, just watch the the tires on truck during a sled-pull.
The rubber bushing around the front spring bolt provides enough give to make up for the different arc-pathways that the bar and spring go through when they move up and down, therefore there are no 'geometry issues' or binding during verticle wheel travel.
I call my bars 'Ride-Control Bars' because of the very noticable improvement in ride and steering they provide. When the truck is driven over washboard roads, railroad tracks, and uneven pavement, the rear axle will not jump all over the place and give several bumps or jars for one bump in the road or pothole in the pavement. No more 'tea-berry-shuffle' over railroad crossings. The truck even tracks straighter on uneven pavement requiring less steering correction to stay in your lane.
I can take my truck over a fresh-plowed field in 2wd and it will not wheel hop, it will eventually just bury the rear axle in the soft ground. Before the bars were added, my truck would be violently hopping and feel like it was about to break some drive line components when driven on soft ground, washboard roads or snow.
There are lots of ways to attach or create control bars, these are designed so that there is no welding required, and can be installed with only drilling a few holes. The designs that require welding to the axle tube have their own characteristics, but the welding adds a lot to the cost of install for the average truck owner. The design that mounts to the top of the axle tube puts the bar in tension rather than compression with forward truck motion, but is more complicated and usually requires welding.
I believe this answers some questions. Greg L