Calculating Applied Forces and Weld Breakage in Horizontal Rod Suspension

[heyjude619]

Let’s say I have a horizontal rod whose total length = ΔXtotal = 5 inches. However, the rod is made up of two pieces (ΔXshaft = 4 inches and ΔXbase = 1 inch) that are welded together, where ΔXtotal = ΔXshaft + ΔXbase and where ΔXshaft > ΔXbase. This rod is horizontally suspended in air by locking mechanisms placed at each end of the total length of the rod.

I want to use a force gauge to bend the shaft at a certain point so that the weld that joins ΔXshaft and ΔXbase breaks. For example, let’s say the weld breaks when I apply 25 pounds to a point on the shaft 1 inch away from the weld (so 5-1=4 inches from the secured end of the shaft).

How much force was applied to the weld and how much force was translated in bending the shaft? I would like to see the applicable equations so I can replicate this process with variable data.

 

[Simon Bridge]

A rod is fixed at points A and B.
Point A is at x=0, B is at x=+5"
The base is in 0<x<1"
The shaft is between 1"<x<5"

Let the y direction be "upwards".
If you apply a force F in the -y direction at x=1" away from the base - then the force is pllied at position x=2" or 3" from point B which is the secured end of the shaft.

The exact relations depends on how you want to model the rod.
Back-of envelope - treat the rod and base as rigid and use the lever equations.
Point B is the pivot and the shaft is the lever. The weld position is where you want the effective force.