Forum Discussion
Ron_Gratz
May 10, 2013Explorer
CHD Dad wrote:I'd say you have a better understanding of the load-deflection characteristics of a cantilever beam than some engineers do.
Definitely not an engineer so please feel free to laugh at my comments...
I thought the whole point of any tapered bar such as what is on the Blue Ox is that tip will flex more than the base.---When a force is applied to the free end of a cantilever beam, a bending moment will be imposed on the beam.
The bending moment will be zero at the tip and will vary linearly along the beam to a maximum moment, at the fixed end, equal to force times length.
The curvature at any point along the beam is directly proportional to the bending moment.
Curvature also is inversely proportional to the beam's area moment of inertia which, for a rectangular cross section, is equal to thickness cubed times width divided by 12.
For a beam of constant cross section, the curvature at any point will be maximum at the fixed end and will vary linearly to zero at the free end. The deflected shape, in this case, would be a parabola.
For a tapered beam, either tapered in width or tapered in thickness, the curvature along the beam might be constant. In this case, the deflected shape would be a circular arc.
If a tapered beam and a non-tapered beam have the same cross section at the fixed end and are subjected to the same force at the free end, the free end of the tapered beam will deflect more.
The tapered beam also will be subjected to greater bending stress along the length of the beam.
In fact, with the correct amount of taper, a tapered beam could be designed to have constant bending stress along its entire length.
If its the same cross section, but the material is thinner it should flex easier and faster than the thicker material towards the end of the bar going into the socket. It should be "progressively" easier to flex the bar the farther away you move from the socket as the bar tapers down in thickness.Yes, as distance from the fixed end increases, the curvature of the tapered beam will be greater and the deflection will be greater than for the non-tapered.
However, the amount of tip deflection for any given beam, remains directly proportional to the applied load.
When the term, "progressive", is applied to a spring it usually means that the "spring rate" (incremental load divided by incremental deflection) increases as the deflection increases. This is not the case for a tapered beam.
While the amount of force exerted to the hitch head is constant, isnt the bar designed to be progressively softer the further away from the head? My thoughts are that is progressive in nature. The tips can flex easier to help absorb any shocks or small movements and as the load against them ramps up during a turn they resist flexing the further out of line it gets.The force acting on the tip of a WD bar with a tilted trunion is close to its maximum when the TV and TT are aligned.
As a turn is made, there is a slight increase in force followed by a relatively rapid decrease.
If not, what is the point of tapering the bar? Weight savings? You could make the entire bar smaller in cross section. It would be much cheaper than having those bars made with the taper to just saw cut mults out of plain bar stock.As mentioned earlier, with a tapered bar, you can achieve a more uniform distribution of bending stress along the length of the bar.
This means you can support a greater tip force with less material.
The bar is lighter, but can support the same load as a non-tapered bar.
In the case of the new Sway Pro, one possible advantage for the tapered bar is greater tip deflection for a given load.
Other WDHs have chains or L-brackets which can be used in combination with ball mount tilt for "fine tuning" the adjustment of the WD bars.
The new Sway Pro only has the rotating latch for "fine tuning".
The tuning resolution provided by a combination of chain links and head tilt probably is finer that that provided by chain links only.
Since the tapered Blue Ox bar has a lower "spring coefficient", a change of one chain link would give a finer tuning than using only the chains on other WDHs.
Ron
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