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The best possible way to prevent the bracket from failure is to ensure that it is enough rigid thereby ensuring absolute zero deflection at all points of the bracket. What is the view on the real world feasibility of this?

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    $\begingroup$ there is no material in the world that would not deflect. $\endgroup$ – kamran Nov 21 '19 at 14:53
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There is no material with zero deflection in the world. Every thing deflects, to different degrees.

The best possible way to prevent a bracket from failure is to design it for the task it must do.

If the load is a vibrating machine, it must be allowed to vibrate by with a frequency that is not likely going to resonate with that of the machine.

if the load is off center, it must be strong enough to resist the moment plus all the shear and normal forces.

If the load is cyclic, it must be designed for fatigue, etc.

If it is part of a structure of an airplane it must be strong enough for all the above and be reliable under extreme temperatures and be light within the reason.

EDIT

As commented by some, I thought a few points may help clarify my answer.

Deflection is actually the way a bracket or any structure undertakes to support the load. Of course it has to be controlled. But a beam or slab or any other member of a structure as long as it is not deflected is not carrying any load.

An archer knows to pull his bow to the most deflection to shoot his arrow faster and farther. Many huge suspension bridges find strength in predesigned deflection.

Strength in engineering is the capacity to support static or dynamic loads or impact of objects while maintaining the geometry within accepted tolerances. it doesn't matter for this discussion the kind of deflection, or strain that has caused it.

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    $\begingroup$ Even if you found a (theoretically) rigid material, you can still have (theoretically) infinite stress concentrations at re-entrant corners, so rigidity would not protect you from failure by a crack propagating through the bracket. $\endgroup$ – alephzero Nov 21 '19 at 16:34
  • $\begingroup$ It might be good to mention that rigidity and strength are two different properties. You could have a very rigid, but brittle, structure that is weak. Compare that to a more flexible structure that while bending has high strength. Chalk might be more rigid than wood, but likely less strong. $\endgroup$ – Eric S Nov 21 '19 at 23:45
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Building on to what was previously said, when designing a bracket or mechanical fastener based connection, my major concern would most likely be the failure of the plate or the bolt/screw. For this, you may need to consider: bolt tearout, hole yielding or general yielding/failure of the plate. Furthermore, you may also need to consider the strength of the fastener.

For further information and the actual regulations, check the AISC steel construction manual or other relevant steel connection codes.

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