the nature of the problem

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Reinforcement of a floor would be called for where the noise you complain of is caused by excessive lateral or vertical deflections (usually heard as creaking or crackling noises). Assuming you have 2x10 floor joists on 16 inch center on that 16.5 foot span, that should not be a significant problem under most uses. Noise can also be transmitted by hard floors or loose materials improperly fastened to floors. These tend to be distict foot steps and higher pitched vibrations. The solution to the problem depends on the source of the noise.

It is possible to install posts and beams under the floors to reduce the span and therefore deflections, but if the noise is simply transmitted vibration or footsteps, that won't help solve the noise problem. In the latter case, better fastening of the subfloor or insulation may be a better solution.

In either case, attachment of plywood to the underside of the floor may reduce transmission of noise and would act as bracing to reduce lateral deflections of joists. You could accomplish the same thing less expensively with blocking or X bracing.

Describe the problem you are trying to solve in more detail and we can help more. Installation of a laminated beam on posts may require footings depending on loads. Also, I think you will be better served by using screws (or nails) for attachments than glue, especially if you need to maintain access to pipes, HVAC, etc.