Will any glue bond 2 long, bendable metal components

I am trying to create stiffness on an 8-foot length of 1/4" acrylic, with minimal visual footprint. I hit on an 8-foot aluminum U-shaped channel (slips right over top of the acrylic), but it wasn't quite stiff enough. [1]

When I combine it with a 1/8" x 3/8" aluminum bar (placed flat on top of the upside down U), the combination is acceptably stiff. But is there any glue that bonds well enough to hold these two 8-foot lengths together, when they may occasionally be flexed an inch or so sideways?

Final mounting would look like this:

========   > top bar    
=======    > u-channel
| *** |    
| *** |    >  flexing goes in <----> direction
| *** |
  ***
  ***      > acrylic panel (slots neatly into u-channel)
  *** 

i looked at questions What is a strong glue for bonding metal? and How can I attach a 1/8" strip of steel to MDF so that it stays secure forever for eternity?, the first had some interesting glue suggestions. I wasn't sure if the flexing would make any glue pretty useless.

Thanks!

[1] Motivation: The goal is to keep our dog from jumping on and damaging the new window; but if the acrylic is too flexible and he jumps on that, the acrylic could still hit the window and damage it. But you didn't really need to know that to answer the question.