a simple solution that, in my point of view will fix tryndamere.
melee carries are always underated because they have to jump right in the face of the enemy team to deal damage, but if they get exposed, they die.
fiora, yi, xin zhao and olaf can be build as ad fighters. mixing armor, mr and health with ad. this way they can deal quite a nice damage without dying like a twitch.
unfortunally, there is one thing that makes them able to deal damage with ad fighter build, and tryndamere doesnt have that.
attack speed spells.
in order to have enough damage and durability, you have to let go on attack speed items, but this way you wont deal enough damage with basic attacks, so what makes it possible for them to be ad fighter is attack speed increasing spells.
olaf's passive: increases 1% as for 1% hp missing
fiora's spell: 120% bonus as for 3 secconds
xin zhao's spell: 80% bonus as for 5 secconds
yi's ultimate: 80% as for 12 secconds
tryndamere doesnt have anything like that.... so the answer to make him viable(at least on my poiny of view) is to give some of his spells an as bonus. my sugestions are
passive: increases AS and crit chance based on fury.
i think it wouldnt work well since he wouldnt be able to build up fury quickly, so either it would have to last really long before decreasing or he would need a new way to generate fury other than basic attacks.
bloodlust: increases AD and AS by health missing
this would be like olaf's passive, but i'm not sure it would work since unlike olaf, tryndamere has nothing to damage other than basic attacks, so he would be weak at high health. unless his spin would become a usefull damage tool like olaf's reckless swing.
giving some of his spells a bonus AS on activation.
mocking shout or bloodlust would grant tryndamere a bonus AS for a few secconds. maybe giving bloodlust a passive or active life steal would work better than a 200hp heal that significantly decreases your damage output.
mixing proposal 1 with 3
this way he wouldnt suck at full health nor suck after his AS burst was on cooldown. but ofc, the bonus's wouldnt be so strong, this way he would have a nice dps at full health, a nice dps at low health when the spell was on cooldown and a great dps when both were up.
and my final proposal is to entirely remake his kit so this could function well without making him weaker than most or too strong to deal with.
ofc, this is only my point of view. i'm sure many of you will disagree with me, but there is no need to trash the thread.