Playing top as a beefy melee champ I tend to have extremely difficult games when they send anyone with good range at me. I either have to stand back and get no cs, or go in and take pot shots from them. My damage is not bursty enough at that level to really force caution on their part.

How can I handle these situations with success.

Frankly, it depends on which melee and which range characters are chosen. But for the most part, you're pretty screwed if you are 1 v 1 ing them. So, my advice to you would be to stay with your turret, or stay with your team. In most cases, your teammates (who are also range) should fight a range character.

melees who have good gap closers usually poop on squishy ranged champs. like panth or xin.

Their damage isn't really bursty either and you do out-trade them once you're actually in range to trade.

It all depends on what champions are involved. Yes, some are simply hard counters to certain melee champions (teemo v singed). Which champion are you usually playing? If we know that we could offer a bit better advice.

The two I usually use are jax and shen. Shen I have a lot more success with being able to pop shield and block while I hit with my dagger throw. But even then if they get an extra shot or two off i lose the exchange.

Jax is much harder even with his jump, because even to get in range to do that, they will get a shot off and run.

I prefer to play mid or bot, but if the team has no one that can top and take a punch, I'll play top for better team chemistry.

For jax, the key is his w ability. The nice thing about it is that it resets his attack animation so if you jump on someone and immediately hit w and attack again, you'll get off a second attack before they can retreat. It won't kill them, but you will definitely win trades by a lot. Play it aggressive and you can force them off the cs.

It isn't too hard to win trades with Shen. Utilizing brush for your poke is a good idea. Sometimes, depending on the skill of the enemy champion (and the champion in question), I will dash in with E and pop my shield or hit them with my Q. It is enough early on to hurt them quite a bit and force them back for a while so you can farm safer.

I do not do this against a Teemo, however, as he can just Blind you, then kite the hell out of you. If you are matched up against Teemo, or any ranged champion you have trouble with, I suggest asking for ganks from Mid or (if you have one) Jungle.

Thanks, ill give that advice a shot next time.

Basically, don't get counterpicked. Someone with ranged is designed to counterpick a champ that has no way to deal with ranged. If you had a gapcloser you could dash in on them whenever they tried to poke you down, but without one they're just going to kill you.

In general:

Melees with gapclosers/dashes/pulls > ranged/poke-heavy champs.
Melees without gapclosers/dashes/pulls > melees with gapclosers/dashes/pulls
Ranged/poke-heavy champs > melees without gapclosers/dashes/pulls

Mobile melees tend to have enough burst to zone squishy ranged champs. Immobile melees tend to have strong burst and high sustained damage to compensate for their lack of mobility, and so can counter-engage when mobile melees go in on them. Ranged champs can safely harass immobile melees without giving them much chance to respond.

There are several exceptions (Yorick is ranged/poke heavy but just beats everyone anyways, while Renekton is just so mobile and deals so little damage he's more like a ranged champ than a melee with a gapcloser), but that's the general rule.

The fact that you're losing to ranged champs as Jax and Shen either means you're getting outplayed badly and don't know how to use your champion nearly as well as your opponent or their range is so insanely long that it beats Jax and Shen (which is fairly uncommon).

Sorry to sound callous or rude but that's just the way it is. Even though they have a range advantage you can mitigate it by dashing in on them. Only people likely to still beat you if you go in on them are the manaless mages you see go top a lot, like Vladimir or Kennen. The trick is, you can usually win the lane if you play aggressively fairly early against mages before they get their burst damage going. If you let them hit 6 too easily you'll be at a disadvantage the rest of the laning phase.