I'd rule the above example in the following way (and it's a bit D&D inspired, but I think it is more to how it works in reality)
the AT 13 and the shirt are both "enchanted armor DB bonus" and if worn together they both provide +10 armor DB so it doesn't stack. In my own games I'd allow like "construction armor DB bonus" to stack with other types, such "enchanted armor DB bonus" but I wouldn't be handing out any AT 20 +20(Constuction) suits ever, so they can't be enchanted on top of that (I actually have some more rules in place about this, but I won't discuss them here)
As for the belt and the ring: IF they are both "Enchanted forcefield DB bonus" then they wouldn't stack, but if the belt was "Enchanted Dodging DB bonus" then they would. Of course it doesn't really matter with such items how they are constructed, or from what kind of material they are made so such bonus aren't part of the equation.
In my house rules you have several types of bonuses available on the available magic items:
Armor (pieces)
Armor material DB
Armor construction DB
Armor magical DB
Armor Dodge DB
Armor forcefield AT
Armor forcefield DB
Weapon
Weapon material OB
Weapon construction OB
Weapon magical guidance OB (is the standard type)
Weapon magical hardness OB (is rare type: "strikes as Mithril will add a certain amount of OB and hit large creatures on Mithril table)
Shield
Shield material DB
Shield material OB
Shield construction DB
Shield construction OB
Shield magical DB
Shield magical guidance OB
Other (ring, belt, head band, glove)
Other item Guidance OB
Other item Dodge DB
Other item Force field DB
Other item force field AT
Notes
Each of the item classes above, apart from other items, is supposed to apply to one statistic of a user: so wielding 2 magical swords doesn't add both the OB's to TWC, just each bonus to each separate attack. One shield adds to DB, unless it is used to attack with, only one armor can be worn, etc.
Other items, on the other hand, when ones owns more than one, would be allowed to stack on a single skill, if the bonus types are different, and when the body locations are different. So a ring of Dodge DB +10, a nose ring of Force field DB +10, an ear ring of Force field AT 16, a high steel (+10 mat) dwarven made (+7 con) chain shirt of (+17 nm tot), yields an of AT 16 and +37 DB.
It should be noted that the bonuses with different names keep stacking when on the same item. These bonuses, unless the PC's have excellent resources, will remain in check, such as the Construction bonus will not go beyond +5 when made by normal humans, +7 for dwarves and +9 for High elves.
The cases where items are worn/ used with the same type of bonus: the highest applies. Example: Armor AT 10 protects as AT 12 and a head band of AT 4: no stacking of the AT's, just the best one applies.
The magical bonusses, added by Alchemists are +5, and never more (unless you are casting lvl 50+ spells) so a lvl 20 alchemist wanting to make a +20 item, must have +15 non magical item on hand to do so. Such an item cannot be made from a magical material, such as mithril and better, since they are already considered enchanted.
Shields are not considered armor and they enhance a different type of defense (more like cover) so the shield bonuses and the armor bonuses stack with eachother. The OB bonuses come into play only when the shield is used to attack with.
Reasoning in this way implies that a maximally enhanced item, without resorting to mithril and better, is a Katana (+5) made from White alloy (+20), Elvish construction (+9) enchanted by a lvl 50 Alchemist (+5) as a +39 weapon (+34 with the Armory). This is almost impossible to make as you need to make weapon smithing skill check against: katana (very hard -20), +9 construction (-180), white alloy (-20) = -220. The -180 is derived from my crafting house rules where for every 20 you beat 101 (success) roll you get +1 construction bonus, capped for humans at +5, dwarves at +7 and High elves at +9. This ensures that usually such an item cannot be in the hands of a low lvl character.
Although this seems rather generous to the average GM, but I'm really not handing out any of this in great quantities. Only when a party decides to pool all their items on a single character will they get anywhere these results that I mentioned. I keep it in check by just handing out items with normal bonuses, but I break them down to the players in more interesting ways. So a +10 magical sword might become a human excellently wrought (+2 con), Low ferrous steel (+3 mat), +5 magical broad sword.
Game on!