Tragen vs. stützen
While both stützen and tragen can translate to to support by holding weight, they are not interchangeable. Tragen describes the general, fundamental act of bearing a load, whereas stützen implies providing targeted support to prevent something unstable from falling or collapsing.
Tragen
A1The verb tragen refers to the fundamental and often passive act of bearing or holding the entire weight of something. It describes a stable situation where one object is designed or inherently able to hold the load of another.
Die Säulen tragen das gesamte Dach des Gebäudes.
(The columns support the entire roof of the building.)
Diese alte Brücke kann keine schweren Lastwagen mehr tragen.
(This old bridge can no longer support heavy trucks.)
Die Grundmauern müssen das Gewicht von drei Stockwerken tragen.
(The foundation walls must support the weight of three floors.)
Prüfe, ob das Eis dein Gewicht tragen wird, bevor du darauf gehst.
(Check if the ice will support your weight before you walk on it.)
Ein Ast muss stark genug sein, um eine Schaukel zu tragen.
(A branch must be strong enough to support a swing.)
Stützen
B1The verb stützen means to prop up, to brace, or to shore up. It is used when providing active or additional support to something that is weak, unstable, or at risk of falling over or collapsing.
Wir mussten die einsturzgefährdete Wand mit Holzbalken stützen.
(We had to support the unstable wall with wooden beams.)
Nach seiner Knieoperation musste er sich auf Krücken stützen.
(After his knee surgery, he had to support himself on crutches.)
Sie stützte ihren schweren Kopf in die Hände und seufzte.
(She supported her heavy head in her hands and sighed.)
Ein Gärtner muss den jungen Baum mit einem Pfahl stützen, damit er gerade wächst.
(A gardener has to support the young tree with a stake so that it grows straight.)
Er lehnte sich an die Theke und stützte die Ellbogen auf.
(He leaned against the counter and supported his elbows on it.)
Summary
In short, use tragen for the primary, fundamental support that bears an entire load, like a foundation that trägt a house. Use stützen for the act of propping up something unstable or weak to prevent it from falling, like using a beam to stützen a sagging ceiling. If something trägt a load, it's performing its main function; if it needs to be gestützt, it requires help.