to support / lean
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to support
To physically hold something or someone so that it does not fall over, sink, or collapse.
Die Decke des alten Kellers muss mit zusätzlichen Balken gestützt werden.
The ceiling of the old cellar has to be supported with additional beams.
to be based on
To base an argument, theory, or decision on something, such as facts, data, or statements.
Die Studie stützt sich auf Daten aus den letzten zwanzig Jahren.
The study is based on data from the last twenty years.
to support
To support a person, an idea, a party, or a measure, often through financial or moral help.
Viele Bürger stützen die Initiative für mehr Grünflächen in der Stadt.
Many citizens support the initiative for more green spaces in the city.
to lean
To place one's body weight with the hands, arms, or elbows on a surface in order to find support or rest.
Erschöpft stützte er die Ellenbogen auf die Knie.
Exhausted, he leaned his elbows on his knees.
The verb 'stützen' (to support) is closely related to the noun 'die Stütze' (support). A 'Stütze' is an object that physically holds something, which explains the basic meaning of the verb.
Der Architekt plant eine zusätzliche Stütze für das Dach.
The architect is planning an additional support for the roof.
The reflexive phrase 'sich stützen auf' (to be based on) is always used with the accusative. You base an argument on a foundation.
Der Anwalt stützte seine Verteidigung auf einen Formfehler im Verfahren.
The lawyer based his defense on a procedural error in the trial.
In the meaning of 'basieren auf' (to be based on), 'sich stützen auf' is often combined with words from the area of knowledge and information: 'sich auf Fakten stützen' (to be based on facts), 'sich auf Daten stützen' (to be based on data), 'sich auf eine Studie stützen' (to be based on a study).
Meine Annahme stützt sich auf die neuesten wissenschaftlichen Erkenntnisse.
My assumption is based on the latest scientific findings.
When 'sich stützen' describes body posture, it is used reflexively. It is often followed by a preposition such as 'auf' or 'mit' to describe what you lean on or what you use for support.
Müde stützte sie ihren Kopf in die Hände.
Tired, she rested her head in her hands.
The meaning of 'stützen' depends strongly on the object. If you support a wall, it is physical. If you support a plan, it is moral or ideological. If you base something on facts, it is argumentative.
Wir müssen die alte Wand mit Brettern stützen.
We have to support the old wall with boards.
to wear / carry
With a structural component, either verb may fit. Tragen emphasizes that it takes the weight of a load. Stützen emphasizes instead that it keeps something stable, thereby preventing it from sinking or collapsing.
Zusätzliche Balken stützen das beschädigte Dach, damit es nicht absinkt.
Additional beams support the damaged roof so that it does not sink.
Die Säulen tragen das Gewicht des Daches.
The columns support the weight of the roof.
