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Is there a general structure for using tener in certain constructions in place of estar or ser?
For example:
Ser. For ' am 11 years old' we say:
Yo tengo once años
not
Yo soy once años
Estar. For 'I am interested in this house' we say:
Tengo interés en esta casa
not
Yo estoy interés en esta casa
As shown by the comment and the answer above, I think we can define a rule for the alternate use of "estar" and "tener" when predicating a state about the subject:
"tener" will be used with an abstract noun as direct object or as the magnitude (whether implicitly or explicitly stated) to which a certain measurement or dimension refers.
"estar" will be used with adjectives.
We thus have, apart from the examples with "interés" (noun) and "interesado" (adjective) above, the following:
Estoy hambriento. (adjective)
Tengo hambre. (noun)
Estoy confiado. (adjective)
Tengo confianza. (noun)
Estoy cansado/somnoliento. (adjectives)
Tengo cansancio/sueño. (nouns)
Whenever magnitudes, such as age, height, weight, width, depth, etc., are involved, we can use the verb "tener" or a more specific verb peculiar to the magnitude involved:
Notice that "estar" and even "ser" will appear whenever there are adjectives in the vicinity.
BUT
El niño tiene cinco años (de edad) más que su hermana.
La niña está 10 Kg. más pesada de lo que correspondería.
BUT
Note: This pattern where "idiomatic tener" is followed by a noun may not appear in grammar books for native speakers, who take it for granted, but is provided as a rule in books for speakers of other languages, as shown below:
In Spanish, "ser" and "estar" will appear with adjectives (or prepositional phrases) respectively denoting permanent or temporary states:
There is, to my knowledge, no general rule for predicting whether tener is appropriate in a given case to replace ser/ester, but rather the usage is idiomatic. There are many examples of this, though using tener ____ años is one which students learn very early when learning Spanish.
If you consider the literal translation of tengo once años, you're actually saying I have 11 years, it makes sense, even in English, though we don't usually say it in this way.
Many other phrases in Spanish take this form, using tener in place of what we (as English speakers), would expect to take ser/estar.
To give a few examples:
tener hambre, literally, to have hunger tener confianza, literally, to have confidence. Although the answers given so far are correct and useful, I think, as pointed out in one of the comments, this is just starting from a wrong premise. Tener, ser and estar are three very different verbs, the last two much more semantically close to each other, but in the end each one having an awful lot of meanings and usages. These have to be learned as part of the logic of Spanish, not as translations from their supposed English equivalents.
Phrases employing tener that cannot be translated literally to English include tener hambre, tener sueño, tener [x] años. These are idiomatical, but note that for conditions like hunger or sleepiness the alternative with estar + adjective is also valid, as in English: estar hambriento, estar somnoliento, only rarer in actual use. It's much more common to find the structure estar con + noun: estar con hambre, estar con sueño. This has no parallel in English, but in fact phrases meaning "being with" or "being next to" something/someone are understood as possessives in many languages.
In Spanish you can also say, in the same vein, estar con problemas "to have problems", estar con muchas cosas para hacer "to have a lot of things to do".
It is perhaps worth pointing out for the benefit of other learners that the position is even more complicated than the OP suggested as sometimes hacer is used to translate "is". This is true for statements about the weather like Hace frio for the English "It is cold". The moral of the story is, as others suggested in answers and comments, that idioms just have to be accepted as they are without attempt to translate them.
The thing about 'tener' is that it not only displays the meaning of 'to have' but has a much wider range of uses and meanings than the word 'have' in English.
tener frío (to be cold) Olvidé mi suéter y ahora tengo mucho frío. (I forgot my sweater, and now I am very cold.)
tener calor (to be hot) Los chicos están sudando. Seguramente tienen mucho calor. (The boys are sweating. They must be very hot.)
tener hambre (to be hungry) ¡Mira los perritos! Tienen hambre. No han comido nada. (Look at the dogs! They are hungry. They have not eaten anything.)
tener sed (to be thirsty) No he tomado agua todo el día. ¡Tengo mucha sed! (I haven’t drank water the whole day. I’m so thirsty!)
tener tos (to have a cough) Esteban está enfermo. Tiene tos. (Esteban is sick. He has a cough.)
This post has heaps of examples of uses of 'tener' when it would normally not be used in English:.https://www.clozemaster.com/blog/spanish-tener-expressions/
