Gemara

(Mishnah): If one was Me'arev in a cabinet, even if he lost the key, it is valid;

R. Eliezer says, if he does not know where the key is, it is invalid.

Question: Why is it valid? He and his Eruv are in different places!

Answer #1 (Rav and Shmuel): The Mishnah discusses a cabinet of arranged bricks [not cemented together]. The first Tana is like R. Meir, who permits to open it.

35a - Answer #2 (Rabah and Rav Yosef): The Mishnah discusses a wooden cabinet;

The first Tana holds that it is a Keli. Binyan and Stirah do not apply to Kelim. (One may break it open);

R. Eliezer holds that it is an Ohel (tent, so one may not destroy it).

Answer #3 (Abaye and Rava): The case is, the lock is tied with ropes, and a knife is needed to break them. R. Eliezer permits using a Kli only for its intended purpose.

Shabbos 102b (Rav): If one makes a hole in a chicken coop, or drives a peg into the handle of a hoe, he is liable for building;

(Shmuel): He is liable for Makeh b'Patish.

146a (Mishnah): One may break a barrel to eat the dry figs inside, as long as he does not intend to make a Kli.

(Rabah): Mid'Oraisa, one is not liable for a hole unless it is made for entrance and exit;

Chachamim decreed to forbid due to a hole in a chicken coop, which lets in air and lets out heat.

Beitzah 33b (Beraisa - R. Eliezer): If one cut fragrant wood to smell it, he is exempt, but it was forbidden. If he cut it to clean his teeth, he is Chayav Chatas.

Chachamim forbid only due to Shevus.

Question: Does R. Eliezer argue with the Mishnah that permits breaking a barrel?

Answer (Rav Ashi): That refers to shards glued together with sap.

Rishonim

Rambam (Hilchos Shabbos 23:1): If one makes a hole for entrance and exit, e.g. a hole in a chicken coop, which lets in air and lets out heat, he is liable for Makeh b'Patish. Therefore, Chachamim decreed to forbid any hole, even if it is only for exit or only for entrance, lest one make a hole for which one is liable.

Rambam (10:14): If one makes a hole of any size in a chicken coop, to let in air and let out heat, he is liable for Boneh.

Question (Kesef Mishneh 10:14): In Halachah 16, and in Perek 23, the Rambam says that he is liable for Binyan!

Answer (Magen Avraham OC 314:3): In Perek 23 [and Halachah 16], the Rambam discusses a coop [or Kli] that is not attached to the ground. Binyan does not apply. He is liable for Makeh b'Patish.

Rosh (3:5): What was the Gemara's question? One may break a Kli to eat the contents, like the Mishnah in Shabbos! I answer that in Beitzah 33b, we say that the Mishnah discusses shards glued together. Because it is such a poor Kli, he is not concerned for it, and we are not concerned lest he intend to make a Kli. Even though we said only according to R. Eliezer that it is shards glued together, we can say the same according to Rabanan. They do not argue about this. R. Eliezer forbids cutting wood to smell it, for if he cuts it to clean his teeth, he is Chayav Chatas. If Chachamim agreed that one is liable in that case, also they would forbid cutting to smell. Chachamim agree that Binyan applies to Tikun Kli, therefore they agree that one may not break a barrel in order to eat figs, unless it is of shards glued together. Total Binyan and Stirah apply to Kelim, like it says in Shabbos [about driving a peg into a hoe handle].

Ran (Shabbos 61b DH Shover): Rashi (146a DH Shover) permits breaking a barrel, for there is no Isur be Mekalkel. This is wrong. Mekalkel is exempt, but it is forbidden! Rather, since Mekalkel is normally exempt but forbidden, for the need of Shabbos it is permitted l'Chatchilah. This is only for a small Kli, but not for a big Kli, since Binyan and Stirah apply.

Poskim

Shulchan Aruch (OC 314:1): Binyan and Stirah do not apply to Kelim. This is when it is not true Binyan, e.g. a barrel (Rema - that does not hold 40 Sa'im) that broke and one stuck the shards together with sap.

Beis Yosef (DH u'Mah): The Rosh learned from Tosfos (34b DH v'Amai) that if one builds an entire Kli, or does a proper Tikun, this is Binyan. Tosfos brought also the Ran's answer, but did not rely on it, for one who drives a peg into a hoe handle is liable for Binyan, even though it is small. The Ran, who holds like Rashi, could agree that Binyan applies to building a Kli from the beginning, or if a Kli came apart and an expert is needed to reassemble it. This is not called Binyan b'Kelim [which we exempt]. Rather, he makes a Kli, and he is liable for Binyan. The Ran (Shabbos 37a DH u'Makshu, 47a DH Tanu) and Magid Mishneh (Hilchos Shabbos 10:13) say so. Tosfos brought the Yerushalmi, which says that the Mishnah discusses a stone cabinet, but one may break a wooden cabinet, just like one may break a barrel to eat the figs inside. The Yerushalmi holds that we discuss a proper wooden barrel. The Rosh did not rely on this, and the Tur rules like the Rosh.

Taz (1): Shabbos 146a connotes that the Torah Isur of fixing a Kli applies only to a chicken coop.

Gra (DH v'Hani): We learn from Eruvin that Binyan and Stirah apply to Kelim. The Gemara asked why the Eruv is valid, and answered that it is a cabinet of bricks. The Hava Amina was that it is of wood [and one may not break it]. Another answer was that it is tied shut with ropes. However, if there was a solid lock, one may not break it.

Gra (DH v'Divek): Also Chachamim must say that it is shards glued together, like Tosfos proved.

Mishnah Berurah (1): Total Binyan and Stirah apply to Kelim. Therefore, we permit only shards glued together. If it was whole, proper Stirah is forbidden. The Acharonim (Sa'if 9) forbid removing braces around small barrels of jam. This is unlike shards glued together. There, l'Chatchilah we make barrels with braces. It is like a proper Kli. Surely it is permitted through a Nochri. If it is tied with ropes, a Yisrael may cut them.

Kaf ha'Chayim (5): Korban Nesan'el (on Rosh Shabbos 22:5) asked why the Beis Yosef did not bring the Rif and Rambam, who permit breaking even whole Kelim. Also the Rashba, Ran, Ritva, Rashbatz and Rashbash permit. Also Aruch ha'Shulchan and Eliyahu Rabah rule like them. I rule like the Shulchan Aruch, but in pressed circumstances if one is pained that he has nothing to eat, one may rely on the lenient opinions, as long as it does not hold 40 Sa'im and the breaking does not make a Kli.

Shulchan Aruch (ibid.): One may break it to take the contents.

Mishnah Berurah (4): The Pri Megadim permits breaking even not where it is stuck with sap.

Kaf ha'Chayim (6): One may break it by hand, or with a Kli. The Levush permits breaking only where it is stuck with sap, but the Pri Megadim disagrees.

Shulchan Aruch (ibid.): However, he may not intend to make a nice hole for an opening. If he does, this is fixing a Kli.

Mishnah Berurah (5): Likewise, one may not slice off the top with intent that a Kli will remain.

Mishnah Berurah (6): The Taz forbids, mid'Rabanan, even a small hole not for entrance and exit.

Kaf ha'Chayim (10): Regarding what is attached to the ground, one is liable for a hole even if it is not for entrance and exit.

Shulchan Aruch (ibid.): One may not break an intact Kli, even in a way that does not make a Kli. One may not make even a new hole.

Beis Yosef (DH u'Mah she'Chasav Aval): Even breaking it in a way that does not make a Kli is forbidden. If the Kli is intact, and not shards glued together, Binyan and Stirah apply.

Mishnah Berurah (7): Normally, one is liable for Stirah only if it is in order to build. If not, it is Mekalkel! However, it is forbidden mid'Rabanan. The Gra holds that Stirah does not apply even to whole Kelim, unless the Stirah makes it a Kli. Then, he is liable in any case due to Makeh b'Patish.

Bi'ur Halachah (DH Asur): Even though it is Mekalkel, mid'Rabanan it is forbidden. The Magen Avraham and other Acharonim say so. Rashi connotes that Mekalkel is permitted l'Chatchilah for needs of Shabbos, but Tosfos, the Rosh and Ran disagree. This applies also to other Melachos. Perhaps Rashi agrees about other Melachos. Regarding a big cabinet, which is an Ohel, it is clear from Rashi and the conclusion in Eruvin that all forbid breaking it to take the Eruv to eat it, even though it is needed for Shabbos. Even the Poskim who permit breaking a whole Kli to take the food, permit only because Stirah does not apply to Kelim at all, but not due to Mekalkel. The Rambam (1:3,17) forbids Mekalkel in all Melachos. One is lashed mid'Rabanan. Acharonim say that no Shevus is permitted through a Yisrael for the sake of Shabbos. Therefore, surely one may not be lenient about this at all.