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 drives a peg into the handle of a hoe, he is liable for Binyan;

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

122b (Beraisa): One may remove the door of a chest, box or cupboard, but may not return it.

(Rava): The Tana holds that Binyan and Stirah do not apply to Kelim. He decrees to forbid returning, lest one firmly insert it [and be 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.

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

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].

Tosfos (34b DH v'Amai): The Hava Amina was that we discuss a wooden cabinet. What was the question? One may break a Kli to eat the contents, like the Mishnah in Shabbos, for Binyan and Stirah do not apply to Kelim! I answer that we assumed that it is a big Kli, to which Binyan and Stirah apply. If it is a small Kli, why does R. Eliezer disqualify the Eruv? Also, Binyan and Stirah apply to Kelim, like we find in Shabbos 102b. We say that Binyan and Stirah do not apply to Kelim regarding Kelim that one may take [apart] but not return (reassemble them). This is not proper Binyan and Stirah. In the conclusion, we establish the Mishnah to discuss a cabinet tied with a rope. This implies that only this (cutting the rope) is permitted, but not to break and destroy the Kli, for Binyan and Stirah apply to Kelim. This is why in Beitzah, we establish the Mishnah in Shabbos to discuss a barrel of shards glued together with sap. Even though we said so only according to R. Eliezer, we must say so also according to Rabanan. They agree that if one were Chayav Chatas for breaking off a chip to clean his teeth, we would forbid breaking to smell. However, the Yerushalmi holds that it discusses a stone cabinet. If it were wooden, one could break it, like a barrel.

Ran (Shabbos 61b DH Shover): Rashi (146a DH Shover) said that we may break a barrel, for there is no Isur to be Mekalkel. This is wrong. Even though Mekalkel is exempt, 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. The Gemara asked "he and his Eruv are in different places!", for we discuss a big cabinet. In a small chest, there is no Binyan or Stirah. Rashi explained like this in Eruvin (35a DH u'Masnisin).

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. One may break it to take the contents.

Beis Yosef (DH v'Chasuv): Terumas ha'Deshen (65, citing Or Zaru'a) permits breaking a barrel only if it does not hold 40 Sa'im. Such a barrel is a Kli, and Stirah does not apply to Kelim. Perhaps also the Ran calls a Kli big only if it holds 40 Sa'im.

Magen Avraham (1): If it holds 40 Sa'im, it is considered an Ohel (Ran, Rashi, Tosfos). Even if it is not proper Binyan, it is forbidden. Proper Binyan applies even to small Kelim. The Ran argues with Rashi, who permits because it is Mekalkel. Tosfos and the Rosh agree [with the Ran].

Gra (DH Kegon): The Rashba and Ran disagree [with the Shulchan Aruch]. They hold that we established the Mishnah to discuss shards glued together with sap only according to R. Eliezer. Chachamim say that one is exempt [for cutting in order to clean his teeth] but it is forbidden. They permit Mekalkel l'Chatchilah (e.g. breaking a proper barrel). The Sugyos in Beitzah and Eruvin prove this. The Hava Amina was that it is a wooden cabinet, which is an Ohel. This shows that according to the opinion that it is a Kli, one may break it. Rashi explains like this there. Alternatively, the Hava Amina is that it is of stone. Also when we answer that it is tied with a rope, it is an Ohel.

Gra (DH she'Einah): Tosfos' first answer is that Eruvin discusses a big barrel. Also Rashi and the Ran say so. The Rashba proves this from the Sugya. Or Zaru'a and Rashi say that it does not hold 40 Sa'im. All agree about [the Isur to break] an Ohel. This is like Rashi holds (74b DH v'Iy Chaitei), that Binyan and Stirah never apply to Kelim. Rav (102b) holds that Binyan and Stirah apply to Kelim, but we hold like Rava (122b) and Shmuel, who obligate due to Makeh b'Patish. R. Yochanan agrees. Rashi explains that one is liable for a Menorah composed of rings (Shabbos 46a) and a box (Eruvin 102b) due to Makeh b'Patish. Shabbos 78b supports this. (If one blows glass, he is liable for Makeh b'Patish.)

Gra (ibid.): The Mordechai asked a contradiction in Rav, for Rav permits burning Kelim [on Yom Tov, even though this destroys them]! He answered that Gerama (mere causation) is permitted. In Eruvin, we assumed that the cabinet is of stone, like Tosfos brought from the Yerushalmi. The Yerushalmi supports Rashi. Rashi explains that we conclude that a big cabinet is tied with ropes. Beitzah 33b proves that Binyan and Stirah do not apply to Kelim. In the Hava Amina that we discuss a proper barrel, we asked [that R. Eliezer should forbid breaking it] due to a decree, but not due to Stirah! The Gemara (146a) says that one may not intend, due to Makeh b'Patish.

Mishnah Berurah (2): If it holds 40 Sa'im, it is an Ohel, and Binyan and Stirah apply, even to any amount.

Bi'ur Halachah (DH she'Einah): If it holds 40 Sa'im, even a flimsy barrel is forbidden. Eliyahu Rabah brings that the Rashba disagrees. One may be lenient to tell a Nochri to break it, for in any case the Isur is only mid'Rabanan, for he is Mekalkel.

Kaf ha'Chayim (2): The opinion that permits shards glued together permits even if it is big. The opinion that permits a small Kli permits even if it is intact. If so, the Shulchan Aruch permits even a big barrel. Even so, the Rema is stringent to require both (small, and shards glued together). The Pri Chodosh says so. Olas Shabbos says that since this matter is mid'Rabanan, one need not be so stringent.

Kaf ha'Chayim (3): It need not be one [Amah] by one by three, as long as it holds 40 Sa'im. However, the roof must be at least a Tefach. If not, it is not an Ohel.