Making a permanent roof is the melacha of Boneh. Making a tent is a toldah of Boneh and taking it down is Sosair. Chazal decreed against making a **temporary** roof and dismantling it. (MB 1)
Spreading a sheet upon four vertical poles to protect against the elements is therefore forbidden – even for a short time. (MB 2)
A mechitza hamatterres is forbidden. Since it facilitates a halacha, it is chashuv like Boneh. For example: setting up a third mechitza for a sukka or a third mechitza to create a reshus hayochid to carry into. (ShA 1 – MB 4)
Setting up vertical partitions just for privacy is permitted. For example: making a mechitza to separate men and women during a derasha. (ShA 1 – MB 5)
Hanging a curtain to block an entrance or for an Aron Kodesh is allowed. Similarly, you may make a vertical partition to block the sun or a cold draft. (Rama 1)
However, to hang a cloth partition and attach it all around, making it immovable, could be ossur d’oraisa if you intend to leave it there for a few days – it's called “Mosif al Ohel Kavua.” Even so, you may hang and tie down a decorative wall hanging – it is not called a mechitza. (MB 6, 7 – ShaH 6)
Another case of mechitza hamatterres **:** It is ossur to make a mechitza in front of a ner or in front of sefarim in order to allow tashmish hamitta. Covering the ner (sefarim require a double covering) for tashmish hamitta is allowed. The Magen Avraham allows even to use a mechitza as a cover. One may rely upon this b’shaas hadchak. (Rama 1 – MB 10)
A mechitza hamatterres that is already blocking one tefach may be added on to or extended. This is allowed whether the tefach exists already from the side (i.e. 10 tefachim high x 1 tefach wide) or hanging from the top (i.e. and is then extended to the floor). (Rama 1 – BeH “she’hoya”)
A folding door that is folded all the way back might be many tefachim thick. Nevertheless it is not considered blocking even one tefach since it is not meant as a partition in that folded state. (MB 11)
“Mosif al Ohel Arai” is allowed. So if the roof is already unrolled by one tefach, you may add to the roof or extend it. Even if only the existing roof frame is a tefach wide, it counts – and you may spread the tent upon the frame. (ShA 2)
Baby cribs sometimes are fitted with a frame on top to spread over a protective covering. There might not be a tefach width to each single section of the frame, but if just two of them are within 3 tefachim of one another (less than 24 cm) they combine with the din of lavud to be more than a tefach to start with – now you may spread the covering over the frame. (MB 12)
When the roof is rolled up, the roll itself might cover a tefach of space underneath. The width of this roll does not count since it is not meant as a roof. Nevertheless, it is ossur to use rolled-up covers as a temporary roof on Shabbos (i.e. to put rolled-up mats next to each other upon an overhead frame for shade). (ShA 2 – MB 16)
“Ohel arai” is when you intend to use the space underneath. Even when you don’t want the space underneath, it is still “ohel arai” if you also erect vertical partitions under the “roof”. You must first hold the horizontal roof part in the air and then erect the “walls”. This, being out of order, will not appear as Boneh ohel. (ShA 3 – MB 17 – see below MB 48)
You are not allowed to close the flue of a chimney if there are coals below that will be choked out. It’s a psik raysha (so you can instruct a non-Jew to close it). (MB 20)
Another hetter for ohel arai is when everything is already attached, and you merely spread it out. Examples: opening a camping chair (made of material folded on a frame) – stretching a chuppa already attached to the poles. (MB 27 – ShaH 34)
You may put one sefer on one side, another on the other side, and a third one on top – because you do not need the space beneath. (ShA 7)
The Chayay Odom allows putting sefarim under the one you are learning from, to lift it to a comfortable height. It is not considered disrespectful for the bottom sefarim. (MB 30)
Ohel arai is forbidden even if the ohel is slanted, unless the material is fitted with drawstrings or is already set up and ready to be pulled across a horizontal rod. In these cases, the slanted ohel does not need to be open even a tefach before Shabbos. (ShA 8, 10, 11 – MB 37, 41)
You aren’t allowed to open an umbrella or parasol on Shabbos. (BeH “tefach”)
You aren’t allowed to spread a cover (even one that is made specially to fit) over the entire opening of a large barrel. This applies if there will be at least a tefach space above the contents of the barrel. Even though you don’t need the space below, and the “walls” of the barrel are in place already, when you cover something very wide it is still like making an ohel. Likewise, it is ossur to cover a wide-open chest unless the lid is attached with hinges. (ShA 13 – MB 48 – BeH “begged”)
Even if the open chest is not so wide, but you moved the chest on Shabbos to a desired place, thus erecting “walls”, you aren’t allowed to put on the lid. Another application of this is if you want to set up a large table board on top of empty barrels – do not put the open barrels in place, right-side-up. Doing so will be making an ohel over the barrel-space when you then put the table board on top. So, instead, place the barrels upside-down. (MB 48)
The Chayay Odom says not to slide in a drawer that hangs under a table (e.g. cutlery drawer) if the drawer has been removed and has the depth of a tefach or more. (MB 48)
If you witness a Jew covering a vessel in the above mentioned forbidden cases, you shouldn’t protest. He is relying on the lenient opinions who allow it. (MB 49)