Do photocopied sheets (such as chumash or gemara) need to be put in sheimos or can they be thrown straight into the garbage?
I have heard Rav Dovid Feinstien shlita quoted as saying (disclaimer: this wasn't heard straight from Rav Feinstein so it may be inaccurate) that photocopies can be thrown into the regular garbage as long as it is first wrapped in its own clean bag. The reason is because photocopies are not made to be permanent and are made to be used once or twice and then disposed of. If they were to be put together in a booklet and bound or stapled, they would need to be put into shaimos because by binding or stapling it, your intention is for it to be kept long-term.
Some sources here:
The Gemara (Makkos 22a) writes that one who destroys one of the Sheimos, names of Hashem, has transgressed the negative commandment of You shall not do this to Hashem your God. (Devarim 12:4)
Rambam takes this a step further and writes (Yesoidey Hatorah 6:5) that one must never burn or destroy Torah writings (except for those written by a heretic, etc.) The Netziv (Meshiv Davar 2:80) limits this prohibition to materials that were written to last. Thus, one would be allowed to dispose of one’s rough notes. Based on this, R’ Yitzchok Yaakov Weiss (Minchas Yitzchak 1:17) permits disposing of newspapers that contain Divrei Torah. R’ Shmuel Wosner (Shevet Halevi 5:162) however, writes that they require burial.
R’ Moshe Feinstein (OC 4:39) writes that often too much is printed, especially in school settings, which just compounds the problem. He writes that if the Gedolim in Eretz Yisrael would agree with him (they didn't..) he would have allowed one to even dispose of a worn Gemara, providing it didn’t contain Sheimos. Once a Sefer becomes unusable, it loses its Kedusha somewhat.
There is much debate about placing such papers in recycling. R’ Moshe Sternbuch (Teshuvos Vehanhagos 1:55) maintains that the ideal solution is to put them in a plastic bag before disposing of them. This way, one is treating them respectfully.