1Used in the pattern 〜はずだ to express the speaker's expectation or logical conviction that something should/ought to/must be the case, based on reason or evidence. Negated as 〜はずがない ('there's no way that...'); used with 〜はずなのに ('even though [it] should be...') or 〜はずだった ('was supposed to be...') when reality contradicts the expectation. One of the standard intermediate Japanese grammar points; today almost always written in kana, rarely with the kanji 筈.
彼女はもう着いているはずだよ。
She should already have arrived.
鍵はここに置いたはずなのに、見当たらない。
I'm sure I put the keys here, but I can't find them.
あの真面目な彼が遅刻するはずがない。
There's no way someone as serious as he is would be late.
本来なら今日が締め切りだったはずだ。
Today was supposed to be the deadline.
この時間なら、お店はまだ開いているはずだ。
At this hour, the shop should still be open.
2The nock of a bow — the part at each end of a bow where the bowstring is attached. A specialized term in kyūdō (Japanese archery); written with the kanji 筈.
弓の両端の筈にしっかりと弦を掛ける。
Fasten the bowstring firmly to the nocks at both ends of the bow.
3The nock of an arrow — the notch at the back end of an arrow that fits onto the bowstring. A kyūdō term; written with the kanji 筈.
矢の筈を弦に当ててから構える。
Set the arrow's nock on the bowstring and then take your stance.
4In sumo, a hand shape formed by spreading the thumb away from the other four fingers, resembling an arrow's nock. Used in the technique 筈押し (hazu-oshi), where the wrestler thrusts this 'nock' against the opponent's armpit or side to push them up.
力士は相手の脇に筈を当て、一気に押し上げた。
The wrestler set his nock-shaped grip against his opponent's side and shoved him up in one motion.
5A wooden frame fitted to the tip of the mast on a traditional Japanese ship to keep the halyard (the rope used to raise the sail) from slipping off. An old nautical term, essentially unused in modern everyday speech.
帆柱の先の筈に綱を通して、帆を支えた。
They threaded the rope through the frame at the masthead to hold up the sail.