If a doorknob fell from a door, is it permissible on Shabbat to affix the knob back on the door so that the door can be opened, at least from that side?
At first glance, replacing a doorknob on Shabbat – even without screws – would transgress the prohibition of "Boneh" (building). The Sages forbade building a structure even without screws out of concern that one might then screw the parts in place on Shabbat, which would violate a Torah prohibition. Seemingly, then, we should forbid replacing a doorknob even without screws.
Rabbi Moshe Halevi, in his work "Menuchat Ahava," rules that one may attach one side of a doorknob onto the door without screws if the knob had fallen from the door before Shabbat, and one had used the door without the doorknob. He contends that since the door had been used without its knob on Shabbat, one has thereby demonstrated that he does not require the knob for opening and closing the door. And since he attaches the doorknob to only one side of the door – a clear deviation from the standard manner of affixing doorknobs – he will be reminded not to attach the knob in its usual fashion, with screws.
However, if the doorknob fell on Shabbat, it would be forbidden to return the knob to the door on Shabbat, even without screws and even on only one side of the door. Of course, screwing a doorknob to a door – even on one side – is forbidden on Shabbat.
Summary: If a doorknob had fallen from a door before Shabbat, and the door had been used in that fashion, without its knob, one may attach the knob to the door on one side on Shabbat, without screws. If the knob fell from the door on Shabbat, this would be forbidden. Under all circumstances, one may not screw a doorknob onto a door on Shabbat, even on one side, or attach a knob to both sides of a door, even without screws.