If there is a patch of invalid sekhakh, made of plastic, for example, in the middle of kosher sekhakh, or if there is a concrete beam that invalidates the sekhakh underneath it, then if the invalid sekhakh is wider than 4 tefaḥim (c. 30 cm), one may not sit underneath it. If the invalid sekhakh is less than 4 tefaḥim but more than 3 (c. 22 cm), le-khatḥila one should not sit or sleep underneath it, but in a time of need one may do so (MB 632:3). If the invalid sekhakh is less than 3 tefaḥim wide, one may eat or sleep there even le-khatḥila, because it is rendered null vis-à-vis the sukka.
If there is an empty gap in the sekhakh, the laws pertaining to it are more stringent, since this is more discernible than invalid sekhakh. If the width of the gap is 3 tefaḥim (c. 22 cm), the area beneath it is not kosher, and one may not sit there. If it is less than 3 tefaḥim, it is rendered null vis-à-vis the sukka, and one may sit and sleep there (SA 632:2) as long as neither most of his head nor most of his body are underneath the gap.[16]
Let us say that one has a large porch, most of which is roofed, but with a small area, 5 tefaḥim wide, under open sky. At first glance, it would seem that there is no way to build a sukka there, as a kosher sukka must be at least 7 tefaḥim wide. However, we have seen that invalid sekhakh that is less than 3 tefaḥim wide is considered part of the sukka, and a person may sit underneath it. A sukka can therefore be built on such a porch, as follows: A sukka 7 tefaḥim wide should be set up at the end of the porch. Since 5 tefaḥim of sekhakh are under open sky and less than 3 tefaḥim are under the roof and invalid, then even those 2 tefaḥim are deemed part of the sukka, and one may sit and sleep beneath them. This is on condition that he puts up a wall separating the 2 tefaḥim of the roofed porch that will be part of the sukka from the rest of the porch that will not. This wall must be 7 tefaḥim long and preferably should reach the sekhakh. One should make a tzurat ha-petaḥ along the rest of the border between the sukka and the porch. (See Ḥazon Ovadia, p. 12; Minḥat Yitzḥak 6:60:20; Shevet Ha-Levi 10:99.)
If a gap of 3 or 4 tefaḥim of invalid sekhakh extends across the sukka, effectively dividing it into two sukkas, one must make sure that each sukka has the requisite three walls (Rema 632:2).
Four tefaḥim of invalid sekhakh invalidates a large sukka, but if a sukka is less than 10 tefaḥim wide, even 3 tefaḥim of invalid sekhakh invalidates it. Less than 3 tefaḥim does not invalidate it (SA 632:1; MB ad loc. 8).
