Basal fiber is about 3GPa tensile, call it a MoS of 6 for a neat 500MPa working strength.
If you plug int wolfram alpha `1 atmosphere * 1 square meter / 500 MPa` you get 2 cm^2 of support (tethering) per sq m of roof. That's reasonable.
But here's the rub: compressive strength lags tensile strength. Even granite is a mere 130 MPa. So even a strut which has some compression resiliance is not gonna be enough to fully abate a collapse. So it's very likely a Martian structure would have some arc to it, as it both benefits tension under nominal operation and some compression in failure mode, at least long enough to keep pressure from dropping too low.
I imagine rip-stop at all sorts of scales will be implemented. It's not gonna be like an inflatable golf dome.
https://www.engineeringtoolbox.com/compression-tension-stren...
In other words, your lip needs to be distributing force onto a sufficient volume of ground to make up 100_000 metric tons of martian soil, per meter of circumference.