The image is a diagram of a spherical-segment membrane-type pressure dome structure, such as might be used on Mars to pressurize acreage for agriculture in a future colony.
The membrane is a uniform tensile stress tension-field structure, tied to a retention ring buried below grade in the surface. The "blowout load" on ring diameter is balanced by the weight of the ring structure, which is in compression in bulk, but locally tension where the membrane ties to it. The tension stress in the membrane is proportional to the spherical radius, and to the net pressure differential across the membrane.
The membrane itself ought not to be a single layer. The material needs to let some visible and some UV light through for photosynthesis, but must be proof against UV damage over time. (This pretty much rules out all known polymers.) Access to that layer actually holding the gas pressure must be unimpeded from below, in order to repair meteroid punctures, which will occur. That's a basic safety thing.
The retention ring would be reinforced concrete if it were built on Earth. Concrete as we know it won't set in the cold on Mars, so I suggest "icecrete". That's a composite of water ice as the matrix, sand, and rounded-by-tumbling rocks as the aggregate, and steel (or other comparably stiff) reinforcing bar. You mix the aggregate up with liquid water, pour into forms containing the reinforcement bars, and let it freeze. It either must be coated or buried to prevent sublimation of the ice.
One should note that the weight per unit circumference of the retention ring scales with diameter of the ring (and its cross section area), whereas the "blowout" load scales as ring diameter squared. For any given collection of materials, there will be a maximum size that can be practically built. This is because the increases in the retention ring cross section area cannot make up the discrepancy between the ring diameter and ring diameter squared factors.
One should also note that the shear stirrups in the ring "beam" are also the tensile connections between the membrane and the circumferential reinforcing bars inside the ring. Those stirrups ought to "loop" at least some of those circumferential bars, as shown in the image. I do not know the details of connecting these stirrups to the membrane, but I do think there ought to be a lot of these stirrups (i.e., the spacing is very close).
I do not have any actual design numbers available. But these are the fundamental structural and safety design criteria.
Have fun .....
UPDATE 1-26-13: See also "Aboveground Mars Houses" dated 1-26-13 for a pressurized building concept that is much closer to an in-hand, practical technology.