We study the electronic properties of rippled freestanding graphene membranes under central load from a sharp tip. To that end, we develop a gauge field theory on a honeycomb lattice valid beyond the continuum theory. Based on the proper phase conjugation of the tight-binding pseudospin Hamiltonian, we develop a method to determine conditions under which continuum elasticity can be used to extract gauge fields from strain. Along the way, we resolve a recent controversy on the theory of strain engineering in graphene: There are no $K$-point-dependent gauge fields. We combine this lattice gauge field theory with atomistic calculations and find that for moderate load, the rippled graphene membranes conform to the extruding tip without a significant increase in elastic energy. Mechanical strain is created on a membrane only after a certain amount of load is exerted. In addition, we find that the deformation potential---even when partially screened---induces qualitative changes on the electronic spectra, with Landau levels giving way to equally spaced peaks.