An analytic formula of the second-order equilibrium beta limit for DRAKONs with triangular connectors of rectilinear elements (CRELs) with arbitrary pressure profile is derived. Its predictions for a parabolic pressure profile are compared with the full third-order numerical results, leading to a semi-analytic formula. The beta limits obtained here are much lower than those obtained previously; for example, for a DRAKON with straight sections and CRELs equal in length and with triangular CRELs of aspect ratio 2, the peak beta limit is 2.2%, compared to the previous result of 12%. Pressure profiles with sharper boundaries have lower beta limits. The equilibrium is governed by the predominant quadrupole Pfirsch-Schlüter current. Small deviations from the CREL condition have almost no effects on the equilibrium and thus the beta limit. Optimal triangular CRELs are found. They give beta limits slightly higher than those for the standard triangular CREL. Other possible ways of raising the beta limit are also discussed.