<p>In this study, an accurate, efficient, and eccentrically loaded beam-column element was proposed based on the co-rotating coordinate method and the stability function. The ultimate load was determined using the nonlinear finite element method. Failure tests were conducted on eccentrically loaded columns and hingeless arches under eccentrically applied loads. The test results indicated that the eccentrically loaded beam-column element proposed in this paper could accurately capture the second-order buckling effects of eccentrically loaded members under loading. The calculated load-displacement curves showed significantly better agreement with the experimentally measured values than those obtained using conventional beam-column elements. For the eccentrically loaded column tests, the relative error between the ultimate load capacity that was calculated using the eccentrically loaded beam-column element and the experimental results was controlled within 3%. The calculation error for the conventional beam-column element reached as high as 21.8%. The stiffness of the eccentric beam-column element was slightly lower than that of a standard beam-column element. When considering eccentricity, the ultimate load-bearing capacity of the beam-column element was further reduced, which rendered it more susceptible to buckling failure. For the failure tests on eccentrically compressed arches, the prediction error of the ultimate load also met the accuracy requirements for engineering analysis. During the elastic stage, the stiffness of the front half of the arch exhibited “stiff spring” behavior. However, once the arch ribs reached their ultimate load-bearing capacity, their “stiff spring“ behavior abruptly transitioned to “soft spring“ behavior.</p>