<p>This study presents an efficient and accurate method for analyzing the large deflections of spatially twisted and curved Timoshenko beams using a fully intrinsic formulation of the geometrically exact beam theory. The proposed approach avoids displacement and rotation variables, preserves quadratic nonlinearity, and eliminates the shear-locking issues and challenges commonly associated with displacement-based methods. It applies the isogeometric collocation method directly to the intrinsic strong-form governing equations of the geometrically exact beam, accommodating both follower and conservative loads. Numerical benchmarks, including the large deflections of in-plane curved and helical beams under various loading scenarios, demonstrate the method’s accuracy and computational efficiency compared to existing numerical solutions. Furthermore, the results confirm the method’s locking-free performance across various load levels and slenderness ratios. A comparative study with the Euler-Bernoulli beam theory reveals that the thickness ratio alone does not dictate the relative importance of shear effects. Instead, the loading condition and resulting equilibrium configuration determine whether the response remains bending-dominated or develops significant shear contributions. These findings highlight the proposed method’s reliability and flexibility for analyzing large deflections of complex, spatially twisted and curved beam-like structures.</p>