Non-prismatic beams are widely employed in several engineering fields, e.g., wind turbines, rotor blades, aircraft wings, and arched bridges. While analytical solutions for variable cross-section beams are desirable, a model describing all stress components for beams with general variation of their cross-section under generalised loading remains an open and important problem to solve. To partly address this issue, we propose an analytical solution for stress recovery of untwisted, asymmetric, non-prismatic beams with smooth and continuous taper shape under general loading, considering plane stress conditions for isotropic materials undergoing small strains. The methodology follows Jourawski’s formulation, including the effect of asymmetric variable cross-section, with internal forces as known variables. We confirm the non-triviality of the stress field of non-prismatic beams, i.e., the dependency on all internal forces and beam geometry to shear and transverse stress distributions. As a particular novelty, the new formulation for transverse direct stress includes internal forces derivatives, resulting in greater accuracy than state-of-the-art models for distributed loading conditions. Also, closed-form solutions are introduced for non-prismatic and linearly tapered, generally asymmetric beams, both with rectangular cross-sections. For validation purposes, we consider three different practical beam models: a symmetric and an asymmetric, both linearly tapered, and an arched beam. The results, checked against commercial finite element analysis, show that the proposed model predicts the stress-field of non-prismatic beams under distributed loads with good levels of accuracy. Traction-free boundary condition requirements are naturally satisfied on the beam surfaces.

非棱柱形梁广泛应用于多个工程领域，例如风力涡轮机、转子叶片、飞机机翼和拱桥。虽然可变截面梁的解析解是可取的，但描述梁的所有应力分量的模型在广义载荷下其截面的一般变化仍然是一个需要解决的开放且重要的问题。为了部分解决这个问题，考虑到承受小应变的各向同性材料的平面应力条件，我们提出了一种在一般载荷下具有光滑和连续锥形的无扭曲、不对称、非棱柱形梁的应力恢复解析解。该方法遵循 Jourawski 的公式，包括非对称可变截面的影响，内力作为已知变量。我们确认了非棱柱梁应力场的非平凡性，即所有内力和梁几何形状对剪切和横向应力分布的依赖。作为一个特别的新颖之处，横向直接应力的新公式包括内力导数，从而比分布式加载条件的最先进模型具有更高的精度。此外，还为非棱柱形和线性锥形、通常不对称的梁引入了封闭形式的解决方案，两者都具有矩形横截面。出于验证目的，我们考虑了三种不同的实际梁模型：对称和不对称（均为线性锥形）和拱形梁。结果，对照商业有限元分析检查，表明所提出的模型以良好的精度预测了分布载荷下非棱柱形梁的应力场。梁表面自然满足无牵引边界条件要求。