A straight, prismatic, homogeneous beam runs along z, with the imported profile in x/y. Point forces and moment couples act at z and absolute profile coordinates x/y. Uniform distributed forces act between their start/end stations; mt is a torque per unit length. All loads act simultaneously. Positive forces follow x/y/z; moments follow the right-hand rule.

Biaxial Euler–Bernoulli bending retains Ixy. N, Vₓ, Vᵧ, Mₓ and Mᵧ follow from exact integration with the selected end conditions. Axial displacement and twist are fixed at the root. Tip axial and twist restraints are independent of bending supports. Bending supports restrain both transverse directions. Reactions refer to forces at the shear center, axial force at the centroid, and moments about these respective axes.

Torsion includes load eccentricity about the shear center. The piecewise analytic Vlasov solution gives T = GJtθ′ − EIωθ‴, B = −EIωθ″ and Tω = dB/dz. Free warping means B = 0; restrained warping means θ′ = 0. End twist constraints and warping restraints are independent. A zero Iω uses pure Saint-Venant torsion.

At the chosen z and cut side, all resultants are passed to the same thin-wall stress calculation used by Cross-Section Analyzer. Local corner/end effects, shear deformation, geometric nonlinearity, yielding and buckling are excluded. Plots are sampled; they are not a global stress-envelope or strength check.

References: TU Delft — Euler–Bernoulli beams · SCI P385 — Torsion.

x/y are absolute profile coordinates in mm. Forces are in N; point moments in N·mm. Distributed q is in N/mm and mt in N·mm/mm. Coordinates affect force eccentricity; moment couples are independent of x/y.

Ready to calculate.

Calculate the beam to evaluate the selected cut.