Series B — Open Formula on Engineering Tools https://eng-tools.dev/series-b/ Recent content in Series B — Open Formula on Engineering Tools Hugo en Wed, 18 Mar 2026 00:00:00 +0000 Derivation of the Euler-Bernoulli Beam Equation EI·y″ = M(x) https://eng-tools.dev/series-b/b1-euler-bernoulli/ Tue, 17 Mar 2026 00:00:00 +0000 https://eng-tools.dev/series-b/b1-euler-bernoulli/ Step-by-step derivation of the moment-curvature relation EI·y″ = M(x), from plane sections assumption to the Euler-Bernoulli bending equation. All hypotheses stated explicitly. Derivation of the Euler Critical Buckling Load Pcr = π²EI/L² https://eng-tools.dev/series-b/b2-euler-buckling/ Tue, 17 Mar 2026 00:00:00 +0000 https://eng-tools.dev/series-b/b2-euler-buckling/ Step-by-step derivation of the Euler buckling formula from equilibrium on the deflected geometry, boundary conditions, and eigenvalue problem. Pinned-pinned column, all assumptions explicit. Derivation of the Curvature Formula κ = y″/(1+y′²)^(3/2) https://eng-tools.dev/series-b/b3-curvature/ Wed, 18 Mar 2026 00:00:00 +0000 https://eng-tools.dev/series-b/b3-curvature/ Step-by-step derivation of the curvature of a plane curve from its geometric definition, with the small-angle simplification to κ ≈ y″ used in beam theory. Derivation of Cantilever Tip Deflection δ = PL³/(3EI) https://eng-tools.dev/series-b/b4-cantilever/ Wed, 18 Mar 2026 00:00:00 +0000 https://eng-tools.dev/series-b/b4-cantilever/ Step-by-step derivation of the cantilever beam tip deflection formula from the moment-curvature relation, double integration, and boundary conditions.