Research / Numerical methods

Classic plastic collapse

After M. R. Horne, “Plastic Theory of Structures” (1979), doi:10.1016/c2013-0-05820-3.

Against the author’s code
Against the paper’s figures
Not compared: the full text was not accessible to us

Research, not a design tool. Nothing here is an engineering result.

One fixed-base portal, three hand-calculated mechanisms, and the production 3D plastic-collapse solver.

First version · 0 reviews

Research, not a design tool.

Span L = 4 m, height h = 3 m, uniform Mp = 100 kN·m. Both bases are fixed. The roof carries λH = λ × 1 kN to the right at the left corner and λV = λ × 2 kN down at midspan. The beam is split at the load. The frame lies in the XZ plane; no out-of-plane load is applied.

Virtual work with rigid members and small rotations gives the three upper bounds below. The combined mechanism cancels one roof hinge: internal work is 6Mpθ, external work is λ(Hh + VL/2)θ. Its minimum governs. Axial deformation is elastic; axial and shear yielding, hardening and geometric instability are outside this hand calculation. Combined →

  • Beam: λ = 8Mp / (VL) = 100.000000
  • Sway: λ = 4Mp / (Hh) = 133.333333
  • Combined: λ = 6Mp / (Hh + VL/2) = 85.714286

A textbook-style example following Horne, Plastic Theory of Structures (1979), sections 2.2 and 2.4. Dimensions are chosen here; this is not a reproduction of a numbered textbook figure. Crossref verifies the book title and year but supplies no authors; the publisher identifies M. R. Horne. Elsevier.

Not yet

  • Independent reviews (0 so far).
  • Exact numbered textbook figure or experimental validation.
  • Other load ratios, sections, axial interaction, buckling or large displacements.
  • 2D plastic collapse: not used because of the reported issue #758 containment.
  • Plastic hinge symbols and curved member deformation; the viewer joins displaced nodes.

Cite this

Stabileo Research, “Classic plastic collapse”, reproduction of M. R. Horne (1979), doi:10.1016/c2013-0-05820-3. Implementation: research/benchmarks/plastic-collapse at commit 8068cd16ea2c. Engine: the Stabileo engine at the same commit. Permanent links to this exact build are planned.