An information view for rescue planning on empty buildings. Turn on the overlay to see voids in the rubble, access through each alley and slabs that would need shoring.
void: next to a standing elementvoid: under a sloped slabother pocketalley open (≥ 3 m)foot access onlyblockedshoring candidate
What the voids mean (and the "triangle of life" myth)
Engineering and search-and-rescue consensus: there is no universal safe spot. Survivable voids tend to form beside strong, still-standing elements (columns, thick wall piers, stair cores) and under slabs that came to rest tilted on debris or wall stubs - but whether they exist at all depends on the structure and on how it failed. The "triangle of life" advice (always lie next to a collapsed object) is a myth; official guidance for earthquakes is "drop, cover and hold on" and for rescuers to treat every void as unstable until shored.
This model is 2-D: its voids are only where the cross-section leaves gaps. It cannot say whether a person could survive, and it contains no people. It is a way to see why rescue teams read damage from the structure type, void geometry and access, not a prediction.
What this simulator does
A block of five empty buildings is modelled as 2.5-D structures: a planar frame (or wall) whose depth is the tributary width of the floor slabs. Each column, half-beam, floor slab piece or masonry block is a rigid body. Bodies are joined by connections with limited capacity - bending (plastic moment), shear, tie tension - so that when one support is lost the model shows which connections can carry the load a different way, and which break. It is a physics teaching model of the alternate load path idea used in structural-robustness guidance, not a design tool.
Differences from neighbouring pages: it is not an earthquake shake table, not a chimney felling and not a demolition ball - it is the multi-storey redundancy question: what happens after one load-bearing element is gone, compared across five structural types with live load-path checks and a rescue-planning overlay.
Load paths and the alternate-path method
Gravity flows slab, beam, column, footing. Remove a ground column and the floors above must span twice as far or hang from the storeys above (Vierendeel action: beams and columns of the upper frame act as a deep truss). If the connections are ductile and tied, large deflections let the beams act as catenaries, carrying the load in tension.
sum of ground reactions = total weight (checked to 1e-6)
Guidance such as the US GSA and DoD UFC 4-023-03 documents applies a dynamic increase to the loads above the lost element in a linear static check (shown in "Analysis"). A structure that fails the linear check can still survive through hinging and catenary action; the rigid-body simulation shows that.
Dynamic amplification of a suddenly removed support
For a linear elastic system suddenly loaded by a force F, equation of motion m x'' + c x' + k x = F gives a peak displacement of (F/k)(1 + exp(-pi z / sqrt(1 - z^2))): exactly 2 without damping. Removing the support over a time t_r reduces it to 1 + |sin(pi r)| / (pi r), r = t_r / T. Plastic structures dissipate energy in hinges, so the observed amplification of column loads is lower than 2. The "Checks" tab verifies the spring-mass case numerically.
DAF = 1 + exp(-pi z / sqrt(1 - z^2)) DAF_ramp = 1 + |sin(pi r)| / (pi r)
Rigid-body-spring connections, plastic hinges, ties
Members are rigid; flexibility lives in the joints. A joint has a rotational spring k = 4EI/L that yields at the plastic moment M_p and fractures after a rotation capacity theta_u; an axial element that yields at the tie capacity T_cap (the reinforcement ties, A_s f_y), elongates and ruptures at an elongation capacity; and a brittle shear/punching limit V_cap. A beam with a mid-span hinge and two end hinges forms the classic plastic collapse mechanism at w L^2 / 16 = M_p. The "ties / redundancy" slider scales M_p, T_cap, V_cap and the rotation and elongation capacities together (poorly connected precast slabs start from a much lower base). Solution uses sequential impulses at 240 Hz with warm starting.
w_collapse = 16 M_p / L^2 (fixed-fixed span) catenary: 2 T sin(theta) = F
Euler buckling and steel in fire
A slender column loses stability at the Euler load, and the usable resistance is reduced further by imperfections (EC3-style curve chi):
P_cr = pi^2 E I / (K L)^2 N_b = chi * A f_y lambda = sqrt(N_pl / P_cr)
At temperature T, steel keeps only the fractions k_y(T) of its yield strength and k_E(T) of its modulus (EN 1993-1-2: k_y = 0.78 at 500 C, 0.47 at 600 C, 0.23 at 700 C; k_E = 0.60, 0.31, 0.13). The fire uses the standard ISO 834 gas curve T_g = 20 + 345 log10(8t + 1) (t in minutes) with the lumped-capacity heating of an unprotected section (A_m/V = 170 1/m). When the column's axial load reaches N_b(T) it buckles; when a heated beam's capacity falls, its hinges form a mechanism. The fire clock is accelerated (slider); thermal expansion and floor-slab membrane action are not modelled.
Masonry and mortar bonds
The brick/block building is made of rigid units joined by cohesive mortar bonds with a tensile strength (about 0.15 MPa) and shear strength (cohesion about 0.3 MPa plus friction 0.7), so cracks follow the mortar joints and the wall breaks into stair-stepped pieces. Floors rest on the walls with weak anchorage that scales with the ties slider - which is exactly what separates old, poorly tied masonry from newer ring-beam construction.
Rubble, bulking and voids
Fractured slab pieces conserve volume and mass exactly (checked). Broken rubble occupies more volume than the solid material: a common planning factor is 1.3 to 1.5 times the solid volume for loose broken material - the number crews use to size debris removal. The pile envelope measured in the simulation is shown next to this planning estimate. Voids are free pockets in the 2-D section that are not connected to the open air. They are classified as next to a standing element, under a sloped slab or other.
Damage grades D1-D5
Generic grades in the spirit of EMS-98: D1 negligible (no yielding), D2 moderate (plastic hinges formed, structure intact), D3 heavy (connections or mortar bonds failed, little mass moved), D4 partial collapse (5-50 % of the mass has moved by more than 1 m), D5 destruction (50 % or more). Real surveys classify by observed damage; this is a simulation output.
What is simplified
- 2-D rigid bodies with a depth: no torsion, no out-of-plane failure, no slab membrane or punching geometry.
- Member capacities are generic round numbers derived from the sliders, not a code design of a real building; the sudden threshold between "arrested" and "collapsed" is real in spirit but its exact position is model-dependent.
- No wind, soil-structure interaction, thermal expansion or progressive concrete spalling; fire exposes one compartment only.
- Debris dynamics are approximate (rigid fracture into two or three pieces, friction 0.6-0.7).
Sources
GSA, Alternate Path Analysis and Design Guidelines for Progressive Collapse Resistance (2013); US DoD, UFC 4-023-03 Design of Buildings to Resist Progressive Collapse (2016); Starossek, Progressive Collapse of Structures (2009); Eurocode 3 part 1-2 (EN 1993-1-2) for steel at high temperature; Eurocode 1 part 1-7 (EN 1991-1-7) accidental actions and robustness; the 1968 Ronan Point partial collapse is the historical reason for tie requirements in building codes; EMS-98 for the damage-grade idea; INSARAG guidance for the search-and-rescue statements. Cited from memory in plain text; check the originals for design work.
Physics teaching model of the structural engineering of resilience on empty inanimate buildings: no people, no explosive charges or yields, no targeting, no real cities or events. Buildings are generic. Assets built in Blender 5.2 (Cycles-baked textures, Draco GLB) and rendered with Three.js; not affiliated with any organisation.