An illustrative topology-optimization demo, running in your browser

The Bench

Pick a span. Watch the solver pour material only where the load needs it. Then flip the constructability constraint and watch the spiderweb become something you can actually build.

solving…

Material budget 40%

How much material the optimizer is allowed. Less material = bigger savings, but watch the stiffness cost climb.

Minimum member size 2.4

Carstensen's constructability knob. Small = delicate spiderweb only a 3D printer loves. Large = chunky members a crew can fabricate.

60%

less material than a solid block

—

compliance (lower = stiffer)

2.4

smallest member (grid units)

—

buildability read

What you're watching — and what it isn't. This is an illustrative topology-optimization demo (a density-based / SIMP-style solver) running a small finite-element model one iteration at a time in your browser. It is not the paper's solver. Schemmer & Carstensen's method is mixed-integer linear programming (MILP) over discrete truss members — a different formulation from the density field you see here. The demo is just a feel for the idea. On a simple span it still finds an arch on its own, the optimizer rediscovering what masons knew for two thousand years. Drop the material budget and the saving climbs — but so does compliance, which is the honest catch: the lightest structure is also the floppiest, and somewhere in that tradeoff is the design you'd actually sign. The paper's headline (below) is 83–90% less material than conventionally-designed recycled-steel trusses — a specific comparison, not a blanket "90%."

The drawing set

The Views

The optimizer gives you one face. A structure gets built from three. Here's the current solve thrown into the orthographic views you'd actually draft.

Elevation. This is the solved load-path — the face the optimizer actually computes. It's where the arch, the truss diagonals, the material thinning all live.

The plan and section are schematic extrusions of the solved elevation across a deck width — not a second optimization, just the same result shown the way a drawing set shows it. The point is the jump every engineer knows: a beautiful 2D optimum still has to become a 3D thing with width, connections, and a deck on top. That translation is exactly the gap the MIT work is trying to close.

The engineer's job

What It's Not Counting

The optimizer minimizes material for one idealized load on rigid, perfect supports. The site has never once agreed to those terms. Flip on what the math left out.

Model saving vs. what survives contact with the site

60%

Nothing toggled yet — the model still thinks it saved 60%. Start switching on reality.

Scour at the piers

The optimizer assumed the supports never move. A river doesn't. Scour can undermine a footing the model drew as a perfect point.hydraulics · your desk

Soil bearing & foundations

Those crisp support points are spread footings or driven piles in real dirt — material the optimizer never drew because it never asked what's under the bridge.geotech

Real load combinations

One static point load is a fiction. Real codes stack live-load lanes, wind, seismic, thermal expansion, and fatigue cycles — each one redraws the load path.AASHTO · the code

Constructability of THIS site

Can you even get a crane here? Stage erection over a live road or river? The cleanest optimum is worthless if it can't be built where it has to stand.means & methods

Connections & fabrication

Every joint the optimizer invents is a detail a human has to design, weld, bolt, and inspect. Complex geometry multiplies connections — and connections are where structures fail.detailing

Cost ≠ material

The optimizer minimizes pounds. The bid is labor, formwork, and time. An organic shape can cost more to form than the steel it saves — the savings can invert.the estimate

Inspection & maintenance access

A structure has a fifty-year life. Someone has to reach every member to inspect it. The optimum that buries a critical member where no one can see it is not optimal.asset management

Durability & exposure

Deicing salt, freeze-thaw, fatigue. Thin optimized members have less material to corrode away before they're gone. The model solved for day one, not year forty.durability

The point isn't that the optimizer is wrong. It's that the optimum is only optimal inside the model's small world — one load, rigid supports, material as the only cost. Designing for this location, this river, this soil, this crew, this fifty-year life, is the part the math hands back to you. That's not a limitation of the tool. That's the job.

The paper that inspired this bench

The Idea

Not a sledgehammer to a pillar. A closing of the oldest gap in the field: the distance between the optimal design and the buildable one.

The savings were never the news. Topology optimization has been cutting material by large fractions for decades. The problem is the part you already know in your bones: it spits out complex, spiderweb structures that even a capable engineer can't actually build — so the method got quarantined into 3D printing and research and basically never touched a real bridge. The paper's specific result: 83–90% less material than conventionally-designed recycled-steel trusses — designs that are also constructible, which is the real headline.

What's new: Schemmer (first author) and Carstensen (senior) moved constructability inside the optimizer, using a mixed-integer linear programming (MILP) formulation over discrete truss members. You constrain how many members meet at a joint, set how small the smallest part can get, work in multiple materials, and account for how each one carries load. The optimizer is no longer allowed to hand you something you can't build. The "minimum member size" knob on this bench is a loose stand-in for that idea — not the MILP itself.

This tool lets you feel that tradeoff instead of reading about it — and then it adds the part no optimizer does: the site that has to hold the thing.

Bench instructor: structures faculty Oskar Simpson (who also teaches Live Beam and The Moment Frame) runs this bench. Note: the formal class around it isn't stood up yet — this is a working bench, not a scheduled course.

Sources

Paper: Schemmer Z & Carstensen J, "Minimum Carbon Trusses: Constructible Multi-Component Designs with Mixed-Integer Linear Programming," Automation in Construction (2026), MIT.
arXiv:2602.07185 · MIT News · EurekAlert release
The paper's method is mixed-integer linear programming (MILP) over discrete truss members, reporting 83–90% less material than conventionally-designed recycled-steel trusses. The solver running on this page is an illustrative topology-optimization demo (a density-based / SIMP-style sketch with sensitivity filtering and an optimality-criteria update) — it is not the paper's MILP solver and produces nothing the paper verified. It exists only to let you feel the material-vs-buildability tradeoff.