Embodied Energy vs Structural Efficiency

Material

Beam Geometry & Load

Cross-section depth h 120 mm

Span length L 2.0 m

Tip load F 2000 N

Live Readouts

Tip deflection δ

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Safety factor

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Beam mass

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Embodied energy

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Eco-efficiency (allowable load per MJ embodied)

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How it works

A cantilever beam of length L, width b (fixed at 100 mm) and depth h carries a point load F at its free end. Standard beam theory gives the second moment of area, tip deflection and maximum bending stress:

I = b·h³ / 12
δ = F·L³ / (3·E·I)          (tip deflection)
σ_max = 6·F·L / (b·h²)      (max bending stress, at the wall)
SF = σ_allow / σ_max        (safety factor)

Sustainable design is not just "use less material" — it is minimizing environmental impact per unit of structural performance. Each material carries an embodied energy e (MJ per kg, from extraction through manufacture):

mass = ρ · b · h · L
E_embodied = mass · e
F_allow = σ_allow · b · h² / (6·L)   (load the section can safely carry)
eco-score = F_allow / E_embodied     (N of capacity per MJ invested)

Material buttons — switch between structural steel, aluminum, glulam timber, carbon-fiber composite and reinforced concrete; each has its own density ρ, stiffness E, allowable stress σ_allow and embodied energy e.
Depth / length / load sliders — resize the beam and its tip load in real time; the 3D beam bends by the actual δ(x) = F(3Lx² − x³)/(6EI) profile (visually amplified ×20 so millimetre-scale deflections are visible).
Eco-efficiency is the punch line of the article's material-selection section: timber and steel usually beat carbon fiber on this metric even though carbon fiber is stiffer and stronger, because its embodied energy per kilogram is far higher.

Real-world relevance: this trade-off — embodied energy against strength-to-weight and stiffness-to-weight ratios — is exactly how structural and sustainability engineers choose materials for bridges, building frames and aircraft.

Beam (bends under load) Load stack at tip

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