How Far Can Ice Span: A Creep-Limited Bound for an Ice Beam Footbridge, and What Sawn Plant Fibre Does to the Bound

An ice beam used as a footbridge does not usually fail because a single crossing overloads it. It fails, if it fails, because ice creeps: under a load that stays in place, the beam slowly bends further, strain accumulates, and a span that was safe on the day it was frozen can cease to be safe weeks later, especially as the temperature rises toward the melting point. This study computes a span bound for a rectangular ice beam 1.2 m wide and 0.35 m deep, simply supported, carrying its own weight plus a sustained pedestrian pressure of 2.5 kN/m² over a stated service life of 60 days. Three limits are applied together: bending strength with a safety factor of 2.0, a creep-strain limit of 0.001 at the outer fibre over the service life, and a total deflection limit of span/250 including creep deflection. For plain ice the governing span is 4.96 m at −20 °C, 4.66 m at −10 °C, 4.34 m at −5 °C, 3.64 m at −2 °C, 3.13 m at −1 °C, and 2.70 m at −0.5 °C. Strength governs at −5 °C and colder; creep strain governs at −2 °C and warmer. Between −10 °C and −1 °C the bound falls by 32.8 percent, and between −10 °C and −0.5 °C it falls by 42.1 percent, because the stated creep rate at 1 MPa rises fifty-fold between −10 °C and −1 °C. A fibre-reinforced variant with 14 percent sawn plant fibre by mass, a stated strength factor of 2.2, and a stated creep-rate factor of 0.20 raises the bound to 6.78 m at −10 °C, but only to 4.01 m at −1 °C: fibre buys span in the cold and buys much less near the melting point, where creep governs both materials. A design based on short-term strength alone, without a safety factor or any creep check, would permit 6.59 m at −10 °C, which does not survive the arithmetic once the 60-day creep limit is applied. The practical rule is that an ice footbridge must be designed for the warmest temperature it will meet late in its life, not for the temperature at which it was frozen.