Structural Engineering & Statics
where the load goes
Series

Continuity — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. 3 continuous spans against 3 simple ones. The bending moment in a continuous beam, solved by the stiffness method, drawn over the moment in the same spans made simply supported. The peak sagging moment falls from 30.6 to 19.6, and a hogging moment of 24.5 appears over the supports where there was none.

    The moment over the support, and what it buys

    Run a beam over its supports instead of stopping at each one, and the mid-span moment falls by a third while a new moment appears where there was none. Nothing was added but continuity.

    part 1 · internal-forces
  2. Under a moving pattern of load the hinged beam gives nothing away. The greatest and least moment at each point over every arrangement of 15 kN/m on whole spans, with 20 kN/m everywhere. Continuous, 152 and -184 kN·m; with hinges at 0.25 of a span, 171 and -161. The largest moment of either kind is 184 and 171.

    Two hinges let in and nothing lost

    Continuity is usually sold as the reason to avoid hinges: a continuous beam shares its moment over the supports, and a chain of simple spans wastes it. Heinrich Gerber's 1866 bridge showed that the choice is not between those two. Put two hinges in the right places and the beam becomes statically determinate, a support can settle as far as it likes without moving a single moment, and under a pattern of moving load the largest moment comes out lower than the continuous beam's. What has been spent is something a moment diagram does not show: if one of those hinges fails, there is no other way for the load to reach the ground.

    part 2 · internal-forces

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