Abstract
The development of a theoretical model to predict the four equilibrium forces of reaction on a simple ladder of non-adjustable length leaning against a wall has long remained an unresolved matter. The difficulty is that the problem is statically indeterminate and therefore requires complementary information to obtain a unique solution. This paper reports 1) a comprehensive theoretical analysis of the three fundamental models based on treating the ladder as a single Euler-Bernoulli beam, and 2) a detailed experimental investigation of the forces of reaction as a function of applied load and location of load. In contrast to previous untested proposals that the solution to the ladder problem lay in the axial constraint on compression or the transverse constraint on flexure, the experimental outcome of the present work showed unambiguously that 1) the ladder could be modeled the best by a pinned support at the base (on the ground) and a roller support at the top (at the wall), and 2) the only complementary relation needed to resolve the static indeterminacy is the force of friction at the wall. Measurements were also made on the impact loading of a ladder by rapid ascent and descent of a climber. The results obtained were consistent with a simple dynamical model of the ladder as a linear elastic medium subject to a pulse perturbation. The solution to the ladder problem herein presented provides a basis for theoretical extension to other types of ladders. Of particular importance, given that accidents involving ladders in the workplace comprise a significant fraction of all industrial accidents, the theoretical relations reported here can help determine whether a collapsed structure, against which a ladder was applied, met regulatory safety limits or not.
Highlights
Determination of the reaction forces on a beam is a standard part of the mechanics of continuous media, the exact conditions under which an actual physical structure comprised of beams is stressed are not always apparent
This paper reports the theoretical solution of three basic models by which to analyze the reaction forces of a fixed ladder represented as a single Euler-Bernoulli (E-B) beam
The question of how to calculate the four forces of reaction on a ladder in static equilibrium against a wall has been an unresolved issue for many years
Summary
Determination of the reaction forces on a beam is a standard part of the mechanics of continuous media, the exact conditions under which an actual physical structure comprised of beams is stressed are not always apparent. Models based on different assumptions can predict hugely different reaction forces, and careful experimentation is required to determine which model may most accurately characterize a structure. One of the most important mechanical structures for which reaction forces need to be determined is that of a ladder. Ladders have been in use since antiquity, to date no definitive model of the reaction forces on a ladder has been experimentally tested and confirmed. This paper reports what the author believes to be the most comprehensive theoretical analysis and definitive experimental test of the reaction forces on a fixed ladder
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