Teaching defensible concrete selection through changing specifications and limiting margins

Abstract

Materials selection teaching should make the conditions supporting a recommendation as visible as the recommendation itself. A concrete selection exercise is developed around ingredient quantities, slump, flow, and 28-day compressive strength for 103 formulations. Learners first minimize cement content subject to simultaneous workability and strength requirements, then reconsider their answer after a requirement or a declared allowance changes. Complete enumeration identifies eligible choices, limiting inequalities, exact selection boundaries, and incompatible requirements. Under the initial brief, fifteen formulations meet the nominal limits, whereas ten satisfy allowances of 1 cm for slump, 2 cm for flow, and 2 MPa for strength. The minimum-cement choice changes from 140.2 to 160.0 kg per cubic metre. Only three of the fifteen eligible formulations remain undominated when cement content and limiting margin are considered together. Across sixty-four combinations of workability bounds and strength minima, forty-two admit a selection; omitting workability produces a nonconforming choice in thirty-five of those cases. A separate infeasibility exercise exposes a direct conflict between its slump interval and strength minimum and quantifies two possible changes to the teaching brief. Six figures, complete worked calculations, a ninety-minute lesson sequence, and an analytic assessment rubric connect the numerical treatment to classroom use. The contribution is an executable teaching technique whose numerical content is verified.