PSI - Issue 78

Galileo Tamasi et al. / Procedia Structural Integrity 78 (2026) 883–890

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assess differences, accuracy, and safety margins. Detailed documentation ensures replicability. Simulated design offers valuable insights for validating modern methods and appreciating past engineers' ingenuity under constraints. 7. Calculation programs for bridge design and seismic analysis using HP 67/97 HP 67/97 programmable calculators, with their RPN architecture and program step memory, were invaluable for engineers needing to automate repetitive and complex calculations (HP USA, 1978a, 1978b). Programs for these machines for bridge design were developed from various sources, with a significant portion customized by HP Italy. Additionally, programs written for the American market by HP USA, those shared by the user community, and some developed in France were also utilized (HP France, 1977; HP USA, 1977a, 1977b). These programs provided a wide range of functionalities, including: • Analysis of sections : Programs determined geometric and static properties like area, moments of inertia, and centroids for complex shapes. Capabilities include arbitrary polygons, standard geometric shapes, and diverse concrete sections (tubular, T-sections, double-T), with reinforcement. • Beam and continuous beam analysis: Programs performed bending moment and shear calculations for isostatic beams, determined stress characteristics, and solved continuous beams (up to eight spans) via the three-moment method, handling mobile loads and support couples. • Reinforced Concrete (RC) and Prestressed Concrete (PC) design and verification: Programs calculated flexural reinforcement and verified normal stresses. For RC, capabilities covered rectangular and T-section design and verification, including combined flexure and axial load. For PC, they estimated prestress losses and performed flexural and shear verification for prestressed beams with parabolic cables, determining maximum cantilevers and isolation sheath lengths. • Static seismic analysis: Using the equivalent static method was supported. Programs simplified seismic actions into horizontal static forces, useful for analyzing simple frame structures and calculating local seismic effects such as moments and shears in piers/abutments. • Simplified modal analyses: Programs for finding polynomial roots (up to 14th degree) were useful for simplified modal analyses with limited degrees of freedom. Other programs calculated eigenvalues and eigenvectors for small systems. • Wind effects: The ability to analyze structures under horizontal forces - as for seismic analysis - allowed for wind load calculations. Specific functionality assisted with wind load distribution. • Foundation design: Foundation design programs provided capabilities for retaining walls (gravity/RC, Rankine/Coulomb), Winkler's theory-based foundation beams (rigid/elastic), bearing capacity (Terzaghi Meyerhof), and pile/sheet pile foundations.

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Fig. 5. HP Italy Civil Engineering Series - Volumes 1(a),2(b),3(c),4(d),5(e).

The efficiency of these programs lay in their compactness and transparency. Engineers needed detailed knowledge of the implemented algorithms, fostering a deep understanding of the problem. HP 67/97 user manuals often provided