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Electric circuits for the simulation of bending in beams

Theoretical and experimental investigation includes a study of the analogies between electrical-resistor networks and loaded beams. Forces are simulated by currents and moments by voltages

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Summary

Analogies between electrical circuits and bending beams are analyzed. Forces are simulated by currents and moments by voltages. The circuits have an attractive simplicity, being resistor networks. After the consideration of circuits for determinate beams, circuits for supported cantilever and fixed-ended beams are studied. The resolutions of indeterminacies are solved by circuits which apply the moment-area theorems. Numerical values of the electrical magnitudes and experimental results for the indeterminate beams are shown.

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Abbreviations

c :

constant of proportionality, kip·in.2/Ω

E :

elastic modulus, kip/in.2

i 1 ,i 2 , …i n ,I 1 ,I 2 , …I n :

electric current, amp

I :

moment of inertia, in.4

M 1 ,M 2 , …M n :

bending moment, in·kip, ft·kip

P 1 ,P 2 , …P n :

bending force, kip

r 1 ,r 2 , …r n :

resistance ohm, Ω

S 1 ,S 2 , …S n :

shearing force, kip

t :

tangential deviation, in.

v 1 ,v 2 , …v n :

voltage, v

x 1 ,x 2 , …x n ,X 1 ,X 2 , …X n :

length, in., ft

θ:

angle, radian

Bibliography

  1. Freiberg, S., “Electrotecnia,”Editorial Bibliografica Argentina, Buenos Aires, p. 174 (1956).

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  2. Karplus, W. S., andSoroka, W. W., Analog Methods, Computation and Simulation, McGraw-Hill Book Co., Inc., New York, p. 4 (1959).

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  3. Scanlan, R. H., “Solution de Quelques Problèmes de la Resistance des Matériaux à l'Aide d'Analogies Electriques,” thesis presented to the Faculté des Sciences de l'Université de Paris, 1956.

  4. Riesz, G. W., andSwain, B. J., “Structural Analysis by Electrical Analogy,”Proceedings of the Society for Experimental Stress Analysis, Vol. XII, No. 1, 13 (1954).

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Authors and Affiliations

  1. Universidad Nacional de Tucuman, Argentina

    S. Frieberg (Professor of Electrotechnology)

  2. Division of Mechanics and Design, University of California, Berkeley, Calif.

    S. Frieberg (Professor of Electrotechnology)

Authors
  1. S. Frieberg
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Additional information

Appointment supported by the International Cooperation Administration under the Visiting Research Scientists Program administered by the National Academy of Sciences of the United States of America.

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Frieberg, S. Electric circuits for the simulation of bending in beams. Experimental Mechanics 2, 24–32 (1962). https://doi.org/10.1007/BF02325808

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  • DOI: https://doi.org/10.1007/BF02325808

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