PSI - Issue 6

L.M. Kagan-Rosenzweig / Procedia Structural Integrity 6 (2017) 216–223 L.M. Kagan-Rosenzweig / Structural Integrity Procedia 00 (2017) 000–000

223

8

0.5 α = , the rigidity at the bot

are found numerically. Exact and approximate solutions are compared in Fig. 4. If

2

= EI

, the exact and approximate moments at support differ by

tom and top end differs by 16 times,

P l c

/

5.0476

0

2

0.8 α = , the rigidity differs by 625 times,

= EI

, moments at support differ by 11%. P is

7.8%. For

P l c

/

0.80762

0

taken as c P P 0.8 = . Curve 0 – no compression, 1 – exact solution, 2 – approximate solution. As the degree of variability of cross-section increases, the accuracy of approximate solution decreases, but re mains acceptable for technical calculations. Again, note that presented accuracy estimations consider a very high level of rod's compression.

5. Conclusion

The traditional approximate formula for bending moment in statically determinate beam-column is generalized to the case of the statically indeterminate one, compressed by a system of concentrated and distributed forces. The result of this generalization consists in the Eq. (14), (19). They have engineering accuracy and are useful for design calculations.

6. References

Rzhanitsyn A. R. 1955. Stability of the equilibrium state of elastic systems. Gostehizdat, Moscow, 475 p. [in Russian] Kagan-Rozenzweig L. M. 2015. Calculation of natural frequencies of compressed rods with variable cross-section. Simplified bending equation (I). Bulletin of civil engineers 6, 84–88. [in Russian] Kagan-Rozenzweig L. M. 2016. Method for internal forces calculation at transverse-longitudinal bending of elastic rods with variable cross sec tion. Simplified bending equation (II). Bulletin of civil engineers 1, 75–82. [in Russian] Kagan-Rozenzweig L. M. 2016. Method to calculate the critical load in elastic rods with variable cross section. Simplified bending equation (III). Bulletin of civil engineers 2, 61–67. [in Russian] Kagan-Rozenzweig L. M. 2017. Development of the applied approach to analysis of bars subjected to bending and compression/ Bulletin of civil engineers 4, 130–134. [in Russian]

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