Elastic Deflection of Beams and frames Using Dream Method

This paper presents a new graphical method for the analysis of linear elastic structures called Dream Method. The method states that the strain energy of a linear elastic multi-member structure undergoing small deformation is the sum of moment of area of the bending moment diagrams of the individual members each about its own diagram base divided by the flexural rigidity of the member. The displacement at any point on the structure is equal to the partial derivative of the total strain energy with respect to the load at that point. The method is applied successfully in the analysis of a built-in stepped beam, a beam on three supports, and a four-member frame.

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Publication Details

Journal
International Journal of Engineering Research and Advanced Technology
Published
2025-01-01
DOI
https://doi.org/10.31695/ijerat.2025.5.2
Primary Topic
Laser and Thermal Forming Techniques
Type
article
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article

Elastic Deflection of Beams and frames Using Dream Method

Mahmoud Yassin Osman
International Journal of Engineering Research and Advanced Technology
Laser and Thermal Forming Techniques
article

Elastic Deflection of Beams and frames Using Dream Method

Mahmoud Yassin Osman
article en

Abstract

This paper presents a new graphical method for the analysis of linear elastic structures called Dream Method. The method states that the strain energy of a linear elastic multi-member structure undergoing small deformation is the sum of moment of area of the bending moment diagrams of the individual members each about its own diagram base divided by the flexural rigidity of the member. The displacement at any point on the structure is equal to the partial derivative of the total strain energy with respect to the load at that point. The method is applied successfully in the analysis of a built-in stepped beam, a beam on three supports, and a four-member frame.

International Journal of Engineering Research and Advanced TechnologyVol. 11(06)
Nile Valley University (SD)
Openalex Percentile: Top 79%
Laser and Thermal Forming Techniques
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