The object of this investigation was to evaluate and compare four approximate methods of limit analysis as they apply to the calculation of the collapse load, the load versus deflection relationship, and the load versus strain relationship, of a horizontal system of rigidly connected, rectangular beams.
The first approximate method considered made use of the stress-strain diagram utilized by Roderick (1948), Luxion and Johnston (1948), Baker (1949), and Roderick and Heyman (1951). The diagram is assumed to be linear until the unit stress reached the value of the upper yield stress in simple tension. The stress was then assumed to decrease to the lower yield stress while the strain remained constant at the value of the elastic limit strain. Thereafter, the strain increased infinitely while the stress remained constant. This first method, being the most exact, served as a basis for comparison of the remaining three methods.
Method Two differed from Method One only in that the upper yield stress was neglected. This gave a stress-strain diagram of the type used by Yang, Beedle and Johnston (1951).
The third approximate method made use of the simplified moment versus angle change relationship utilized by Van den Broek (1948), and Yang, Beedle and Johnston (1951). In this method, it was assumed that the flexural moment existing on a cross section of a beam varied linearly with the angle change at the same cross section until the moment reached an ultimate value. After reaching this value, the angle change increased infinitely while the moment remained constant. It was assumed in this third method that the ultimate moment was equal to one and one-half times the elastic limit moment for a rectangular beam.
The fourth approximate method assumed that the material remained rigid until the ultimate value of moment was developed, and that after this ultimate moment was reached, the angle change increased infinitely while the moment remained constant. It was also assumed in method four that the ultimate moment which can be resisted by a rectangular beam is equal to one and one-half times the elastic limit moment.
Each of the approximate methods outlined above was used in the analysis of two structures. The first was composed of two horizontal rectangular beams of unequal lengths which intersect one another at right angles at their midspans. These beams are rigidly connected and are absolutely fixed at their ends. The second structure was similar to the first structure except that the beams in the second structure are of equal lengths. Both structures were loaded by a single concentrated load applied at the intersection of the center lines of the two beams. This load was increased in value until collapse of the structure was imminent. In this manner the collapse load, the load versus deflection relationship, and the load versus strain relationship were determined throughout the entire range of loading.
All methods gave identical values for the collapse load. Method one gave the most accurate load versus deflection relationship and load versus strain relationship. Methods two, three, and four gave less accurate results, in that order.
It was shown that the theory of elasticity indicated that the structure analyzed in Example Two was the stronger; whereas, the theory of limit analysis indicated that the structure in Example One was stronger. This showed that the elastic theory does not always give a good indication of the load which can be sustained by a redundant structure before collapse. / M.S.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/104274 |
| Date | January 1955 |
| Creators | Watson, Frederic Warren |
| Contributors | Structural Engineering |
| Publisher | Virginia Polytechnic Institute |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis, Text |
| Format | 115 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 25850879 |
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