Masters Theses


"Two types of dynamic analysis of multistory structures are presented in this thesis . First presented is the dynamic stiffness matrix method in which the masses are distributed along the constituent members. This method is composed of statics, stiffness and loading matrices. The statics matrices are established from the structural configurations, the stiffness coefficients are formulated from the elastic properties of the members, and the loading matrices are functions of the time dependent forces or time dependent foundation movements. The applied forces may be uniform, concentrated, triangular or joint forces. Computer programs are given to carry out the laborious calculations for the solutions of moments, shears and displacements. Two example problems are investigated, one a continuous beam and the other a frame with sidesway, in which various types of loading are considered. The solutions obtained by the presented method have been compared satisfactorily with another method presented elsewhere. Typical computer programs and flow charts are given for which the sample computer input and output are shown . Also presented is a lumped mass method of dynamic analysis. Unlike the usual shear building type of analysis, however, joint rotations are considered, thereby permitting a more realistic analytical model. A finite difference method is used to solve the differential equation. In this method, the acceleration is approximated by a linear combination of the displacements from three previous time periods and the unknown displacement to be solved for. This method also uses the displacement approach for formulating the stiffness and loading matrices, which are modified to include the dynamic effect. The lumped mass method has been extended for the analysis of elasto-plastic systems for which bilinear relationships between moments and rotations are assumed. To account for a plastic moment at some location, the stiffness matrix is modified so that a real hinge is inserted, and then the loading matrix is changed so that the actual plastic moment is included as external loading. Two computer programs are given, along with flow charts, which are used to investigate the two example problems. The first example is the analysis of a three story frame which experiences elastic deformations only. The same frame was analyzed elsewhere and the results are compared. This frame is then analyzed for a set of loads that force it into the plastic region, and these results are compared with the purely elastic case"--Abstract, Pages ii-iii.


Cheng, Franklin Y.

Committee Member(s)

Best, John, 1925-2015
Cunningham, Floyd M.


Civil, Architectural and Environmental Engineering

Degree Name

M.S. in Civil Engineering


University of Missouri--Rolla

Publication Date



xi, 103 Pages

Note about bibliography

Includes bibliographical references (pages 188-190).


© 1970 Mark Eugene Botkin, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Tall buildings -- Materials -- Dynamic testing
Structural analysis (Engineering) -- Matrix methods

Thesis Number

T 2331

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