Carry-over Factors Research Articles

Stiffness Coefficients of Beam-Columns with Non-Prismatic Members

The objective of this paper is to determine the stiffness and carry-over factors of non-prismatic members, taking into consideration the effect of axial loads, and to construct charts that can be readily used. The method of successive approximations was used for the numerical formulation of the problem, a program in Fortran IV was written, and a high speed digital computer was used for the determination of the numerical solutions. Charts indicating the variation of stiffness and carry-over factors as a function of kL for various haunched members were plotted by the computer, where kL is a function of the axial load. The values can be readily used either for the solution of frame problems with non-prismatic members including the effect of the axial loads, or for determining the buckling loads of frames with non-prismatic members.

Algorithm for Calculation of Carry-over Factors, Stiffness Factors, and Fixed-End Moments for Beams with Variable Cross Sections

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The Elastic Critical Loads of Coupled Struts

In previous notes approximate values of the elastic critical loads of continuous and composite struts were obtained. In the case of continuous struts a semi-graphical technique was employed, while for composite struts values were derived from approximate solutions of the transcendental equations governing the behaviour of the struts. In the present note, the approximate elastic critical loads of coupled struts are investigated by a third method, using approximate expressions for the stiffness and carry-over factors entering into the equations expressing the critical conditions of the struts.

Matrix Analysis of Structures Curved in Space

General solution is given in matrix form for analysis of member curved or segmental in space and continuous between 2 supports; solution also yields general slope deflection equation which involves stiffness matrix; stiffness matrix contains all stiffness and carryover factors for ends of member.

Rapid Computation of Flexural Constants

Short algebraic formulas for computing stiffness, fixed-end moments, and carry-over factors in terms of three functions and their components are given. This paper has attempted to systematize and thereby simplify the evaluation of these factors by the introduction of the flexural functions. A numerical method for rapidly computing the values of the functions for nonprismatic beams is presented.

Torsion-Bending Stresses in Box Beams

Since the problem of determining bending stresses due to torion in a box beam is closely related to the problem of finding end loments in a continuous beam, it is possible to determine torsionending stresses by a procedure similar to the Cross method of loment distribution widely used in the analysis of continuous :ames. The method, as applied to the simplest case—the prismatic ox of rectangular section—is described in this paper. Cases inolving flexible bulkheads and complete cutouts of one or both urfaces are considered. Expressions for constants analogous to he fixed end moments, stiffness, carry-over, and rigidity factors f moment distribution are presented, and application of the lethod is illustrated with numerical examples.

Design Constants for Beams. with Nonsymmetrical Straight Haunches

Tables are presented in this paper, with outlines of the procedure to be followed in their use, to assist the structural designer in determining the stiffness, carry-over factors, and fixed-end moments for various loadings of beams having straight haunches placed nonsymmetrically with respect to the center of the span. Although this work was performed to determine these factors for nonsymmetrically haunched beams, it is also applicable to beams having straight haunches a t only one end and to symmetrical cases as well.

Analysis of the General Beam-Column Bv the Collocation Method

The method-of collocation is applied to the determination of critical axial loads and deflection curves for the general type of beam-columns under any conditions of end fixity, lateral loading, and flexural rigidity distribution. Slope deflection equations are also derived and the expressions for fixed-end moments, stiffness and carry-over factors established for use in the rigid frame analysis of structures involving such members. For the purpose of illustration and comparison, the method is applied to several problems, some of which have already been solved by standard methods.