Fixed-end Forces Research Articles

Semi-rigid Analysis of Metal Plate-connected Wood Trusses Using Fictitious Members

The focus of this article is analysis of a truss by including the semi-rigidity of the truss joints using fictitious members. Results from simulating the semi-rigid connection with fictitious members are compared with results from analyses made with the following truss joint connection assumptions: 1) pin connection; 2) rigid connection; 3) the Truss Plate Institute (TPI) specification for truss analysis; and 4) semi-rigid connection simulated by modifying the fixed-end forces and element stiffness matrices. Sensitivity analyses were conducted to examine the effect of: 1) truss slope; 2) axial and rotational stiffnesses of the joints; and 3) random assignment of modulus of elasticity (MOE) for truss members on the maximum truss deflection, and maximum axial force and bending moment of members as determined by the fictitious member method.

Analysis of Metal-Plate-Connected Wood Trusses with Semi-rigid Joints

Metal-plate-connected wood trusses with semi-rigid joints were investigated by the matrix method of structural analysis. The element-stiffness matrix and fixed-end forces of an individual member with one or both ends semi-rigid were derived as modifications of the idealized cases. The case of unequal elastic connections at two ends of a member can also be handled by this method of analysis. When one end is semi-rigid, the other end may be specified as pinned, rigid, or semi-rigid. The truss was analyzed for three different joint assumptions: pin, rigid, and semi-rigid joints. The truss performance, based on deflection, varied greatly depending on the joint assumption. Including semi-rigid-joint behavior in the analysis of a wood truss decreased maximum deflection by 34% compared with the pinned-joint assumption and maximum moment by 13% compared with the rigid-joint assumption. By incorporating semi-rigid behavior of joints, more accurate member forces can be obtained enabling closer prediction of actual truss behavior.

Matrix analysis of structures

1. INTRODUCTION Historical Background / Classical, Matrix, and Finite-Element Methods of Structural Analysis / Flexibility and Stiffness Methods / Classification of Framed Structures / Analytical Models / Fundamental Relationships for Structural Analysis / Linear versus Nonlinear Analysis / Software / Summary 2. MATRIX ALGEBRA Definition of a Matrix / Types of Matrices / Matrix Operations / Gauss-Jordan Elimination Method / Summary / Problems 3. PLANE TRUSSES Global and Local Coordinate Systems / Degrees of Freedom / Member Stiffness Relations in the Local Coordinate System / Finite-Element Formulation Using Virtual Work / Coordinate Transformations / Member Stiffness Relations in the Global Coordinate System / Structure Stiffness Relations / Procedure for Analysis / Summary / Problems 4. COMPUTER PROGRAM FOR ANALYSIS OF PLAIN TRUSSES Data Input / Assignment of Structure Coordinate Numbers / Generation of the Structure Stiffness Matrix / Formation of the Joint Load Vector / Solution for Joint Displacements / Calculation of Member Forces and Support Reactions / Summary / Problems 5. BEAMS Analytical Model / Member Stiffness Relations / Finite-Element Formation Using Virtual Work / Member Fixed-End Forces Due to Loads / Structure Stiffness Relations / Structure Fixed-Joint Forces and Equivalent Joint Loads / Procedure for Analysis / Computer Programs / Summary / Problems 6. PLANE FRAMES Analytical Model / Member Stiffness Relations in the Local Coordinate System / Coordinate Transformations / Member Stiffness Relations in the Global Coordinate System / Structure Stiffness Relations / Procedure for Analysis / Computer Program / Summary / Problems 7. MEMBER RELEASES AND SECONDARY EFFECTS Member Releases in Plane Frames and Beams / Computer Implementation of Analysis for Member Releases / Support Displacements / Computer Implementation of Support Displacement Effects / Temperature Changes and Fabrication Errors / Summary / Problems 8. THREE-DIMENSIONAL FRAMED STRUCTURES Space Trusses / Grids / Space Frames / Summary / Problems 9. SPECIAL TOPICS AND MODELING TECHNIQUES The Structure Stiffness Matrix Including Restrained Coordinates-An Alternative Formulation of the Stiffness Method / Approximate Matrix Analysis of Rectangular Building Frames / Condensation of Degrees of Freedom, and Substructuring / Inclined Roller Supports / Offset Connections / Shear Deformations / Nonprismatic Members / Solution of Large Systems of Stiffness Equations / Summary / Problems / APPENDICES / A. Computer Software / B. Flexibility Method / BIBLIOGRAPHY / ANSWERS TO SELECTED PROBLEMS / INDEX / TABLE OF FIXED-END MOMENTS

三次元撓角法の座屈問題への拡張

In analysis of structural frames the effect due to axial force for straight members is usually ignorced for the moment distribution. In this papers this effect is considered for moment distributions in the straight member of uniform corss section with solving usual differential equtions (1-a) and (1-b). Consequently the modified slope deflection coefficients for bending depending upon the intensity of axial force introduced to the generalized slope deflection equations which are reported previously by the author. These coefficents are identical with those represented in several referred papers and are given in Fig. 2, but in which is a new coefficient for end force equations. In equations (1-a) and (1-b), the applied loads are expanded with Fourier sine series which is available to use for various loading cases, then the fixed end moments and fixed end forces are also expressed with modified coefficients. The procedure of analysis is nearly the same as mentioned before by the author. The result can be optained with the successive approximation if the determinant of the stiffness matrix is not zero. When the determinant becomes zero which yield critical values for buckling. In view of engineering the lowest one is practically important. Examples in Fig. 6 and 7 are given to illustrate a feature of analysis in braced frames.