Title Numerical structural analysis / Steven E. O'Hara, Carisa H. Ramming

Published New York [New York] (222 East 46th Street, New York, NY 10017) : Momentum Press, 2015

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Description 1 online resource (1 PDF (xix, 277 pages)) : illustrations Series Sustainable structural systems collection Momentum Press sustainable structural systems collection. Contents 1. Roots of algebraic and transcendental equations -- 1.1 Equations -- 1.2 Polynomials -- 1.3 Descartes' rule -- 1.4 Synthetic division -- 1.5 Incremental search method -- 1.6 Refined incremental search method -- 1.7 Bisection method -- 1.8 Method of false position or linear interpolation -- 1.9 Secant method -- 1.10 Newton-Raphson method or Newton's tangent -- 1.11 Newton's second order method -- 1.12 Graeffe's root squaring method -- 1.13 Bairstow's method -- References 2. Solutions of simultaneous linear algebraic equations using matrix algebra -- 2.1 Simultaneous equations -- 2.2 Matrices -- 2.3 Matrix operations -- 2.4 Cramer's rule -- 2.5 Method of adjoints or cofactor method -- 2.6 Gaussian elimination method -- 2.7 Gauss-Jordan elimination method -- 2.8 Improved Gauss-Jordan elimination method -- 2.9 Cholesky decomposition method -- 2.10 Error equations -- 2.11 Matrix inversion method -- 2.12 Gauss-Seidel iteration method -- 2.13 Eigenvalues by Cramer's rule -- 2.14 Faddeev-Leverrier method -- 2.15 Power method or iteration method -- References 3. Numerical integration and differentiation -- 3.1 Trapezoidal rule -- 3.2 Romberg integration -- 3.3 Simpson's rule -- 3.4 Gaussian quadrature -- 3.5 Double integration by Simpson's one-third rule -- 3.6 Double integration by Gaussian quadrature -- 3.7 Taylor series polynomial expansion -- 3.8 Difference operators by Taylor series expansion -- 3.9 Numeric modeling with difference operators -- 3.10 Partial differential equation difference operators -- 3.11 Numeric modeling with partial difference operators -- References 4. Matrix structural stiffness -- 4.1 Matrix transformations and coordinate systems -- 4.2 Rotation matrix -- 4.3 Transmission matrix -- 4.4 Area moment method -- 4.5 Conjugate beam method -- 4.6 Virtual work -- 4.7 Castigliano's theorems -- 4.8 Slope-deflection method -- 4.9 Moment-distribution method -- 4.10 Elastic member stiffness, X-Z system -- 4.11 Elastic member stiffness, X-Y system -- 4.12 Elastic member stiffness, 3-D system -- 4.13 Global joint stiffness -- References 5. Advanced structural stiffness -- 5.1 Member end releases, X-Z system -- 5.2 Member end releases, X-Y system -- 5.3 Member end releases, 3-D system -- 5.4 Non-prismatic members -- 5.5 Shear stiffness, X-Z system -- 5.6 Shear stiffness, X-Y system -- 5.7 Shear stiffness, 3-D system -- 5.8 Geometric stiffness, X-Y system -- 5.9 Geometric stiffness, X-Z system -- 5.10 Geometric stiffness, 3-D system -- 5.11 Geometric and shear stiffness -- 5.12 Torsion -- 5.13 Sub-structuring -- References About the authors -- Index Summary As structural engineers move further into the age of digital computation and rely more heavily on computers to solve problems, it remains paramount that they understand the basic mathematics and engineering principles used to design and analyze building structures. The analysis of complex structural systems involves the knowledge of science, technology, engineering, and math to design and develop efficient and economical buildings and other structures. The link between the basic concepts and application to real world problems is one of the most challenging learning endeavors that structural engineers face. A thorough understanding of the analysis procedures should lead to successful structures Analysis adjoint matrix algebraic equations area moment beam deflection carry- over factor, castigliano's theorems cofactor matrix column matrix complex conjugate pairs complex roots conjugate beam conjugate pairs convergence diagonal matrix differentiation distinct roots distribution factor eigenvalues elastic stiffness enke roots extrapolation flexural stiffness geometric stiffness homogeneous identity matrix integer integration interpolation inverse joint stiffness factor linear algebraic equations lower triangular matrix matrix matrix minor member end release member relative stiffness factor member stiffness factor moment-distribution non-homogeneous non-prismatic members partial pivoting pivot coefficient pivot equation polynomials principal diagonal roots rotation rotational stiffness row matrix second-order stiffness shear stiffness slope-deflection sparse matrix square matrix stiffness matrix structural flexibility structural stiffness symmetric transformation torsional stiffness transcendental equations transformations transmission transposed matrix triangular matrix upper triangular matrix virtual work visual integration Notes Title from PDF title page (viewed on January 10, 2015) Bibliography Includes bibliographical references and index Subject Structural analysis (Engineering) -- Mathematical models TECHNOLOGY & ENGINEERING -- Civil -- General. Structural analysis (Engineering) -- Mathematical models Form Electronic book Author Ramming, Carisa H., author ISBN 9781606504895 1606504894

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