Numerical structural analysis

✍ Scribed by O'Hara, Steven E.; Ramming, Carisa H

• Publisher: Momentum Press
• Year: 2015
• Tongue: English
• Leaves: 302
• Series: Sustainable structural systems collection
• Category: Library

✦ Synopsis

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 link between the basic concepts and application
to real world problems is one of the most challenging learning endeavors that structural engineers face. The primary purpose of Numerical Structural Analysis is to assist structural engineering students with developing the ability to solve complex structural analysis problems. This book will cover numerical techniques to solve mathematical formulations, which are necessary in developing the analysis procedures for structural engineering. Once the numerical formulations are understood, engineers can then develop structural analysis methods that use these techniques. This will be done primarily with matrix structural stiffness procedures. Finally, advanced stiffness topics will be developed and presented to solve unique structural problems, including member end releases, non-prismatic, shear, geometric, and torsional stiffness.

✦ Table of Contents

Content: 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.

✦ Subjects

Structural analysis (Engineering) -- Mathematical models. TECHNOLOGY & ENGINEERING / Civil / General adjoint matrix algebraic equations area moment beam deflection carry- over factor, castigliano's theorems cofactor matrix column matrix complex conjugate pairs complex roots