The statics and mechanics of structures form a core aspect of civil engineering. This book provides an introduction to the subject, starting from classic hand-calculation types of analysis and gradually advancing to a systematic form suitable for computer implementation. It starts with statically determinate structures in the form of trusses, beams and frames. Instability is discussed in the form of the column problem - both the ideal column and the imperfect column used in actual column design. The theory of statically indeterminate structures is then introduced, and the force and deformation methods are explained and illustrated.
An important aspect of the book's approach is the systematic development of the theory in a form suitable for computer implementation using finite elements. This development is supported by two small computer programs, MiniTruss and MiniFrame, which permit static analysis of trusses and frames, as well as linearized stability analysis. The book's final section presents related strength of materials subjects in greater detail; these include stress and strain, failure criteria, and normal and shear stresses in general beam flexure and in beam torsion.
The book is well-suited as a textbook for a two-semester introductory course on structures.
Author(s): Steen Krenk; Jan Høgsberg
Publisher: Springer
Year: 2013
Language: English
Pages: 506
Statics and Mechanics of Structures
Preface
Contents
1 Equilibrium and Reactions
1.1 Forces
1.1.1 The parallelogram rule
1.1.2 Parallel forces
1.2 Moments
1.2.1 Moment from forces in a plane
1.2.2 Moment from forces in space
1.2.3 Force couples
1.3 Equilibrium
1.3.1 Virtual work of rigid bodies
1.3.2 Equilibrium in a plane
1.3.3 Distributed load
1.4 Support conditions
1.5 Reactions by equilibrium equations
1.5.1 Plane beams
1.5.2 Simple frames
1.5.3 Three-hinge frame
1.5.4 Space structures
1.6 Reactions by virtual work
1.7 Exercises
2 Truss Structures
2.1 Basic principles
2.1.1 Building with triangles
2.1.2 Counting joints and bars
2.1.3 Qualitative tension-compression considerations
2.2 Method of joints
2.2.1 Planar truss structures
2.2.2 Space trusses
2.3 Method of sections
2.3.1 Bar forces via the method of sections
2.3.2 Special types of planar trusses
2.4 Stiffness and deformation of truss structures
2.4.1 Axial stress and strain
2.4.2 Linear elastic bars
2.4.3 Virtual work for truss structures
2.4.4 Displacements of elastic truss structures
2.5 Finite element analysis of trusses
2.5.1 Elastic bar element
2.5.2 Finite Element Method for trusses
2.5.3 The MiniTruss program
2.6 Exercises
3 Statics of Beams and Frames
3.1 Internal forces and moments
3.2 Beams with concentrated loads
3.2.1 Variation of internal forces for concentrated loads
3.3 Beams with distributed load
3.3.1 Differential equations for internal forces
3.3.2 Maximum moment
3.4 Combined loads
3.4.1 Superposition of load cases
3.4.2 Superimposing the distributed load
3.5 Internal forces in frames
3.5.1 Influence of load distribution
3.5.2 Influence of support conditions
3.5.3 Three-hinge frame
3.5.4 Principle of the arch
3.6 Exercises
4 Deformation of Beams and Frames
4.1 Bending of elastic beams
4.1.1 Homogeneous bending
4.1.2 Linear kinematic relations
4.2 Bernoulli beam theory
4.2.1 Statically determinate beams
4.2.2 Statically indeterminate beams
4.3 Shear flexible beams
4.4 Virtual work and displacements of beams
4.4.1 Principle of virtual work
4.4.2 Displacements in elastic beams
4.4.3 Virtual work and displacements in frames
4.5 Exercises
5 Column Stability
5.1 Beam with normal force
5.1.1 Stiffness reduction from normal force
5.2 Stability of the ideal column
5.2.1 Equivalent column length
5.2.2 Buckling direction and intermediate supports
5.3 Design of columns
5.3.1 Column length and slenderness
5.3.2 Geometric imperfections
5.3.3 Stresses in column cross-sections
5.3.4 Perry-Robertson's column design criterion
5.4 Exercises
6 The Force Method
6.1 Principle of the force method
6.2 The general force method
6.2.1 Released structure
6.2.2 The basic steps
6.2.3 Summary of the force method
6.3 Application of the Force Method
6.4 The force method for frame structures
6.4.1 Simply supported frames
6.4.2 Frames with fixed supports
6.5 Exercises
7 Deformation and Element Methods for Frames
7.1 Stiffness of beams
7.1.1 Symmetric and anti-symmetric bending
7.1.2 Basic cases of imposed deformation
7.1.3 Loads on constrained beams
7.2 Deformation method for frames
7.3 Beam elements
7.3.1 Beam bending element
7.3.2 Beam-column element
7.3.3 Transformation to global form
7.4 Finite element method for frames
7.4.1 The MiniFrame program
7.4.2 Stability analysis of frames
7.5 Exercises
8 Stresses and Strains
8.1 Stress
8.1.1 The stress vector
8.1.2 General stress components
8.1.3 Equilibrium
8.2 Deformation and strain
8.2.1 Strain
8.2.2 Rotation at a point
8.2.3 Displacement decomposition
8.3 Virtual work
8.3.1 Equation of virtual work
8.3.2 Matrix and tensor notation
8.4 Special states of stress and strain
8.4.1 Plane stress and plane strain
8.4.2 Stress and strain transformations
8.4.3 Principal stresses and strains in a plane
8.4.4 Principal stresses in three dimensions
8.5 Exercises
9 Material Behavior
9.1 Elastic materials
9.1.1 Internal elastic energy
9.1.2 Linear isotropic elasticity
9.2 Mean and deviator components
9.3 Yield conditions for metals
9.3.1 Von Mises' yield condition
9.3.2 Tresca's yield condition
9.4 Coulomb's theory of friction materials
9.4.1 Critical section and stress state
9.4.2 Coulomb failure surface
9.5 Exercises
10 General Bending of Beams
10.1 Bending of non-symmetric beams
10.1.1 Kinematic formulation
10.1.2 Stresses and section forces
10.2 Cross-section analysis
10.2.1 Elastic center
10.2.2 Moments of inertia
10.2.3 Principal coordinate system
10.3 Axial stresses and strains
10.3.1 Neutral axis and line of curvature
10.4 Exercises
11 Flexure and Torsion of Beams
11.1 Shear stresses in beam flexure
11.1.1 Shear flow – Grashof's formula
11.1.2 Shear stress on cross-section
11.2 Thin-walled cross-sections in shear
11.2.1 Shear center
11.2.2 Shear flexibility
11.3 Torsion of circular cylinders
11.4 General homogeneous torsion of beams
11.4.1 The Prandtl stress function
11.5 Torsion of thin-walled beams
11.5.1 Open sections
11.5.2 Single-cell sections
11.5.3 Multi-cell sections
11.6 Exercises
References
Index
