A structure can be defined as a rigid body that resists external effects (e.g : loads, temperature changes and support settlements) without excessive deformation. Typical structures such as residential buildings, industrial buildings, halls, towers, bridges, dams, tanks, channels and pavements are of interest to civil engineers.
Structural analysis is the determination of the response of a structure to external effects (e.g. : loads, temperature changes and support settlements) using theory of structures.
Theory of structures may be classified from different points of view as follows: static or dynamic, and if static, statically determinate or statically indeterminate, planar or space, linear or non-linear. Only, linear static analysis will be discussed here.
Structural design is the selection of a suitable arrangement of members (elements), and a selection of materials and member sections, to withstand the stress resultants (internal forces) of a specified set of loads, and satisfy the specified displacement constraints and the other code requirements.
This course introduces the basic concepts of structural analysis. The student will be able to analyze Beam, Frame, Truss and Arch structures. In addition, he/she can calculate the internal forces in structural members and draw the normal, shear and bending moment diagrams.
Chapter 1: Introduction to Structural Modeling
1.1 Introduction
51.2 Free-body diagram
9Chapter 2: Loads
2.1 Introduction
132.2 Types of loads
142.2.1 Point load
162.2.2 Uniform load
172.2.3 Non-uniformly distributed load
172.2.4 Moments
202.3 Load distribution in concrete structures
22Chapter 3: Supports and Reactions
3.1 Introduction
353.2 Types of supports
353.2.1 Roller support
373.2.2 Hinged support
393.2.3 Fixed support
413.2.4 Link support
433.2.5 Intermediate hinge
443.3 Equilibrium
463.4 Calculation of reactions
483.5 Examples
49Chapter 4: Stability and Determinacy
4.1 Introduction
694.2 Stability
694.3 Determinacy
73Chapter 5: Internal Forces for Beams
5.1 Introduction
835.2 Determination of internal forces at a section
865.2.1 Normal force
875.2.2 Shear force
915.2.3 Bending moment
965.3 Relations between load, shear and moment
1005.4 Internal force diagrams
1065.4.1 Normal force diagram
1065.4.2 Shear force diagram
1095.4.3 Bending moment diagram
1185.5 Maximum bending moment and its position
1295.6 Common cases of loading
1315.7 Principle of superposition
1395.8 General Examples
1415.9 Problems
151Chapter 6: Analysis of Statically Determinate Frames
6.1 Introduction
1576.2 Calculation of reactions
1576.3 Determination of internal forces
1676.4 Internal force diagrams
1676.5 Problems
188Chapter 7: Analysis of Statically Determinate Arches
7.1 Introduction
1937.2 Calculation of reactions
1947.3 Determination of internal forces at a section
198Chapter 8: Analysis of Statically Determinate Trusses
8.1 Introduction
2018.2 Classification of trusses
2058.3 Stability and determinacy
2078.4 Method of joints
2138.5 Method of sections
2248.6 Space trusses
237Chapter 9: Influence Lines
9.1 Introduction
2439.2 Methods used to plot influence lines
2479.3 Basic Method
2479.3.1 Influence lines for beams
2489.3.2 Influence lines for trusses
2729.3.3 Influence lines for frames
2769.4 Kinematic Method
2839.5 Calculation of maximum influence at a point
2899.5.1 Maximum influence due to concentrated loads
2899.5.2 Absolute maximum influence
2919.5.3 Maximum influence due to uniform loads
2959.6 Cases of loading and envelopes
296Chapter 10: Computer Applications
10.1 Introduction
31510.2 Selecting units
31610.3 Editing the frame
31610.4 Editing supports
31910.5 Assigning member sections
32010.6 Assigning static load cases
32110.7 Defining material properties
32310.8 Running analysis
32410.9 Checking the results
325This course introduces the basic concepts of structural analysis. The student will be able to calculate the properties of plane areas. In addition, he/she can calculate the normal, shear, combined and principle stresses at any section of structural element.
Chapter 1: Properties of Sections
1.1 Introduction
51.2 Area
51.3 Centroid
61.4 Moments of inertia
191.5 Parallel axis theorem
261.6 Polar moment of inertia
311.7 Product of inertia
331.8 Radius of gyration
381.9 Moments of inertia about inclined axes
401.10 Principal axes of inertia
421.11 Graphical solution by Mohr’s circle
461.12 Centroids of general bodies
..1.13 Examples on general areas
..Chapter 2: Straining Actions
2.1 Introduction
632.2 Normal forces
652.3 Shear forces .
662.4 Bending moments
672.5 Relations between load, shear and moment
682.6 Internal forces diagrams
69Chapter 3: Normal Stresses
3.1 Introduction
733.2 Normal stresses due to axial forces
783.3 Composite system
913.4 Normal stresses due to bending moments
973.5 Economic sections
1133.6 Unsymmetrical beams
1183.7 Superimposed (built-up) beams
1303.8 Combined effects of axial forces and bending moments
1333.9 The general bending equation
145Chapter 4: Shear Stresses
4.1 Introduction
1514.2 Direct shear in bolts and rivets
1524.3 Shear stress due to bending
1624.4 Shear stress due to twisting moment (Torsion)
167Chapter 5: Principal Stresses
5.1 Introduction
1935.2 Plane state of stress
1935.3 Coordinate transformations
1945.4 Principal directions and principal stresses
1955.5 Maximum shear stress direction
1665.6 Mohr’s circle
167Chapter 6: Deformations of Statically Determinate Structures
6.1 Introduction
2076.2 Double integration method
2086.3 Moment-area method
2326.4 Conjugate beam method
2556.5 Castigiliano's theorems
268Chapter 7: Virtual work method
7.1 Principle of superposition
2837.2 Maxwell-Betti Theorem (Reciprocal Theorem)
2847.3 Deformation of members
2857.4 Principle of virtual work
2907.5 Evaluation of integrals
291Chapter 8: Euler Theory in Buckling
8.1 Introduction
3118.2 Maxwell-Betti Theorem (Reciprocal Theorem)
311REFERENCES
333This course introduces the basic concepts of structural analysis. The student will be able to draw Influence lines for statically determinate structures (beams, frames, arches, trusses) due to moving loads. In addition, he/she can calculate the deformation of structures using different methods (double integration, conjugate beam, moment area, and virtual work methods).
Chapter 1: Influence Lines
1.1 Introduction
51.2 Methods used to plot influence lines
91.3 Basic Method
91.3.1 Influence lines for beams
101.3.2 Influence lines for trusses
341.3.3 Influence lines for frames
381.4 Kinematic Method
451.5 Calculation of maximum influence at a point
511.5.1 Maximum influence due to concentrated loads
511.5.2 Absolute maximum influence
531.5.3 Maximum influence due to uniform loads
571.6 Cases of loading and envelopes
58Chapter 2: Deformations of Statically Determinate Structures
2.1 Introduction
772.2 Double integration method
2.3 Moment-area method
1022.4 Conjugate beam method
1252.5 Castigiliano’s theorems
138Chapter 1: Statically Indeterminate Structures
1.1 Introduction
51.2 Advantages and disadvantages of indeterminate structures
61.2.1 Response to settlement of support
61.2.2 Response to changes in temperature
71.2.3 Response to tolerance problems during construction
71.2.4 Construction aspects
81.2.5 Behavior aspects
81.3 Redundancy
91.4 Boundary conditions
151.5 Compatibility
161.6 Degrees of freedom
161.7 Principle of superposition
171.8 Maxwell-Betti Theorem (Reciprocal Theorem)
181.9 Deformation of structures
191.10 Principle of virtual work
241.11 Methods for the solution of statically indet. structures
251.11.1 The compatibility method (the force method)
251.11.2 The equilibrium method (the displacement method)
26Chapter 2: Three-Moment Equation
2.1 Introduction
312.2 Derivation of three-moment equation
312.3 Sign conventions
342.4 Applications
35Chapter 3: Virtual Work Method
3.1 Introduction
513.2 Solution procedure using the virtual work method
513.3 Evaluation of integrals
543.4 Applications to statically in determinate beams
593.5 Applications to statically in determinate frames
71Chapter 4: Slope Deflection Method
4.1 Introduction
954.2 Sign conventions
964.2.1 Sign convention for deformation
964.2.2 Sign convention for end moment
974.3 Slope deflection equations of equilibrium
974.3.1 Member with two fixed ends
984.3.2 Member with a fixed end and a hinged end
1034.4 Applications to statically indeterminate beams
1074.5 Applications to statically indeterminate frames
112Chapter 5: Moment Distribution Method
5.1 Introduction
1375.2 Definition of terms
1385.2.1 Fixed end moment
1385.2.2 Stiffness (rotational stiffness factor)
1385.2.3 Distribution Factors
1425.2.4 Carry over factor
1435.3 Sign Convention
1435.4 Solution procedure using the moment distribution method
1445.5 Applications
1455.6 Structures having sway
1615.6.1 Solution as if the structure is restrained structure
1615.6.2 Sway correction
1625.6.3 Structures with multiple degrees of freedom
1635.7 Symmetrical and Anti-symmetrical structures
1705.7.1 Symmetrical structures with symmetrical loads
1725.7.2 Symmetrical structures with anti-symmetrical loads
1775.8 Effect of temperature change
1785.8.1 Uniform change of temperature
1785.8.2 Non-uniform change of temperature
179Chapter 1
1.1 Introduction
51.2 Advantages and disadvantages of indeterminate structures
61.3 Redundancy
91.4 Boundary conditions
101.5 Compatibility
111.6 Degrees of freedom
111.7 Methods for the solution of indeterminate structures
121.7.1 The compatibility method (the force method)
121.7.2 The equilibrium method (the displacement method)
13Chapter 2: Stiffness Method
2.1 Introduction
192.2 Assumptions
202.3 Sign convention
212.3.1 Sign convention for displacements
212.3.2 Sign convention for forces
212.4 Derivation of the element stiffness matrix
222.4.1 Plane frame element
232.4.2 Beam element
272.4.3 Truss (bar) element
282.5 Loads between nodes
292.6 Transformation matrix
302.7 Element stiffness matrix in global coordinates
332.8 Applications
39Chapter 3: Modeling
3.1 Introduction
993.2 Structural modeling
1003.3 Types of Elements
1013.4 Types of Boundary Elements
1043.5 Types of Materials
1043.5.1 Material Modeling Guidelines
1053.6 Types of Loads
1063.7 Modeling Discretization
1073.8 SAP2000
1083.9 Examples
109