The Elastic Beam Calculations Handbook presents a concise, yet mathematically rigorous treatment of beams based on elastic theory written at a clear technical level in order that practitioners can quickly learn the essentials and apply elastic beam calculations in their work. This much-needed comprehensive reference covers elastic beams with varying material and section properties, support conditions, span lengths, and other important geometric features. It provides simple and logical presentations of elastic beam problems by addressing each as corollaries of a more general theorem, consequently resulting in numerical work that can be planned and executed with ease, clarity, and optimal results. Structural engineers concerned directly with structural analysis of elastic beam problems will find many examples of useful and neat solutions and the rationale for their validity.
1 BASIC THEORY
2 SIMPLE BEAMS: AN INTRODUCTION TO THE GENERAL APPROACH
2.1 A Concentrated Force at an Arbitrary Point of the Span
2.2 Uniform Load
2.3 Triangular Load on Part of the Span
2.4 Triangular Load on the Entire Span
2.5 General Load Intensity Functions and Applications
2.6 A Concentrated Couple at an Arbitrary Point of the Span
2.7 The Principle of Superposition and Load Combinations
2.8 Explorations and Observations
3 CONTINUOUS BEAMS
3.1 Two Span Continuous Beams
3.1.1 A Concentrated Force at an Arbitrary Point of the Beam
3.1.2 An Alternative Approach to the Problem of Concentrated Force
3.1.3 Generic Problem, Arbitrary Load and the Principle of Superposition – A Regression
3.1.4 Uniform Load on One Span: General Case
3.1.5 Uniform Load on One Span: Special Case with Equal Span Lengths
3.1.6 Uniform Load on One Span: Special Case with Constant Material and Section Properties
3.1.7 Uniform Load on One Span: Special Case with Constant Material and Geometric Characteristics
3.1.8 Triangular Load on One Span: General Case
3.1.9 Triangular Load on One Span: Special Case with Equal Span Lengths
3.1.10 Triangular Load on One Span: Special Case with Constant Material and Section Properties
3.1.11 Triangular Load on One Span: Special Case with Constant Material and Geometric Characteristics
3.1.12 A Concentrated Couple at an Arbitrary Point of a Span
3.2 Three Span Continuous Beams
3.2.1 A Concentrated Force at an Arbitrary Point of an Exterior Span
3.2.2 Arbitrarily Distributed Load on an Exterior Span
3.2.3 Uniform Load on an Exterior Span
3.2.4 An Alternative Treatment of the Problem of Uniform Load on an Exterior Span
3.2.5 Triangular Load on an Exterior Span
3.2.6 A Concentrated Couple at an Arbitrary Point of an Exterior Span
3.2.7 A Concentrated Force at an Arbitrary Point of the Interior Span
3.2.8 Uniform Load on the Interior Span3.2.9 Triangular Load on the Interior Span
4 BEAMS ON ELASTIC FOUNDATIONS
4.1 Beams of Infinite Length
4.1.1 A Concentrated Force on the Beam
4.1.2 Uniform Load on the Beam
4.2 Beams of Semi-infinite Length
4.2.1 A Concentrated Force and Moment Acting at the End of the Beam
4.2.2 Uniform Load on the Beam with a Simply Supported End
4.2.3 Uniform Load on the Beam with a Fixed End
5 CANTILEVERS
5.1 Introduction
5.2 Uniform Load on Part of the Span
5.3 Triangular Load on Part of the Span
5.4 General Load Intensity Functions with Applications
5.5 A Concentrated Couple at an Arbitrary Point of the Span
5.6 Explorations and Observations
6 EXAMPLES OF BEAM FORMULAE: EXPLORATION AND COMMENTARY6.1 Introduction
6.2 Uniform Load on One Span of a Two Span Continuous Beam: General Case
6.3 Triangular Load on One Span of a Two Span Continuous Beam: General Case
6.4 A Concentrated Couple at an Arbitrary Point on a Two Span Continuous Beam: General Case
6.5 A Concentrated Force at an Arbitrary Point of an Exterior Span of a Three Span Continuous Beam: General Case
6.6 Uniform Load on an Exterior Span of a Three Span Continuous Beam: General Case
6.7 Triangular Load on an Exterior Span of a Three Span Continuous Beam: General Case
6.8 A Concentrated Couple at an Arbitrary Point of an Exterior Span of a Three Span Continuous Beam: General Case
6.9 Uniform Load on the Interior Span of a Three Span Continuous Beam: General Case
6.10 Triangular Load on the Interior Span of a Three Span Continuous Beam: General Case
6.11 A Concentrated Force at an Arbitrary Point of an Exterior Span of a Three Span Continuous Beam: Constant J
6.12 A Concentrated Force at an Arbitrary Point of an Exterior Span of a Three Span Continuous Beam: Constant Span Length
6.13 Uniform Load on an Exterior Span of a Three Span Continuous Beam: Constant J
6.14 Uniform Load on an Exterior Span of a Three Span Continuous Beam: Constant Span Length
6.15 Triangular Load on an Exterior Span of a Three Span Continuous Beam: Constant J
6.16 Triangular Load on an Exterior Span of a Three Span Continuous Beam: Constant Span Length
6.17 A Concentrated Couple at an Arbitrary Point of an Exterior Span of a Three Span Continuous Beam: Constant J
6.18 A Concentrated Couple at an Arbitrary Point of an Exterior Point of a Three Span Continuous Beam: Constant Span Length
6.19 A Concentrated Force at an Arbitrary Point of the Interior Span of a Three Span Continuous Beam: Constant J
6.20 A Concentrated Force at an Arbitrary Point of the Interior Span of a Three Span Continuous Beam: Constant Span Length
6.21 Uniform Load on the Interior Span of a Three Span Continuous Beam: Constant J
6.22 Uniform Load on the Interior Span of a Three Span Continuous Beam: Constant Span Length
6.23 Triangular Load on the Interior Span of a Three Span Continuous Beam: Constant J
6.24 Triangular Load on the Interior Span of a Three Span Continuous Beam: Constant Span Length
6.25 Two Span Continuous Beams with Symmetry
6.26 Four Span Continuous Beams with Symmetry
6.27 Principle of Superposition
6.28 Possible Directions for Future Work
Appendices
A. Some Properties of Ej – a Ek
B. Some Relations Among Ej , (j = 2 , 3 , 4 , 5 ,)
C. Proof of S > 0, Upper and Lower Bounds for the Entity S in Section 60
D. Upper and Lower Bounds for T in Section 60
E. Upper and Lower Bounds for R4 in Section 61
F. Single Span Beams with a Fixed End and a Simply Supported End
Dr. Jih-Jiang Chyu, P.E., Fellow ASCE, Member NYAS, holding MS and Eng. Sc. D. Degrees in Civil Engineering and Engineering Mechanics from Columbia University, is a registered professional engineer with four decades of professional experience in both consulting engineering encompassing design and research of bridges, buildings, and special structures in addition to teaching engineering and mathematics. Dr. Chyu has been an active participant of ASCE programs over the course of his career.