Elastic Beam Calculations Handbook

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.

• ForewordPrefaceAcknowledgments1BASIC THEORY2SIMPLE BEAMS: AN INTRODUCTION TO THE GENERAL APPROACH2.1A Concentrated Force at an Arbitrary Point of the Span2.2Uniform Load2.3Triangular Load on Part of the Span2.4Triangular Load on the Entire Span2.5General Load Intensity Functions and Applications2.6A Concentrated Couple at an Arbitrary Point of the Span2.7The Principle of Superposition and Load Combinations2.8Explorations and Observations3CONTINUOUS BEAMS3.1Two Span Continuous Beams3.1.1A Concentrated Force at an Arbitrary Point of the Beam3.1.2An Alternative Approach to the Problem of Concentrated Force3.1.3Generic Problem, Arbitrary Load and the Principle of Superposition - A Regression3.1.4Uniform Load on One Span: General Case3.1.5Uniform Load on One Span: Special Case with Equal Span Lengths3.1.6Uniform Load on One Span: Special Case with Constant Material and Section Properties3.1.7Uniform Load on One Span: Special Case with Constant Material and Geometric Characteristics3.1.8Triangular Load on One Span: General Case3.1.9Triangular Load on One Span: Special Case with Equal Span Lengths3.1.10Triangular Load on One Span: Special Case with Constant Material and Section Properties3.1.11Triangular Load on One Span: Special Case with Constant Material and Geometric Characteristics3.1.12A Concentrated Couple at an Arbitrary Point of a Span3.2Three Span Continuous Beams3.2.1A Concentrated Force at an Arbitrary Point of an Exterior Span3.2.2Arbitrarily Distributed Load on an Exterior Span3.2.3Uniform Load on an Exterior Span3.2.4An Alternative Treatment of the Problem of Uniform Load on an Exterior Span3.2.5Triangular Load on an Exterior Span3.2.6A Concentrated Couple at an Arbitrary Point of an Exterior Span3.2.7A Concentrated Force at an Arbitrary Point of the Interior Span3.2.8Uniform Load on the Interior Span3.2.9Triangular Load on the Interior Span4BEAMS ON ELASTIC FOUNDATIONS4.1Beams of Infinite Length4.1.1A Concentrated Force on the Beam4.1.2Uniform Load on the Beam4.2Beams of Semi-infinite Length4.2.1A Concentrated Force and Moment Acting at the End of the Beam4.2.2Uniform Load on the Beam with a Simply Supported End4.2.3Uniform Load on the Beam with a Fixed End5CANTILEVERS5.1Introduction5.2Uniform Load on Part of the Span5.3Triangular Load on Part of the Span5.4General Load Intensity Functions with Applications5.5A Concentrated Couple at an Arbitrary Point of the Span5.6Explorations and Observations 6EXAMPLES OF BEAM FORMULAE: EXPLORATION AND COMMENTARY6.1Introduction6.2Uniform Load on One Span of a Two Span Continuous Beam: General Case6.3Triangular Load on One Span of a Two Span Continuous Beam: General Case6.4A Concentrated Couple at an Arbitrary Point on a Two Span Continuous Beam: General Case6.5A Concentrated Force at an Arbitrary Point of an Exterior Span of a Three Span Continuous Beam: General Case6.6Uniform Load on an Exterior Span of a Three Span Continuous Beam: General Case6.7Triangular Load on an Exterior Span of a Three Span Continuous Beam: General Case6.8A Concentrated Couple at an Arbitrary Point of an Exterior Span of a Three Span Continuous Beam: General Case6.9Uniform Load on the Interior Span of a Three Span Continuous Beam: General Case6.10Triangular Load on the Interior Span of a Three Span Continuous Beam: General Case6.11A Concentrated Force at an Arbitrary Point of an Exterior Span of a Three Span Continuous Beam: Constant J6.12A Concentrated Force at an Arbitrary Point of an Exterior Span of a Three Span Continuous Beam: Constant Span Length6.13Uniform Load on an Exterior Span of a Three Span Continuous Beam: Constant J6.14Uniform Load on an Exterior Span of a Three Span Continuous Beam: Constant Span Length6.15Triangular Load on an Exterior Span of a Three Span Continuous Beam: Constant J6.16Triangular Load on an Exterior Span of a Three Span Continuous Beam: Constant Span Length6.17A Concentrated Couple at an Arbitrary Point of an Exterior Span of a Three Span Continuous Beam: Constant J6.18A Concentrated Couple at an Arbitrary Point of an Exterior Point of a Three Span Continuous Beam: Constant Span Length6.19A Concentrated Force at an Arbitrary Point of the Interior Span of a Three Span Continuous Beam: Constant J6.20A Concentrated Force at an Arbitrary Point of the Interior Span of a Three Span Continuous Beam: Constant Span Length6.21Uniform Load on the Interior Span of a Three Span Continuous Beam: Constant J6.22Uniform Load on the Interior Span of a Three Span Continuous Beam: Constant Span Length6.23Triangular Load on the Interior Span of a Three Span Continuous Beam: Constant J6.24Triangular Load on the Interior Span of a Three Span Continuous Beam: Constant Span Length6.25Two Span Continuous Beams with Symmetry6.26Four Span Continuous Beams with Symmetry6.27Principle of Superposition6.28Possible Directions for Future WorkAppendicesA. Some Properties of Ej - a EkB. Some Relations Among Ej , (j = 2 , 3 , 4 , 5 ,) C. Proof of S > 0, Upper and Lower Bounds for the Entity S in Section 60D. Upper and Lower Bounds for T in Section 60E. Upper and Lower Bounds for R4 in Section 61F. Single Span Beams with a Fixed End and a Simply Supported End