Bending moment

About: Bending moment is a research topic. Over the lifetime, 14577 publications have been published within this topic receiving 158834 citations. The topic is also known as: bending moment.

Axial Load–Moment Interaction Diagram of Circular Concrete Columns Reinforced with CFRP Bars and Spirals: Experimental and Theoretical Investigations

Abstract: North America’s current design codes and guidelines allow the use of fiber–reinforced polymer (FRP) bars as the primary reinforcement in concrete structures and provide design recommendations for using these bars. Because of a lack of experimental data, however, FRP bars have not been recommended for resisting compression stresses as longitudinal reinforcement in columns or compression reinforcement in flexural elements. This paper presents test results of an experimental program to investigate the structural performance of 10 full-scale circular concrete columns reinforced with carbon fiber–reinforced polymer (CFRP) bars and spirals subjected to combined axial compression loads and bending moments. The test variables include different eccentricity-to-diameter ratios and two types of reinforcement (CFRP and steel). The test results show that the CFRP- and steel-reinforced concrete columns behaved similarly up to their peak loads. The failure of the test specimens under different levels of eccentri...

Hysteretic shear–flexure interaction model of reinforced concrete columns for seismic response assessment of bridges

Abstract: This paper presents the methodology, model description, and calibration as well as the application of a coupled hysteretic model to account for nonlinear shear–flexure interactive behavior of RC columns under earthquakes, a critical consideration for seismic demand evaluation of bridges. The proposed hysteretic model consists of a flexure and a shear spring coupled at element level, whose nonlinear behavior are governed by the primary curves and a set of loading/unloading rules to capture the pinching, stiffness softening, and strength deterioration of columns due to combined effects of axial load, shear force, and bending moment. The shear–flexure interaction (SFI) is considered both at section level when theoretically generating the primary curves and at element level through global and local equilibrium. The model is implemented in a displacement-based finite element framework and calibrated against a large number of column specimens from static cyclic tests to dynamic shake table tests. The numerical predictions by the proposed model show very good agreement with experimental data for both flexure- and shear-dominated columns. The application of the proposed model for seismic assessment of bridges has been successfully demonstrated for a realistic prototype bridge. The factors affecting the SFI and its significance on bridge system response are also discussed. Copyright © 2010 John Wiley & Sons, Ltd.

Applied Strength of Materials

Abstract: Preface 1 Basic Concepts in Strength of Materials The Big Picture 1-1 Objective of This Book - To Ensure Safety 1-2 Objectives of This Chapter 1-3 Problem-solving Procedure 1-4 Basic Unit Systems 1-5 Relationship Among Mass, Force, and Weight 1-6 The Concept of Stress 1-7 Direct Normal Stress 1-8 Stress Elements for Direct Normal Stresses 1-9 The Concept of Strain 1-10 Direct Shear Stress 1-11 Stress Element for Shear Stresses 1-12 Preferred Sizes and Standard Shapes 1-13 Experimental and Computational Stress 2 Design Properties of Materials The Big Picture 2-1 Objectives of This Chapter 2-2 Design Properties of Materials 2-3 Steel 2-4 Cast Iron 2-5 Aluminum 2-6 Copper, Brass, and Bronze 2-7 Zinc, Magnesium, Titanium, and Nickel-Based Alloys 2-8 Nonmetals in Engineering Design 2-9 Wood 2-10 Concrete 2-11 Plastics 2-12 Composites 2-13 Materials Selection 3 Direct Stress, Deformation, and Design The Big Picture and Activity 3-1 Objectives of this Chapter 3-2 Design of Members under Direct Tension or Compression 3-3 Design Normal Stresses 3-4 Design Factor 3-5 Design Approaches and Guidelines for Design Factors 3-6 Methods of Computing Design Stress 3-7 Elastic Deformation in Tension and Compression Members 3-8 Deformation Due to Temperature Changes 3-9 Thermal Stress 3-10 Members Made of More Than One Material 3-11 Stress Concentration Factors for Direct Axial Stresses 3-12 Bearing Stress 3-13 Design Bearing Stress 3-14 Design Shear Stress 4 Torsional Shear Stress and Torsional Deformation The Big Picture 4-1 Objectives of This Chapter 4-2 Torque, Power, and Rotational Speed 4-3 Torsional Shear Stress in Members with Circular Cross Sections 4-4 Development of the Torsional Shear Stress Formula 4-5 Polar Moment of Inertia for Solid Circular Bars 4-6 Torsional Shear Stress and Polar Moment of Inertia for Hollow Circular Bars 4-7 Design of Circular Members under Torsion 4-8 Comparison of Solid and Hollow Circular Members 4-9 Stress Concentrations in Torsionally Loaded Members 4-10 Twisting - Elastic Torsional Deformation 4-11 Torsion in Noncircular Sections 5 Shearing Forces and Bending Moments in Beams The Big Picture 5-1 Objectives of this Chapter 5-2 Beam Loading, Supports, and Types of Beams 5-3 Reactions at Supports 5-4 Shearing Forces and Bending Moments for Concentrated Loads 5-5 Guidelines for Drawing Beam Diagrams for Concentrated Loads 5-6 Shearing Forces and Bending Moments for Distributed Loads 5-7 General Shapes Found in Bending Moment Diagrams 5-8 Shearing Forces and Bending Moments for Cantilever Beams 5-9 Beams with Linearly Varying Distributed Loads 5-10 Free-Body Diagrams of Parts of Structures 5-11 Mathematical Analysis of Beam Diagrams 5-12 Continuous Beams - Theorem of Three Moments 6 Centroids and Moments of Inertia of Areas The Big Picture 6-1 Objectives of This Chapter 6-2 The Concept of Centroid - Simple Shapes 6-3 Centroid of Complex Shapes 6-4 The Concept of Moment of Inertia 6-5 Moment of Inertia for Composite Shapes Whose Parts have the Same Centroidal Axis 6-6 Moment of Inertia for Composite Shapes - General Case - Use of the Parallel Axis Theorem 6-7 Mathematical Definition of Moment of Inertia 6-8 Composite Sections Made from Commercially Available Shapes 6-9 Moment of Inertia for Shapes with all Rectangular Parts 6-10 Radius of Gyration 6-11 Section Modulus 7 Stress Due to Bending The Big Picture 7-1 Objectives of This Chapter 7-2 The Flexure Formula 7-3 Conditions on the Use of the Flexure Formula 7-4 Stress Distribution on a Cross Section of a Beam 7-5 Derivation of the Flexure Formula 7-6 Applications - Beam Analysis 7-7 Applications - Beam Design and Design Stresses 7-8 Section Modulus and Design Procedures 7-9 Stress Concentrations 7-10 Flexural Center or Shear Center 7-11 Preferred Shapes for Beam Cross Sections 7-12 Design of Beams to be Made from Composite Materials 8 Shearing Stresses in Beams The Big Picture 8-1 Objectives of this Chapter 8-2 Importance of Shearing Stresses in Beams 8-3 The General Shear Formula 8-4 Distribution of Shearing Stress in Beams 8-5 Development of the General Shear Formula 8-6 Special Shear Formulas 8-7 Design for Shear 8-8 Shear Flow 9 Deflection of Beams The Big Picture 9-1 Objectives of this Chapter 9-2 The Need for Considering Beam Deflections 9-3 General Principles and Definitions of Terms 9-4 Beam Deflections Using the Formula Method 9-5 Comparison of the Manner of Support for Beams 9-6 Superposition Using Deflection Formulas 9-7 Successive Integration Method 9-8 Moment-Area Method 10 Combined Stresses The Big Picture 10-1 Objectives of this Chapter 10-2 The Stress Element 10-3 Stress Distribution Created by Basic Stresses 10-4 Creating the Initial Stress Element 10-5 Combined Normal Stresses 10-6 Combined Normal and Shear Stresses 10-7 Equations for Stresses in Any Direction 10-8 Maximum Stresses 10-9 Mohr's Circle for Stress 10-10 Stress Condition on Selected Planes 10-11 Special Case in which Both Principal Stresses have the Same Sign 10-12 Use of Strain-Gage Rosettes to Determine Principal Stresses 11 Columns The Big Picture 11-1 Objectives of this Chapter 11-2 Slenderness Ratio 11-3 Transition Slenderness Ratio 11-4 The Euler Formula for Long Columns 11-5 The J. B. Johnson Formula for Short Columns 11-6 Summary - Buckling Formulas 11-7 Design Factors and Allowable Load 11-8 Summary - Method of Analyzing Columns 11-9 Column Analysis Spreadsheet 11-10 Efficient Shapes for Columns 11-11 Specifications of the AISC 11-12 Specifications of the Aluminum Association 11-13 Non-Centrally Loaded Columns 12 Pressure Vessels The Big Picture 12-1 Objectives of this Chapter 12-2 Distinction Between Thin-Walled and Thick-Walled Pressure Vessels 12-3 Thin-Walled Spheres 12-4 Thin-Walled Cylinders 12-5 Thick-Walled Cylinders and Spheres 12-6 Analysis and Design Procedures for Pressure Vessels 12-7 Spreadsheet Aid for Analyzing Thick-Walled Spheres and Cylinders 12-8 Shearing Stress in Cylinders and Spheres 12-9 Other Design Considerations for Pressure Vessels 12-10 Composite Pressure Vessels 13 Connections The Big Picture 13-1 Objectives of this Chapter 13-2 Modes of Failure 13-3 Riveted Connections 13-4 Bolted Connections 13-5 Allowable Stresses for Riveted and Bolted Connections 13-6 Example Problems - Riveted and Bolted Joints 13-7 Eccentrically Loaded Riveted and Bolted Joints 13-8 Welded Joints with Concentric Loads Appendix Answers to Selected Problems Index