TAILIEUCHUNG - Lecture Mechanics of materials (Third edition) - Chapter 9: Deflection of beams

The following will be discussed in this chapter: Deformation of a beam under transverse loading, equation of the elastic curve, direct determination of the elastic curve from the load di, statically indeterminate beams, application of superposition to statically indeterminate, moment-area theorems,. | Third Edition CHAPTER MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Deflection of Beams Lecture Notes: J. Walt Oler Texas Tech University © 2002 The McGraw-Hill Companies, Inc. All rights reserved. Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Deflection of Beams Deformation of a Beam Under Transverse Loading Equation of the Elastic Curve Direct Determination of the Elastic Curve From the Load Di. Statically Indeterminate Beams Sample Problem Sample Problem Moment-Area Theorems Application to Cantilever Beams and Beams With Symmetric . Bending Moment Diagrams by Parts Sample Problem Sample Problem Application of Moment-Area Theorems to Beams With Unsymme. Method of Superposition Maximum Deflection Sample Problem Use of Moment-Area Theorems With Statically Indeterminate. Application of Superposition to Statically Indeterminate . © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 9-2 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Deformation of a Beam Under Transverse Loading • Relationship between bending moment and curvature for pure bending remains valid for general transverse loadings. 1 ρ = M ( x) EI • Cantilever beam subjected to concentrated load at the free end, 1 ρ =− Px EI • Curvature varies linearly with x 1 • At the free end A, ρ = 0, A • At the support B, © 2002 The McGraw-Hill Companies, Inc. All rights reserved. 1 ρB ρA = ∞ ≠ 0, ρ B = EI PL 9-3 Third Edition MECHANICS OF MATERIALS Beer • Johnston • DeWolf Deformation of a Beam Under Transverse Loading • Overhanging beam • Reactions at A and C • Bending moment diagram • Curvature is zero at points where the bending moment is zero, ., at each end and at E. 1 ρ = M ( x) EI • Beam is concave upwards where the bending moment is positive and concave downwards where it is negative. • Maximum curvature occurs where the moment magnitude is a maximum. • An .

• Kiến trúc - Xây dựng
• Mechanics of materials
• Cơ học vật liệu
• Lecture Mechanics of materials
• Deflection of beams
• Elastic curve
• Statically indeterminate beams
• Composite materials
• Mechanics of composite materials
• Mechanics of composite materials with MATLAB
• Effective elastic constants
• Homogenization of composite materials
• Introduction to damage mechanics
• Mechanical properties of materials
• Material impact on deformation
• Rectangular cross section
• Elastic and plastic regions
• Tension test
• Material constants
• Modulus of elasticity
• Logic in structural analysis
• Mechanics materials
• Recycling fiber reinforced composites
• Macromechanical analysis of a lamina
• Fracture mechanics
• mechanics
• racks in materials
• analytical solid mechanics
• modern materials science
• macroscopic mechanical
• Structure free body diagram
• Component free body diagram
• Method of joints
• Axial loading
• Normal strain
• Stress strain test
• Torsional loads
• Axial shear components
• Shaft deformations
• Pure bending
• Symmetric member
• Bending deformations
• Beams for bending
• Bending moment diagrams
• Bending moment
• Shearing stresses in beams
• Thinwalled members
• Beam element
• Transformations of stress
• Transformation of plane stress
• Maximum shearing stress
• Principle stresses
• Transmission shaft
• Stresses under combined loadings
• Stability of structures
• Pin ended beams
• Eccentric loading
• Energy methods
• Strain energy
• Strain energy density
• Torsion of Shafts
• Internal Torque
• Homogeneous cross section
• Concept of stress
• Stress on a surface
• Tensile stress
• Contructions of stress element
• Stress components
• Concept of strain
• Lagrangian strain
• Eulerian strain
• Preliminary definitions
• Average normal strain
• Average shear strain
• Axial members
• Prelude to theory
• Internal axial force
• Strain distribution
• Material model
• Axial formulas
• Theory for circular shafts
• Torsion formulas
• Circular cross section