TAILIEUCHUNG - Lecture Strength of Materials I: Chapter 7 - PhD. Tran Minh Tu

Lecture Strength of Materials I - Chapter 7: Bending. The following will be discussed in this chapter: Introduction, bending stress, shearing stress in bending, strength condition, sample problems, deflections of beam, statically indeterminate beams. | Lecture Strength of Materials I: Chapter 7 - PhD. Tran Minh Tu STRENGTH OF MATERIALS 1/10/2013 TRAN MINH TU - University of Civil Engineering, 1 Giai Phong Str. 55, Hai Ba Trung Dist. Hanoi, Vietnam CHAPTER 7 BENDING 1/10/2013 Contents . Introduction . Bending stress . Shearing stress in bending . Strength condition . Sample Problems . Deflections of beam . Statically indeterminate beams 1/10/2013 3 . Introduction In previous charters, we considered the stresses in the bars caused by axial loading and torsion. Here we introduce the third fundamental loading: bending. When deriving the relationship between the bending moment and the stresses causes, we find it again necessary to make certain simplifying assumptions. We use the same steps in the analysis of bending that we used for torsion in chapter 6. 1/10/2013 4 . Introduction Classification of Beam Supports 1/10/2013 5 . Introduction Limitation 1/10/2013 6 . Introduction Segment BC: Mx≠0, Qy=0 => Pure Bending Segments AB,CD: Mx≠0, Qy≠0 => Nonuniform Bending 1/10/2013 7 . Introduction Pure Bending: Prismatic members subjected to equal and opposite couples acting in the same longitudinal plane 1/10/2013 8 . Bending stress Simplifying assumptions 1/10/2013 9 . Bending stress The positive bending moment causes the material within the bottom portion of the beam to stretch and the material within the top portion to compress. Consequently, between these two regions there must be a surface, called the neutral surface, in which longitudinal fibers of Neutral axis the material will not undergo a change in length. 1/10/2013 10 . Bending stress Compatibility 1 2 Consider a segment of the beam a b bounded by two cross-sections that c y d are separated by the infinitesimal distance dz. dz 2 1 Due to bending moment Mx caused d Neutral fiber by

• Kiến trúc - Xây dựng
• Strength of Materials
• Sức bền vật liệu
• Bài giảng Sức bền vật liệu
• Bending stress
• Shearing stress
• Strength condition
• Finite element modelling
• Rectangular concrete filled steel tube stub columns incorporating high strength
• Ultra high strength materials
• Concentric axial compression
• Axial compression
• Theory and problems of strength of materials
• Statically indeterminate force systems tension
• Direct shear stresses
• Bending moment
• Moments of inertia
• Lecture Strength of materials
• Modulus of elasticity
• Statically indeterminate systems
• Statically indeterminate
• Stress transformation
• Plane stress state
• Transformation of plane stress
• Failure theories
• Permanently distorted
• Ductile material deforms
• Properties of cross sections
• Center of gravity – centroid
• Moment of Inertia of an area
• Radius of gyration
• Beam deflection
• Beam under transverse loading
• Statically indeterminate beams
• Torsional loads on circular shafts
• Torsion of noncircular members
• Helical spring under axial load
• Combined loading
• Eccentric axial loadings
• General combined loadings
• The secant formula
• Stability of structures
• Eccentric loadings
• Cementitious materials
• high strength concrete
• Strength required
• Placing procedures
• Splitting tensile strength
• Concentrically loaded columns
• Selected topics on strength
• The strength of materials
• Basic hypothesis
• Internal forces
• Three dimensional state
• Dimensional state
• Deflection of beams
• Torsional loads
• Circular shafts
• Engineering materials
• Their properties
• Price and availability
• The elastic moduli
• Yield strength
• Tensile strength
• Fast fracture
• Toughness and fatigue
• Mechanical engineering principles
• Forces acting at a point
• Forces in structures
• Analysis of stress
• The elastic limit
• Deflection of transversally leaded beams
• Statically indeterminate problems
• Energy of strain
• Combines bending
• Helical spring
• Close coiled
• Critical load
• Applied strength of materials
• Engineering stress
• Thermal expansion
• Properties of areas
• Torsion in round shafts
• Beam reactions
• Shear diagrams
• Moment diagrams
• Stresses in beams
• Combined stresses
• Visualizing stress
• Elastic deflection
• Double integration method
• Plastic deformations
• Mechanics and strength of materials
• The stress tensor
• The strain tensor
• Constitutive law
• Fundamental concepts
• Shear force
• Bending deflections
• Structural stability
• Energy theorems
• The total potential energy