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Chapter 20

Bending

Bending
Bending
Pure bending occurs when a prismatic member possesses a plane of symmetry and experiences couples of equal magnitudes acting within that plane. This type ...
Symmetric Member in Bending
Symmetric Member in Bending
Consider a prismatic member subjected to two couples, equal in magnitude but in opposite directions, acting within the symmetric plane of the member. A ...
Deformations in a Symmetric Member in Bending
Deformations in a Symmetric Member in Bending
Consider the deformations of a symmetric prismatic member subjected to equal and opposite couples. As the member bends uniformly, the lines on the wider ...
Flexural Stress
Flexural Stress
Consider a bending moment where a symmetric member endures stress within the elastic limit. The longitudinal stress can be expressed using Hooke's ...
Deformations in a Transverse Cross Section
Deformations in a Transverse Cross Section
When a material is subjected to uniaxial stress, the material undergoes elongation or contraction in the direction of the applied stress. At the same ...
Bending of Material: Problem Solving
Bending of Material: Problem Solving
Consider two metallic pipes having an inner radii of 1.5 cm and 1 cm, respectively, and an outer radii of 1.8 cm. If both pipes can withstand a maximum ...
Bending of Members Made of Several Materials
Bending of Members Made of Several Materials
Consider a member of two different materials that have the same cross-sectional area. The equation of stress for such a member is expressed in terms of ...
Stress Concentrations
Stress Concentrations
The equation for stress for a member under pure bending having a plane of symmetry and a uniform cross-section assumes that the stress is evenly ...
Plastic Deformations
Plastic Deformations
For pure bending, when maximum stress exceeds the yield strength of the member's material, it undergoes plastic deformation. The strain at any point ...
Members Made of Elastoplastic Material
Members Made of Elastoplastic Material
Consider a member made up of an elastoplastic material with a rectangular cross-section. Within the elastic limit, the stress distribution across the ...
Plastic Deformations of Members with a Single Plane of Symmetry
Plastic Deformations of Members with a Single Plane of Symmetry
Consider a member experiencing plastic deformation due to bending and having one plane of symmetry. The stresses are uniformly distributed above and below ...
Residual Stresses in Bending
Residual Stresses in Bending
If a sufficiently large bending moment is applied to an elastoplastic member, plastic zones will develop in the member. Now, if the bending moment is ...
Eccentric Axial Loading in a Plane of Symmetry
Eccentric Axial Loading in a Plane of Symmetry
Eccentric axial loading refers to the application of an axial load that is not aligned with the centroidal axis of the member. Consider a member having a ...
Unsymmetric Bending
Unsymmetric Bending
Unsymmetric bending occurs when the bending moment is not acting along the plane of the symmetry of the member or if the member does not possess any plane ...
Unsymmetric Bending - Angle of Neutral Axis
Unsymmetric Bending - Angle of Neutral Axis
Consider a member with a vertical plane of symmetry subjected to bending couples in a plane at an angle θ with respect to the vertical axis of the ...
General Case of Eccentric Axial Loading
General Case of Eccentric Axial Loading
Consider a member subjected to equal and opposite eccentric forces. These forces are applied at a horizontal distance of a and a vertical distance of b ...
Bending of Curved Members - Strain Analysis
Bending of Curved Members - Strain Analysis
Consider a curved member having a transverse section symmetric with the y-axis. Its upper and lower surfaces intersect with xy-planes along arcs of ...
Bending of Curved Members - Neutral Surface
Bending of Curved Members - Neutral Surface
For a curved member with a uniform cross-section, the strain equation along the section shows that it varies non-linearly with the distance from the ...
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