# 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

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

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

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

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

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

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

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

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

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

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

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 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 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

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 …

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

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

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 …

## A Bending Test for Determining the Atterberg Plastic Limit in Soils

The thread rolling test is the most commonly used method to determine the plastic limit (PL) in soils. It has been widely criticized, because a …

## A Novel Biaxial Testing Apparatus for the Determination of Forming Limit under Hot Stamping Conditions

The hot stamping and cold die quenching process is increasingly used to form complex shaped structural components of sheet metals. Conventional …

## Ultrasonic Fatigue Testing in the Tension-Compression Mode

Ultrasonic fatigue testing is one of a few methods which allow investigating fatigue properties in the ultra-high cycle region. The method is based on …