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Deformations in a Symmetric Member in Bending

Deformations in a Symmetric Member in Bending

When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
When the member is segmented into tiny cubic elements, it is observed that the primary stress...

Bending of Curved Members - Strain Analysis

Bending of Curved Members - Strain Analysis

The mechanics of deformation in curved members, such as beams or arches, under bending moments, involve complex responses. When such a member, symmetric about the y-axis and shaped like a segment of a circle centered at point C, is subjected to equal and opposite forces, its curvature and surface lengths change significantly. This alteration results in the shift of the curvature's center from C to C', indicating a tighter curve.
The important part of bending analysis for such a member...

Design of Prismatic Beams for Bending

Design of Prismatic Beams for Bending

The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and...

Plastic Deformations

Plastic Deformations

It is essential to understand how structural members behave under plastic deformation when the bending stress exceeds the material's yield strength. This state of deformation permanently alters the shape of the member, in contrast to the linear elastic behavior observed before yielding. The strain at any point in the member is expressed in terms of maximum strain. Notably, the neutral axis, which coincides with the centroid during elastic bending, shifts away from the centroid under plastic...

Plastic Deformations of Members with a Single Plane of Symmetry

Plastic Deformations of Members with a Single Plane of Symmetry

When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...

Bending of Curved Members - Neutral Surface

Bending of Curved Members - Neutral Surface

In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within...

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Related Experiment Video

Updated: Sep 27, 2025

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques

Author Spotlight: Development of a Novel Finite Element Analysis Model for Improved Orthognathic Surgical Techniques

Published on: October 20, 2023

The Development of B-Splines for CAD.

Richard F Riesenfeld, Chris Johnson, Dave Kasik

IEEE Computer Graphics and Applications

|April 13, 2022

Summary

Nonuniform B-splines, initially slow to adopt, are now the international standard for geometric representation in computer-aided design (CAD). This thesis explores their foundational applications in geometric problem-solving within CAD.

Area of Science:

Computer-aided design (CAD)
Geometric modeling
Spline approximation

Background:

The development of the author's doctoral thesis focused on B-spline approximation for geometric problems.
The computer-aided design industry has evolved significantly in its representation methods.

Purpose of the Study:

To describe the context, including people, events, and research, surrounding the creation of the thesis.
To highlight the significance of B-spline approximation in geometric problem-solving for CAD.

Main Methods:

Historical review of research activities and milieu.
Analysis of the adoption and impact of B-spline approximation in CAD.

Main Results:

Nonuniform B-splines have become the international de facto standard in the CAD industry.

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Last Updated: Sep 27, 2025

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Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

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The thesis laid groundwork for the widespread adoption of B-spline applications.

Conclusions:

B-spline approximation is a critical tool for geometric problems in CAD.
The research contributed to establishing nonuniform B-splines as a standard representation.