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Euler's Formula to Columns: Problem Solving

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Euler's formula is used in structural engineering to determine the buckling load of columns under various conditions. However, when dealing with systems that incorporate both rigid elements and elastic components, such as springs, the analysis requires a finer approach to determine the critical load. The problem described involves two rigid bars connected at a pivot point with a spring attached and a vertical load applied at one end.
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Members Made of Elastoplastic Material

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The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.

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In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...

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Related Experiment Video

Updated: Jun 28, 2026

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Published on: April 11, 2018

Static progressive versus three-point elbow extension splinting: a mathematical analysis.

Shrikant J Chinchalkar¹, Joshua Pearce, George S Athwal

¹Hand and Upper Limb Center, St. Joseph's Health Care, London, ON, Canada. Shrikant.Chinchalkar@sjhc.london.on.ca

Journal of Hand Therapy : Official Journal of the American Society of Hand Therapists

|October 28, 2008

Summary

Three-point static progressive splinting offers superior rotational forces for elbow extension compared to standard static progressive splints. This method enhances treatment for elbow contractures, particularly in regaining terminal extension.

Related Experiment Videos

Last Updated: Jun 28, 2026

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion

Published on: April 11, 2018

Area of Science:

Orthopedic biomechanics
Rehabilitation engineering

Background:

Elbow joint contractures limit range of motion.
Static progressive splinting is common but less effective for terminal extension.
Regaining full elbow extension remains a clinical challenge.

Purpose of the Study:

To mathematically analyze forces in static progressive and three-point static progressive splints.
To compare the effectiveness of three-point static progressive splinting versus standard splinting for elbow extension.

Main Methods:

Mathematical analysis of compressive and rotational forces.
Comparison of force application between static progressive splints and three-point static progressive splints.

Main Results:

Three-point static progressive splinting applies greater rotational forces.
This enhanced force application is beneficial for terminal elbow extension.

Conclusions:

Three-point static progressive splinting is biomechanically superior for regaining terminal elbow extension.
This technique represents an advancement in treating elbow contractures.