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Related Concept Videos

Method of Joints: Problem Solving II01:30

Method of Joints: Problem Solving II

Consider a truss structure with frictionless joints fixed to a wall and roller support. If a force of 150 N is applied to joint A, the forces in each member of the truss can be determined using the method of joints.
Method of Joints: Problem Solving I01:30

Method of Joints: Problem Solving I

The method of joints is a commonly used technique to analyze the forces in structural trusses. The method is based on the principle of equilibrium, which assumes that the truss members are connected by frictionless pins. The forces at each joint can be determined by considering the equilibrium of the forces acting on that joint. Consider a truss structure with two forces of 20 N and 10 N acting at joints C and D, respectively. The method of joints can be used to determine the forces FCB, FDC,...
Applications of Stress01:04

Applications of Stress

Consider a structure made of a boom and a rod designed to support a load. These two components are connected by a pin and stabilized by brackets and pins. The boom and the rod are detached from their supports to assess the different stresses imposed on this structure, and a free-body diagram is drawn. Then, all the forces applied, including the load acting on the structure, are identified. The reaction forces exerted on both the boom and the rod are computed using the equilibrium equations.
The...
Method of Sections: Problem Solving I01:27

Method of Sections: Problem Solving I

Consider a symmetrical roof truss structure, composed of vertical, diagonal, and horizontal members. The length of each horizontal member is 4 m. The lengths of the vertical members FB and HD are 4 m, while the length of member GC is 6 m. The loads acting at joints F, G, and H are 2 kN, while those at joints A and E are 1 kN.
Generalized Hooke's Law01:22

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
Method of Joints01:30

Method of Joints

The method of joints is a commonly used technique to analyze the forces in structural trusses. The method is based on the principle of equilibrium, which assumes that the truss members are connected by frictionless pins. The forces at each joint can be determined by considering the equilibrium of the forces acting on that joint.
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Related Experiment Video

Updated: May 13, 2026

Imaging of the Microstructural Failure Mechanism in the Human Hip
08:43

Imaging of the Microstructural Failure Mechanism in the Human Hip

Published on: September 29, 2023

A new discrete element analysis method for predicting hip joint contact stresses.

Christine L Abraham1, Steve A Maas, Jeffrey A Weiss

  • 1Harold K. Dunn Orthopaedic Research Laboratory, University of Utah School of Medicine, Salt Lake City, UT 84108, USA.

Journal of Biomechanics
|March 5, 2013
PubMed
Summary

Discrete element analysis (DEA) models hip osteoarthritis by simulating cartilage contact stress. Subject-specific geometry in DEA yields realistic contact patterns, offering a faster alternative to finite element analysis (FEA) for surgical planning.

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

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Area of Science:

  • Biomechanics
  • Orthopedics
  • Computational modeling

Background:

  • Quantifying cartilage contact stress is crucial for understanding hip osteoarthritis.
  • Discrete element analysis (DEA) is computationally efficient but previously underestimated stress and produced unrealistic patterns due to simplified geometry.
  • Subject-specific modeling is needed to improve DEA accuracy.

Purpose of the Study:

  • Develop a subject-specific DEA hip joint model.
  • Validate the DEA model against a validated finite element analysis (FEA) model.
  • Verify both models using a linear-elastic boundary value problem.

Main Methods:

  • Created a DEA model incorporating subject-specific bone and cartilage geometry.
  • Spring elements in DEA represented combined cartilage thickness and joint gap.
  • Simulated walking, descending, and ascending stairs under equivalent conditions to FEA.

Main Results:

  • DEA solution time was significantly faster (~7 s) than FEA (~65 min).
  • DEA accurately predicted complex, irregular contact patterns, closely matching FEA.
  • DEA showed slightly smaller contact areas but higher peak and average stresses than FEA.

Conclusions:

  • Subject-specific geometry in DEA enables realistic prediction of hip joint contact patterns.
  • DEA offers a computationally efficient alternative to FEA for pre-operative planning in joint-preserving surgeries.
  • DEA may aid in surgical planning for procedures like acetabular reorientation.