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Indeterminate Structure

Indeterminate Structure

Indeterminate structures refer to structures where internal forces and reactions cannot be determined using only the equations of static equilibrium. Indeterminate structures have more unknown forces and reaction forces than equations of static equilibrium that can be used to determine them. Indeterminate structures are often used in engineering to create complex, efficient, and aesthetically pleasing structures. There are various types of indeterminate structures used in engineering and some...

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

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.

Bending of Members Made of Several Materials

Bending of Members Made of Several Materials

In analyzing a structural member composed of two different materials with identical cross-sectional areas, it is crucial to understand how their distinct elastic properties affect the member's response under load. The analysis involves assessing stress and strain distributions using the transformed section concept, which accounts for variations in material properties.
Hooke's Law determines stress in each material, stating that stress is proportional to strain but varies due to each material's...

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...

Unsymmetric Loading of Thin-Walled Members: Problem Solving

Unsymmetric Loading of Thin-Walled Members: Problem Solving

The shear center of a channel section with uniform thickness, height, and width, is determined by computing the shear force in the member and calculating the moments of inertia of the sections.
To compute the shear forces, find the shear flow at a specific distance from the endpoint using the vertical shear and the moment of inertia values. The total shear force on the flange is calculated by integrating the shear flow from one end of the flange to the other.
Next, calculate the moments of...

Three-Dimensional Analysis of Strain

Three-Dimensional Analysis of Strain

Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...

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Related Experiment Video

Updated: Jun 19, 2026

An In Vitro Organ Culture Model of the Murine Intervertebral Disc

An In Vitro Organ Culture Model of the Murine Intervertebral Disc

Published on: April 11, 2017

[Finite element modeling and simulation study of solid-liquid biphase fiber-reinforced lumbar intervertebral disc].

Yongchang Gao¹, Yantao Fu¹, Qingfeng Cui¹

¹National Engineering Laboratory for Highway Maintenance Equipment, Chang'an University, Xi'an 710064, P. R. China.

Sheng Wu Yi Xue Gong Cheng Xue Za Zhi = Journal of Biomedical Engineering = Shengwu Yixue Gongchengxue Zazhi

|August 31, 2025

Summary

This study introduces a new solid-liquid biphasic model for lumbar intervertebral discs. The model accurately simulates daily movements, revealing the crucial roles of fluid and solid phases in load-bearing.

Keywords:

Fiber-reinforced Finite element analysis Fluid support ratio Lumbar intervertebral disc Solid-liquid biphasic

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Last Updated: Jun 19, 2026

An In Vitro Organ Culture Model of the Murine Intervertebral Disc

An In Vitro Organ Culture Model of the Murine Intervertebral Disc

Published on: April 11, 2017

A Proinflammatory, Degenerative Organ Culture Model to Simulate Early-Stage Intervertebral Disc Disease.

A Proinflammatory, Degenerative Organ Culture Model to Simulate Early-Stage Intervertebral Disc Disease.

Published on: February 14, 2021

Optical Sectioning and Visualization of the Intervertebral Disc from Embryonic Development to Degeneration

Optical Sectioning and Visualization of the Intervertebral Disc from Embryonic Development to Degeneration

Published on: July 8, 2021

Area of Science:

Biomechanics
Biomaterials Science
Computational Modeling

Context:

The lumbar intervertebral disc's mechanical properties are critically influenced by dynamic water content changes.
Previous isotropic models failed to capture the complex solid-liquid phase behaviors of the disc.
Understanding these behaviors is key to exploring the disc's load-bearing mechanism.

Purpose:

To develop a more realistic mechanical model of the lumbar intervertebral disc.
To explore the load-bearing mechanism of the lumbar intervertebral disc.
To simulate the four movements of the human lumbar spine using a novel model.

Summary:

A solid-liquid biphasic, fiber-reinforced finite element model was developed to simulate lumbar intervertebral disc movements.
Analysis revealed fluid pressure concentrates in the nucleus pulposus and solid stress in the annulus fibrosus.
Lateral bending induced maximum fluid pressure, while flexion resulted in maximum solid stress.

Impact:

This study provides a more accurate understanding of the lumbar intervertebral disc's load-bearing mechanisms.
It highlights the dominant role of the liquid phase in daily load-bearing.
The findings advance the prediction of solid-liquid phase co-load-bearing in the lumbar intervertebral disc.