Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Kirchhoff's Current Law01:04

Kirchhoff's Current Law

In the realm of electrical engineering, physicist Gustav Robert Kirchhoff made a significant contribution in 1847 by introducing Kirchhoff's laws for electric circuit analysis. These laws, particularly Kirchhoff's Current Law (KCL), have become foundational principles in understanding and analyzing electrical circuits.
Kirchhoff's Current Law is based on the principle of charge conservation. It states that at any node (a point where two or more circuit elements meet) in an electrical circuit,...
Kirchhoff's Voltage Law01:04

Kirchhoff's Voltage Law

Kirchhoff's Voltage Law (KVL) is another fundamental principle in electrical engineering, introduced by physicist Gustav Robert Kirchhoff. This law is rooted in the principle of energy conservation, which states that energy can neither be created nor destroyed, only transferred or converted from one form to another.
KVL states that the algebraic sum of all voltages around a closed path or loop within a circuit is zero. This means that the total voltage supplied in a loop is equal to the total...
Kirchhoff's Rules01:21

Kirchhoff's Rules

Gustav Kirchhoff (1824–1887) devised two rules known as Kirchhoff's rules to analyze complex circuits, which cannot be analyzed with series-parallel techniques. These rules can be used to analyze any circuit, simple or complex.
Kirchhoff's first rule is called the junction rule. A junction, also known as a node, is a connection of three or more wires. The rule states that the sum of all currents entering a junction must equal the sum of all currents leaving the junction.
Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...
Stability of structures01:14

Stability of structures

In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
Temperature Dependent Deformation01:12

Temperature Dependent Deformation

In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added together...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

[Clinical investigation of in-stent restenosis following self-expanding intracranial artery stenting].

Zhonghua nei ke za zhi·2026
Same author

[The role and molecular mechanism of transcription factor EB and its target genes in multiple myeloma treatment with bortezomib].

Zhonghua xue ye xue za zhi = Zhonghua xueyexue zazhi·2025
Same author

[Feasibility of polyetheretherketone loaded with bone morphogenetic protein 2 for orbital fracture repair].

[Zhonghua yan ke za zhi] Chinese journal of ophthalmology·2025
Same author

[Prevalence and risk factors of food allergies among children in North China grassland: a cross-sectional study based on Zhangbei County, Hebei Province].

Zhonghua yu fang yi xue za zhi [Chinese journal of preventive medicine]·2025
Same author

[Analysis of perioperative complications of flow-diverter devices in the treatment of unruptured intracranial aneurysms].

Zhonghua wai ke za zhi [Chinese journal of surgery]·2024
Same author

[Advances in diagnosis and subtyping of Gaucher disease & assessment and monitoring of neurological symptoms].

Zhonghua nei ke za zhi·2024

Related Experiment Video

Updated: Jun 8, 2026

A Millimeter Scale Flexural Testing System for Measuring the Mechanical Properties of Marine Sponge Spicules
11:25

A Millimeter Scale Flexural Testing System for Measuring the Mechanical Properties of Marine Sponge Spicules

Published on: October 11, 2017

Size effects in Kirchhoff flexible rods.

R J Zhang1

  • 1School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China. zhangrj@tongji.edu.cn

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

The Kirchhoff equations for flexible rods now account for size effects, applicable from macroscopic to ultrathin scales. Thinner rods require greater forces for the same deformation, revealing extensional size effects.

More Related Videos

Force System with Vertical V-Bends: A 3D In Vitro Assessment of Elastic and Rigid Rectangular Archwires
08:46

Force System with Vertical V-Bends: A 3D In Vitro Assessment of Elastic and Rigid Rectangular Archwires

Published on: July 24, 2018

Effect of Bending on the Electrical Characteristics of Flexible Organic Single Crystal-based Field-effect Transistors
08:43

Effect of Bending on the Electrical Characteristics of Flexible Organic Single Crystal-based Field-effect Transistors

Published on: November 7, 2016

Related Experiment Videos

Last Updated: Jun 8, 2026

A Millimeter Scale Flexural Testing System for Measuring the Mechanical Properties of Marine Sponge Spicules
11:25

A Millimeter Scale Flexural Testing System for Measuring the Mechanical Properties of Marine Sponge Spicules

Published on: October 11, 2017

Force System with Vertical V-Bends: A 3D In Vitro Assessment of Elastic and Rigid Rectangular Archwires
08:46

Force System with Vertical V-Bends: A 3D In Vitro Assessment of Elastic and Rigid Rectangular Archwires

Published on: July 24, 2018

Effect of Bending on the Electrical Characteristics of Flexible Organic Single Crystal-based Field-effect Transistors
08:43

Effect of Bending on the Electrical Characteristics of Flexible Organic Single Crystal-based Field-effect Transistors

Published on: November 7, 2016

Area of Science:

  • Solid Mechanics
  • Materials Science
  • Continuum Mechanics

Background:

  • The classical Kirchhoff equations model flexible rods but do not inherently capture size-dependent phenomena.
  • Macroscopic assumptions in traditional models limit their applicability to micro and nanoscale structures.

Purpose of the Study:

  • To extend the Kirchhoff equations to incorporate size effects in flexible rods.
  • To enable the accurate modeling of both macroscopic and ultrathin rod behaviors.

Main Methods:

  • Modification of the Kirchhoff equations to include size-dependent material length parameters.
  • Theoretical analysis of the extended equations for flexible rod mechanics.

Main Results:

  • The developed equations successfully describe size effects in flexible rods.
  • Extensional size effects were identified: thinner rods necessitate increased external forces for identical deformations.

Conclusions:

  • The extended Kirchhoff equations provide a more comprehensive model for flexible rods across various scales.
  • Size effects, specifically extensional ones, are significant in ultrathin rods and must be considered in mechanical analyses.