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

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving01:30

Hyperbolic and Inverse Hyperbolic Functions: Problem Solving

166
An arched gate can be effectively modeled using a hyperbolic cosine profile because this type of function is smooth and symmetric about the vertical axis. When the arch is centered at the origin, its maximum height occurs at the center point. This symmetry ensures that any height below the crown of the arch is reached at two horizontal positions that are equal in distance from the centerline but lie on opposite sides.To determine where the gate reaches a height of five meters, the height of the...
166
Second Derivatives of Implicit Functions01:29

Second Derivatives of Implicit Functions

119
Elliptical arches are fundamental in architectural and structural engineering, offering aesthetic appeal and structural efficiency. The shape of an elliptical arch follows a constrained geometric relationship where the height and horizontal position are implicitly related. This means that the height y cannot be explicitly expressed as a function of the horizontal position x, necessitating implicit differentiation for slope and curvature analysis.The equation of an ellipse centered at the origin...
119
Moment-Area Theorems01:17

Moment-Area Theorems

835
The Moment-Area Theorem is crucial in structural engineering for analyzing beam bending, particularly in applications like building floor supports. This theorem utilizes the geometric properties of the elastic curve, which depicts how a beam deforms under load, to simplify the calculations of deflections and slopes.
The theorem is divided into two parts. The first part connects the angle between tangents at any two points on the beam's elastic curve to the area under a curve derived by...
835
Principle of Moments01:20

Principle of Moments

2.6K
The principle of moments, also known as Varignon's theorem, is a fundamental concept in physics and engineering that describes the equilibrium of a rigid body under the influence of external forces. The principle states that the moment of a force about a point is equal to the sum of the moments of the components of the force about the same point.
The moment is calculated by multiplying the magnitude of the force by the perpendicular distance from the point of application to the point about...
2.6K
Beams with Symmetric Loadings01:15

Beams with Symmetric Loadings

475
The moment-area method is an analytical tool used in structural engineering to determine the slope and deflection of beams under various loads. Consider a cantilever with a concentrated load and moment at the free end. The first step is constructing a free-body diagram to calculate the reactions at the fixed end. Next, the bending moment diagram is plotted to visualize how the bending moment varies along the beam's length, focusing on points where the bending moment equals zero.
The M/EI...
475
Mathematical Modeling: Problem Solving01:29

Mathematical Modeling: Problem Solving

499
Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...
499

You might also read

Related Articles

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

Sort by
Same author

Constant stress arches and their design space.

Proceedings. Mathematical, physical, and engineering sciences·2022
See all related articles

Related Experiment Video

Updated: Mar 17, 2026

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

11.4K

Mathematical model of a moment-less arch.

W J Lewis1

  • 1School of Engineering, University of Warwick , Coventry CV4 7AL, UK.

Proceedings. Mathematical, Physical, and Engineering Sciences
|July 21, 2016
PubMed
Summary

This study introduces a new mathematical model for designing moment-less arches, considering self-weight and various load conditions. The model reveals that optimized moment-less arches exhibit significantly lower stresses than traditional parabolic arches under realistic loading scenarios.

Keywords:
catenarymoment-less archparabolic form

More Related Videos

Measuring the Complete-arch Distortion of an Optical Dental Impression
06:51

Measuring the Complete-arch Distortion of an Optical Dental Impression

Published on: May 30, 2019

8.1K
Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
09:32

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

Published on: April 11, 2018

10.4K

Related Experiment Videos

Last Updated: Mar 17, 2026

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

11.4K
Measuring the Complete-arch Distortion of an Optical Dental Impression
06:51

Measuring the Complete-arch Distortion of an Optical Dental Impression

Published on: May 30, 2019

8.1K
Subject-specific Musculoskeletal Model for Studying Bone Strain During Dynamic Motion
09:32

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

Published on: April 11, 2018

10.4K

Area of Science:

  • Structural Engineering
  • Applied Mathematics
  • Civil Engineering

Background:

  • Traditional arch design often relies on simplified load assumptions.
  • Existing models for moment-less arches may not account for self-weight or general loading conditions.

Purpose of the Study:

  • To develop a comprehensive mathematical model for predicting moment-less arch geometries.
  • To analyze the structural behavior of moment-less arches under combined uniform and self-weight loads.
  • To compare the stress development in optimized moment-less arches versus traditional parabolic arches.

Main Methods:

  • Formulation of a novel mathematical model for rigid, two-pin, moment-less arches.
  • Inclusion of arch self-weight (q) and uniformly distributed load per unit span (w) in the model.
  • Derivation of classical parabolic and catenary arch forms as special cases.
  • Analysis of arch behavior under combined permanent loading (w+q) for various span/rise and w/q ratios.

Main Results:

  • The model accurately predicts moment-less arch shapes for any span/rise ratio and load combination (w/q).
  • Optimized moment-less arches demonstrate substantially lower stress levels compared to parabolic arches under identical loading conditions.
  • Even with minor geometric differences, stress variations between moment-less and parabolic arches can be significant.

Conclusions:

  • The developed model offers a more realistic approach to designing moment-less arches.
  • Accounting for self-weight and general loads leads to superior structural performance in moment-less arch designs.
  • This research provides valuable insights for optimizing arch structures in engineering applications.