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Related Concept Videos

Stress: General Loading Conditions01:15

Stress: General Loading Conditions

389
To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes....
389
Stress Concentrations01:13

Stress Concentrations

338
The concept of stress concentration is crucial for understanding how materials respond under bending stresses, particularly when there are irregularities or discontinuities in the material's geometry. Normally, stress in a symmetric member subjected to pure bending is assumed to be uniformly distributed across the entire cross-section. However, this assumption does not hold when there are variations in the cross-sectional geometry or the presence of notches and holes.
The stress...
338
Principal Stresses01:24

Principal Stresses

405
The graphical depiction of normal and shearing stress equations is represented by a circle, demonstrating the interplay between these stresses under different angular conditions. The center of this circle C, located on the vertical axis, represents the average normal stress, while its radius shows the range of stress variations. At points A and B, where the circle intersects the horizontal axis, the maximum and minimum normal stresses are observed, occurring without shearing stress. These...
405
General State of Stress01:21

General State of Stress

321
The general state of stress within a material can be accurately depicted using a stress tensor. This tensor encapsulates the internal forces distributed within a material subjected to external forces or deformations.
Specifically, consider a tetrahedral element where one face, labeled XYZ, is perpendicular to the line OA, and the remaining faces align with the coordinate axes with point O as the origin. At any point, such as point O, the stress tensor can be used to determine the stress...
321
Stress on an Oblique Plane01:16

Stress on an Oblique Plane

744
Understanding stress on an oblique plane under axial loading is pivotal in material mechanics. This analysis offers insight into a material's durability and strength, which is crucial for civil engineering and structural design. Axial loading refers to force application along the material's central axis, causing compression or elongation and leading to normal stress. Normal stress occurs when a force acts perpendicularly to the material's area, resulting in compressive or tensile...
744
Normal Stress01:19

Normal Stress

747
Normal stress is a type of stress that occurs when forces act perpendicular, or normal, to a material's cross-sectional area. This stress often arises in structures when subjected to axial loading, which is the application of force along the axis of an object. A practical example of this can be found in bridge truss members.
When a rod is under axial loading, the internal forces and corresponding stress are normal to the plane of the section, so it is termed normal stress. It's...
747

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Mathematical model of a moment-less arch.

Proceedings. Mathematical, physical, and engineering sciences·2016
See all related articles

Related Experiment Video

Updated: Oct 3, 2025

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

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Constant stress arches and their design space.

Wanda J Lewis1

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

Proceedings. Mathematical, Physical, and Engineering Sciences
|February 14, 2022
PubMed
Summary

This study proposes constant axial stress as a design criterion for moment-less arches, ensuring durability under variable loads. This approach optimizes arch design beyond just minimizing weight.

Area of Science:

  • Structural Engineering
  • Applied Mechanics
  • Form-Finding Analysis

Background:

  • Traditional arch design prioritizes funicular (moment-less) form and minimal weight.
  • Minimal weight can compromise structural durability and limit design flexibility.
  • Natural structures exhibit constant axial stress for resilience.

Purpose of the Study:

  • To propose constant axial stress as a novel design criterion for moment-less arches.
  • To ensure structural integrity and durability under permanent and variable loads.
  • To analyze asymmetric and symmetric arches, including least-weight solutions.

Main Methods:

  • Building on Lewis's analytical form-finding approach.
  • Deriving equations for arch centerline profile, reactions, and cross-sectional area for asymmetric arches.
Keywords:
constant stress archdesign spaceform-findingmoment-less arch

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  • Analyzing symmetric arches and deriving a volume-minimizing span/rise ratio for least-weight structures.

    • Main Results:

    • A new design space for constant axial stress arches is defined by two non-dimensional parameters.
    • For stand-alone arches, a constraint relationship exists between constant stress and span/rise ratio.
    • The proposed method ensures no part of the arch is over-stressed relative to others under variable loads.

    Conclusions:

    • Constant axial stress offers a robust design criterion for moment-less arches, enhancing durability.
    • The study provides a theoretical framework and practical limits for designing such arches.
    • This approach offers a new perspective on optimizing arch structures beyond traditional weight minimization.