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Shear on the Horizontal Face of a Beam Element01:16

Shear on the Horizontal Face of a Beam Element

398
To understand shear on the flat side of a prismatic beam element, consider the vertical and horizontal shearing forces, and the normal forces, acting on the element. The element's upper (U) and lower (L) sections, which are divided by the beam's neutral axis, are examined. The equilibrium of these forces is determined by applying the equilibrium equation, which helps identify the horizontal shearing force. This force is directly related to the bending moments and the cross-section's...
398
Beams with Unsymmetric Loadings01:17

Beams with Unsymmetric Loadings

281
Analyzing a supported beam under unsymmetrical loadings is essential in structural engineering to understand how beams respond to varied force distributions. This analysis involves calculating the deflection and identifying points where the slope of the beam is zero, which are crucial for ensuring structural stability and functionality.
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...
281
Deformation of a Beam under Transverse Loading01:15

Deformation of a Beam under Transverse Loading

537
Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
The insights from the bending moment diagram extend to...
537
Bending of Members Made of Several Materials01:11

Bending of Members Made of Several Materials

458
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...
458
Deflection of a Beam01:19

Deflection of a Beam

499
Accurately determining beam deflection and slope under various loading conditions in structural engineering is crucial for ensuring safety and structural integrity. Singularity functions offer a streamlined approach to analyzing beams, especially when multiple loading functions complicate the bending moment equation.
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
499
Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

418
A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by creating...
418

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Related Experiment Video

Updated: Nov 21, 2025

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads
07:58

Automatic Laser-based Geometry Capture for Finite Element Analysis of Weld Beads

Published on: July 25, 2025

457

Shape-Sensing of Beam Elements Undergoing Material Nonlinearities.

Pierclaudio Savino1, Marco Gherlone2, Francesco Tondolo1

  • 1Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

Sensors (Basel, Switzerland)
|January 16, 2021
PubMed
Summary

The inverse finite element method (iFEM) now reconstructs deformed shapes of nonlinear concrete structures, like bridges, using strain data. This advancement enables accurate real-time structural health monitoring for civil engineering applications.

Keywords:
displacementsiFEMnonlinearitiesstrain monitoringstructural health monitoring

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Area of Science:

  • Structural Engineering
  • Computational Mechanics
  • Materials Science

Background:

  • In situ strain measurements are crucial for real-time structural monitoring.
  • The inverse finite element method (iFEM) efficiently reconstructs structural displacements from strain data.
  • Traditional iFEM is limited to structures with linear material behavior.

Purpose of the Study:

  • To extend the application of iFEM to nonlinear concrete structures, common in civil engineering (e.g., bridges).
  • To investigate the effectiveness of iFEM for reinforced concrete beams, considering material nonlinearities in steel and concrete.
  • To evaluate the impact of measurement configurations and mesh densities on reconstruction accuracy.

Main Methods:

  • Adaptation of the inverse finite element method (iFEM) for material nonlinearities.
  • Analysis of simply supported and continuous reinforced concrete beams under yielding conditions.
  • Development of hybrid procedures combining iFEM with moment-curvature relationships for plastic zones.
  • Parametric studies considering various measurement station layouts and mesh discretizations.

Main Results:

  • Demonstrated the feasibility of iFEM for nonlinear reinforced concrete structures.
  • Quantified the influence of measurement and mesh parameters on displacement and strain reconstruction accuracy.
  • Validated hybrid iFEM approaches for scenarios with limited data in plastic regions.
  • Confirmed the reliability and effectiveness of the proposed iFEM advancements.

Conclusions:

  • The enhanced iFEM effectively reconstructs the deformed shape of nonlinear concrete structures.
  • The method provides a versatile and computationally efficient tool for structural health monitoring in civil engineering.
  • Hybrid procedures enhance iFEM's robustness, particularly in the presence of material nonlinearities and data gaps.