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Related Concept Videos

Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

215
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...
215
Plastic Deformations01:14

Plastic Deformations

131
It is essential to understand how structural members behave under plastic deformation when the bending stress exceeds the material's yield strength. This state of deformation permanently alters the shape of the member, in contrast to the linear elastic behavior observed before yielding. The strain at any point in the member is expressed in terms of maximum strain. Notably, the neutral axis, which coincides with the centroid during elastic bending, shifts away from the centroid under plastic...
131
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

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

327
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.
327
Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

125
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...
125
Deformation of a Beam under Transverse Loading01:15

Deformation of a Beam under Transverse Loading

429
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...
429
Elastic Curve from the Load Distribution01:16

Elastic Curve from the Load Distribution

257
The structural behavior of beams under distributed loads is critical for engineering analysis, which focuses on predicting how beams bend and react under such conditions. Different types of beams (e.g., cantilever, supported, or overhanging) behave differently under distributed load conditions.
For all beams, the analysis of the beam's reaction to distributed loads begins by understanding the relationship between a beam's load and the resulting shear forces and bending moments.
257

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Evaluation of collapsible deformation of foundation under rectangular load based on the improved binary medium model.

Nadeem Abbas1, Muhammad Akbar2,3, S B A Elsayed4

  • 1Department of Disaster Mitigation for Structures, Tongji University, Shanghai, China.

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|August 7, 2025
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Summary

Extreme weather and climate change exacerbate foundation soil collapsibility. A new model accurately predicts collapsible loess deformation under load, crucial for geotechnical engineering hazard mitigation.

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Area of Science:

  • Geotechnical Engineering
  • Environmental Science
  • Soil Mechanics

Background:

  • Extreme weather events and climate change increasingly impact foundation soil stability.
  • Collapsible soils, particularly loess, pose significant geotechnical engineering challenges due to deformation and collapse phenomena.
  • Soil moisture regimes and soil suction are critical factors influenced by climate change, affecting soil behavior.

Purpose of the Study:

  • To formulate and solve differential equations for collapsible loess foundation deformation under concentrated force.
  • To develop mathematical models for predicting lateral displacement, vertical displacement, and pore water pressure.
  • To provide a validated model for analyzing the behavior of collapsible loess foundations under load.

Main Methods:

  • Utilized an improved two-dimensional medium model combined with Biot consolidation theory, fracture mechanics, and continuum theory.
  • Employed Laplace and Hankel transforms for solving differential equations, incorporating boundary conditions.
  • Developed mathematical models considering vertical depth, radial distance, and saturation under rectangular load.

Main Results:

  • The formulated differential equations accurately describe collapsible consolidation deformation.
  • Mathematical models were established for displacement and pore water pressure in collapsible loess foundations.
  • Numerical validation confirmed the model's accuracy, showing similarity to real-world engineering deformation.

Conclusions:

  • The proposed model effectively simulates the deformation of collapsible loess foundations under load.
  • This research significantly advances the theoretical understanding of collapsible loess foundation behavior.
  • Findings are crucial for mitigating geotechnical hazards associated with collapsible soils in changing environmental conditions.