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Related Concept Videos

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
Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

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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...
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Deflection of a Beam01:19

Deflection of a Beam

374
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.
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Temperature Dependent Deformation01:12

Temperature Dependent Deformation

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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...
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Design of Prismatic Beams for Bending01:23

Design of Prismatic Beams for Bending

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The design of prismatic beams, structural elements with a uniform cross-section, focuses on ensuring safety and structural integrity under load. The design process begins by determining the allowable stress, either from material properties tables, or by dividing the material's ultimate strength by a safety factor. This safety factor is essential for accommodating uncertainties, and varies depending on the material—timber, steel, or concrete—with each having unique strength and...
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Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

257
When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
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Related Experiment Video

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Three-Dimensional Deformation Calculation of Wind Tunnel Flexible Wall Using Orthogonal Beam Function.

Xiuxuan Yang1, Yueyin Ma1, Guishan Wang1

  • 1Facility Design and Instrumentation Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China.

Materials (Basel, Switzerland)
|August 14, 2025
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Summary

Researchers developed new models to accurately predict flexible nozzle deformation in transonic wind tunnels. This improves control of Mach numbers for advanced aircraft development.

Keywords:
elliptic integral solutionflexible walllarge-deflection deformationorthogonal beam functiontransonic/supersonic wind tunnel

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Area of Science:

  • Aerospace Engineering
  • Computational Fluid Dynamics
  • Mechanical Engineering

Background:

  • Transonic and supersonic wind tunnels are crucial for advanced aircraft development.
  • Flexible nozzle deformation is key to controlling Mach numbers in these facilities.
  • Accurate modeling of flexible wall plate deformation is challenging due to nonlinearities and complex boundary conditions.

Purpose of the Study:

  • To develop accurate and efficient mathematical models for flexible wall plate deformation.
  • To investigate deformation characteristics in two orthogonal directions.
  • To improve computational efficiency and accuracy in transonic wind tunnel simulations.

Main Methods:

  • Systematic investigation of flexible wall deformation characteristics.
  • Proposal of an orthogonal beam function (OBF) model for small-deflection deformations.
  • Introduction of an elliptic integral (EI) solution and modification of the OBF model for large-deflection deformations.

Main Results:

  • The orthogonal beam function (OBF) model effectively characterizes small-deflection deformations.
  • The modified OBF model with elliptic integral (EI) solution accurately describes large-deflection deformations.
  • Experimental validation confirmed the model's effectiveness.

Conclusions:

  • The developed OBF model provides an effective solution for large-deflection deformation in flexible wall plates.
  • This research enhances computational efficiency and accuracy for transonic wind tunnel design and operation.
  • The findings contribute to the advancement of high-speed aerodynamic testing.