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Related Concept Videos

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...
412
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

509
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.
509
Plastic Deformation in Circular Shafts01:20

Plastic Deformation in Circular Shafts

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When materials are subjected to forces that surpass their yield strength, they undergo a process known as plastic deformation. This results in a permanent alteration or strain in their structure. This concept can be specifically applied to circular shafts, where the deformation leads to a change in its shape. The precise evaluation of this plastic deformation requires understanding the stress distribution within the circular shaft, which is achieved by calculating the maximum shearing stress in...
415
Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

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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...
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Plastic Deformations01:19

Plastic Deformations

380
Plastic deformation represents a fundamental concept in materials science, which explains the irreversible change in the shape of a material when it experiences stress beyond its elastic capability. This phenomenon is important in structural engineering, especially in designing and analyzing cantilever beams—structures that are securely fixed at one end and bear loads at the opposite end. When these beams are subjected to loads within their elastic range, they will return to their...
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Plastic Deformations01:14

Plastic Deformations

366
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...
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    This study introduces a novel method for creating 2D element packings using deformable geometric shapes. The physics-based simulation optimizes element fit and composition, resulting in uniform negative space.

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    Area of Science:

    • Computer Graphics
    • Computational Geometry
    • Artistic Composition

    Background:

    • Artistic compositions often involve filling shapes with geometric elements.
    • Achieving uniform spacing and natural element deformation in digital art is challenging.

    Purpose of the Study:

    • To develop a computational method for generating 2D element packings.
    • To enable deformable geometric elements to fill container shapes artistically.

    Main Methods:

    • Elements represented as mass-spring systems for deformation.
    • Physics simulation balances packing evenness and element deformation.
    • Shape matching for element placement in corners and preferred orientations.

    Main Results:

    • Generated 2D artistic compositions with deformable geometric elements.
    • Achieved uniform width of negative space between elements.
    • Explored tileable packings and validated with statistical measurements.

    Conclusions:

    • The proposed method effectively creates aesthetically pleasing element packings.
    • Deformable elements and physics simulation enhance naturalistic composition.
    • The approach offers control over element placement and packing properties.