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The plastic section modulus is calculated as the sum of the areas of the cross section on either side of the PNA, each multiplied by the distance from their respective local centroids to the PNA. [16] = + where: A C is the area in compression A T is the area in tension y C, y T are the distances from the PNA to their centroids. Plastic section ...
In structural engineering, the plastic moment (M p) is a property of a structural section. It is defined as the moment at which the entire cross section has reached its yield stress . This is theoretically the maximum bending moment that the section can resist – when this point is reached a plastic hinge is formed and any load beyond this ...
Flexural modulus measurement For a 3-point test of a rectangular beam behaving as an isotropic linear material, where w and h are the width and height of the beam, I is the second moment of area of the beam's cross-section, L is the distance between the two outer supports, and d is the deflection due to the load F applied at the middle of the ...
Section capacity (Ms in AS 4100) is equal to Ze x fy, where Ze is effective section modulus, which depending on section slenderness can be a function of elastic or plastic section modulus or both. For compact sections, Ze = MIN(S,1.5Z), non-compact Ze is a function of Z and compact Ze, and slender Ze is a function of Z.
Use of the Dirac function greatly simplifies such situations; otherwise the beam would have to be divided into sections, each with four boundary conditions solved separately. A well organized family of functions called Singularity functions are often used as a shorthand for the Dirac function, its derivative, and its antiderivatives.
The beam is initially straight with a cross section that is constant throughout the beam length. The beam has an axis of symmetry in the plane of bending. The proportions of the beam are such that it would fail by bending rather than by crushing, wrinkling or sideways buckling. Cross-sections of the beam remain plane during bending.
Elastic properties describe the reversible deformation (elastic response) of a material to an applied stress.They are a subset of the material properties that provide a quantitative description of the characteristics of a material, like its strength.
is the cross section area. is the elastic modulus. is the shear modulus. is the second moment of area., called the Timoshenko shear coefficient, depends on the geometry. Normally, = / for a rectangular section.