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In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members.Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness.
Section 179 of the United States Internal Revenue Code (26 U.S.C. § 179), allows a taxpayer to elect to deduct the cost of certain types of property on their income taxes as an expense, rather than requiring the cost of the property to be capitalized and depreciated.
In 1820, the French engineer A. Duleau derived analytically that the torsion constant of a beam is identical to the second moment of area normal to the section J zz, which has an exact analytic equation, by assuming that a plane section before twisting remains planar after twisting, and a diameter remains a straight line.
Internal Revenue Service (IRS) Publication 551 contains the IRS's definition of basis: "Basis is the amount of your investment in property for tax purposes. Use the basis of property to figure depreciation, amortization, depletion, and casualty losses. Also, use it to figure gain or loss on the sale or other disposition of property."
The universal property of the tensor product V ⊗ V ∗ automatically implies that this bilinear map is induced by a linear functional on V ⊗ V ∗. [ 9 ] Similarly, there is a natural bilinear map V × V ∗ → Hom( V , V ) given by sending ( v , φ) to the linear map w ↦ φ( w ) v .
An arbitrary shape. ρ is the distance to the element dA, with projections x and y on the x and y axes.. The second moment of area for an arbitrary shape R with respect to an arbitrary axis ′ (′ axis is not drawn in the adjacent image; is an axis coplanar with x and y axes and is perpendicular to the line segment) is defined as ′ = where
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 ...
The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: . Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),