Elastic and Plastic Section Modulus [PDF]

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Elastic section modulus[ For general design, the elastic section modulus is used, applying up to the yield point for most metals and other common materials. The elastic section modulus is defined as S = I / y, where I is the second moment of area (or moment of inertia) and y is the distance from the neutral axis to any given fibre. [3] It is often reported using y = c, where c is the distance from the neutral axis to the most extreme fibre, as seen in the table below. It is also often used to determine the yield moment (My) such that My = S × σy, where σy is the yield strength of the material.[3] Elastic Section Modulus can also be defined as the first moment of area. Section modulus equations[4] Crosssectional



Figure



Equation



Comment



shape Solid arrow Rectangle



represents neutr al axis



doubly symmetric Isection (stron g axis)



doubly symmetric Isection (wea k axis)



NA indicates neutral axis



NA indicates neutral axis



Solid arrow Circle



represents neutr [4]



al axis



Solid arrow Circular tube



represents neutr al axis



Rectangular tube



NA indicates neutral axis



NA Diamond



indicates neutral axis



NA C-channel



indicates neutral axis



Plastic section modulus[edit] The Plastic section modulus is used for materials where (irreversible) plastic behaviour is dominant. The majority of designs do not intentionally encounter this behaviour. The plastic section modulus depends on the location of the plastic neutral axis (PNA). The PNA is defined as the axis that splits the cross section such that the compression force from the area in



compression equals the tension force from the area in tension. So, for sections with constant yielding stress, the area above and below the PNA will be equal, but for composite sections, this is not necessarily the case. The plastic section modulus is then the sum of the areas of the cross section on each side of the PNA (which may or may not be equal) multiplied by the distance from the local centroids of the two areas to the PNA:



Descripti on



Figure



Equation



Comment



Rectangul ar section



[5]



Hollow



where: b=width,



rectangula



h=height, t=wall



r section



thickness



,[6] For the



where: 



 =



two



width, 



=thi



flanges of an I-



ckness, 



beamwith



distances from



the web



the neutral axis



excluded



to the centroids



are the



of the flanges respectively. For an I Beam including the web For an I



 



[7]



Beam (weak axis) Solid Circle Hollow Circle The plastic section modulus is used to calculate the plastic moment, Mp, or full capacity of a crosssection. The two terms are related by the yield strength of the material in question, F y, by Mp=Fy*Z. Sometimes Z and S are related by defining a 'k' factor which is something of an indication of capacity beyond first yield. k=S/Z Therefore for a rectangular section, k=1.5