Section modulus 1

Section modulusSection modulus is a geometric property for a given cross-section used in the design of beams or flexural members.Other geometric properties used in design include area for tension, radius of gyration for compression, and momentof inertia for stiffness. Any relationship between these properties is highly dependent on the shape in question.Equations for the section moduli of common shapes are given below. There are two types of section moduli, theelastic section modulus (S) and the plastic section modulus (Z).

NotationNorth American and British/Australian convention reverse the usage of S & Z. Elastic modulus is S in NorthAmerica,[1] but Z in Britain/Australia,[2] and vice versa for the plastic modulus. Eurocode 3 (EN 1993 - SteelDesign) resolves this by using W for both, but distinguishes between them by the use of subscripts - Wel and Wpl.

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

Section modulus equations[4]

Cross-sectional shape Figure Equation Comment

Rectangle Solid arrow represents neutral axis

doubly symmetric I-section (strong axis) NA indicates neutral axis

doubly symmetric I-section (weak axis) NA indicates neutral axis

Circle[4]

Solid arrow represents neutral axis

Circular tube Solid arrow represents neutral axis

Rectangular tube NA indicates neutral axis

Section modulus 2

Diamond NA indicates neutral axis

C-channel NA indicates neutral axis

Plastic section modulusThe Plastic section modulus is used for materials where (irreversible) plastic behaviour is dominant. The majority ofdesigns 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 theaxis that splits the cross section such that the compression force from the area in compression equals the tensionforce from the area in tension. So, for sections with constant yielding stress, the area above and below the PNA willbe 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 ormay not be equal) multiplied by the distance from the local centroids of the two areas to the PNA:

Description Figure Equation Comment

Rectangular section

For the two flanges of anI-beam with the webexcluded

,[5] where: =width, =thickness,are the distances from the neutral axis

to the centroids of the flanges respectively.

For an I Beam includingthe web

[6]

For an I Beam (weakaxis)

Solid Circle

Hollow Circle

The plastic section modulus is used to calculate the plastic moment, Mp, or full capacity of a cross-section. The twoterms are related by the yield strength of the material in question, Fy, by Mp=Fy*Z. Sometimes Z and S are related bydefining a 'k' factor which is something of an indication of capacity beyond first yield. k=Z/STherefore for a rectangular section, k=1.5

Section modulus 3

References[3][3] Kulak, G.L. and Grondin, G.Y., 2006, Limit States Design in Structural Steel 8th Ed., Canadian Institute of Steel Construction.[4][4] Gere, J. M. and Timoshenko, S., 1997, Mechanics of Materials 4th Ed., PWS Publishing Co.[5][5] American Institute of Steel Construction: Load and Resistance Factor Design, 3rd Edition, pp. 17-34.

External links• http:/ / www. engineeringtoolbox. com/ american-wide-flange-steel-beams-d_1318. html - List of section moduli

for common beam shapes• http:/ / www. novanumeric. com/ samples. php?CalcName=SectionModulus - Online Calculation for Section

Modulus

Article Sources and Contributors 4

Article Sources and ContributorsSection modulus  Source: http://en.wikipedia.org/w/index.php?oldid=555141680  Contributors: Bbanerje, Bigmonolith, Carl.bunderson, Chaley67, David Eppstein, Drendy88, Earlyehlinger,Gogo Dodo, HMSSolent, Hess88, J Milburn, Jefflayman, Khakiandmauve, KostisNikolaou, LanaMohinder, Lmi005, Magioladitis, Michael Devore, Michael Hardy, Muchado, Rjwilmsi,Rmendozajr, RonRodex, Roofstrider, Rzarx, Seam.us, Sehlstrom, Sookiasp, Stephenb, Sturm55, Syth, Wizard191, Yeokaiwei, Zojj, 105 anonymous edits

Image Sources, Licenses and ContributorsImage:Area moment of inertia of a rectangle.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Area_moment_of_inertia_of_a_rectangle.svg  License: Creative CommonsAttribution-ShareAlike 3.0 Unported  Contributors: Hemmingsen, WikipediaMasterImage:Section modulus-I-beam-strong axis.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Section_modulus-I-beam-strong_axis.svg  License: Public Domain  Contributors:Section_modulus-I-beam-weak_axis.svg: *Area_moment_of_inertia_of_a_I-beam.svg: Zielu20 derivative work: Wizard191 (talk) derivative work: Wizard191 (talk)Image:Section modulus-I-beam-weak axis.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Section_modulus-I-beam-weak_axis.svg  License: Public Domain  Contributors:Area_moment_of_inertia_of_a_I-beam.svg: Zielu20 derivative work: Wizard191 (talk)Image:Area moment of inertia of a circle.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Area_moment_of_inertia_of_a_circle.svg  License: Creative CommonsAttribution-ShareAlike 3.0 Unported  Contributors: Hemmingsen, INVERTED, WikipediaMaster, 1 anonymous editsImage:Area moment of inertia of a circular area.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Area_moment_of_inertia_of_a_circular_area.svg  License: Creative CommonsAttribution-ShareAlike 3.0 Unported  Contributors: Hemmingsen, WikipediaMasterFile:Section modulus-rectangular tube.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Section_modulus-rectangular_tube.svg  License: Public Domain  Contributors:Area_moment_of_inertia_of_a_rectangle2.svg: Zielu20 derivative work: Wizard191 (talk)File:Secion modulus-diamond.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Secion_modulus-diamond.svg  License: Public Domain  Contributors:Area_moment_of_inertia_of_a_square2.svg: Zielu20 derivative work: Wizard191 (talk)Image:Section modulus-C-channel.svg  Source: http://en.wikipedia.org/w/index.php?title=File:Section_modulus-C-channel.svg  License: Public Domain  Contributors:Area_moment_of_inertia_of_a_channel.svg: Zielu20 derivative work: Wizard191 (talk)

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