MOMENT OF INERTIA OF STANDARD SECTIONS

Moment of Inertia of Standard Sections

The previous presentations defined moment of inertia and the determination of moment of inertia for simple and composite shapes. However, most construction is with 'standard sections' or 'standard structural shapes'

Both phrases typically refer to common structural steel sections, but can also be used to define common aluminum sections

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Standard sections are defined by the industry. The common I-beam, hollow circular tube, hollow square tube, and L-sections are

amongst the definition of standard sections.

Moment of Inertia of Standard Sections

Historically, wooden beams of any shape were built-up onsite. As such, the idea of a standard section was never really applied to structural shapes derived of wood material. However, this has changed in recent years. Laminated sections are available with standardized dimensioning.

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To date, standard wood sections are glued I-beam sections often

used as joists.

Standard SectionFor our purposes, we will define a 'standard section' in terms of a structural steel section. According to Wikipedia, structural steel may be defined as follows:

Structural steel is steel construction material, a profile, formed with a specific shape or cross section and certain standards of chemical composition and mechanical properties. Structural steel shape, size, composition, strength, storage, etc., is regulated in most industrialized countries.

Although this definition is for structural steel, structural aluminum section may be similarly defined.

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Standard structural shapes are designated with an alphanumeric string that defines the shape, the depth (height) of the shape, and the weight of the shape per unit length. Common alpha designations are:

S – Standard section with sloped inner flanges

W – Wide flange section with parallel flange surfaces

ST, WT, MT – A T-section cut from a W-, S-, or M-Section

HP – Bearing Pile section with parallel flange surfaces and equal thickness of flange and web

C – Channel section with sloped inner flanges

L – Angle sections (equal or unequal legs)

M – Miscellaneous I-beam section

MC – Miscellaneous channel sections

HSS – Hollow Structural Section. May be an RSS, CSS, or SHS for rectangular, circular, and square structural sections respectively. These designations are used frequently in the UK.

Structural Shapes

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European standard sections carry different designations. They are dimensioned in millimeters rather than inches and weighed in kilograms per meter rather than pounds per foot. Typical designations are:

IPE – Parallel flange surfaces, height of 80 to 600 mm

IPN – Flange has 14% inner slope, height of 80 to 600 mm

HE – Wide flange, parallel flange surfaces, height of 100 to 1000 mm

HL – Extra wide flange, parallel flange surfaces, height of 920 to 1100 mm

HD – Wide flange column section, parallel flange surfaces, section height of 260 to 400 mm

HP – Wide flange bearing piles, parallel flange surfaces, height 200-400 mm

L – Angles (equal and unequal length legs)

UPE – Channel with parallel flange, depth 80 – 400 mm

UPN – Channel with tapered flange, depth 80 – 400 mm

U – Channel with tapered flange, depth 40 – 65 mm

Structural Shapes

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Examples of designations are:W18x119 – A wide flange section with a nominal depth* of 18 inches and a weight of 119 lbs/ft

C15x50 – An American Standard Channel with a nominal depth of 15 inches and a weight of 50 lbs/ft

L6x4x7/8 – An American unequal leg angle with legs of 6” and 4” and a thickness of 7/8”

UPN 100** - A European Channel with tapered flanges and a depth of 100mm

L20x20x3 – A European angle with equal length legs of 20mm and a thickness of 3mm

* The height of a section is referred to as depth

** Unlike American designations, European designations include only nominal height, and do not reference weight. The sole exception are angle sections which are designated in a manner similar to American designations.

Structural Shapes

Moment of Inertia of Standard Sections

Since standard sections have defined geometry as well as metalurgical properties, all of these properties can be and are tabulated as handbook data.

This data includes geometric dimensions as well as elastic design properties, many of which you will not use until a strength of materials course. The elastic properties listed will include the moment of inertia of the section.

Abridged tables are included in the appendix of this online text. You can also visit http://www.structural-drafting-net-expert.com/ for additional information on structural sections.

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Moment of Inertia of Specialized Sections

Specialized industries may also have 'standard' sections for use within the industry. For example, in the marine industry, mast and boom sections and their properties are made available to naval architects for use in their designs.

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Moment of Inertia of Laminated Wood Sections

The same holds true for laminated wood sections. Although moments of inertia still need be calcuated for unique sections, 'standard' sections are available with their properties as shown in the table below.

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Examples for Moment of Inertia

In the end, moments of inertia for standard sections are provided in handbook data and from the manufacturer. You can simply look them up and apply them as appropriate

However, many structural sections are built-up from standard sections. This is the topic of the next module