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I-beams (also known as H-beams, W-beams (for "wide flange"), rolled steel joist (RSJ), or double-T (especially in Polish, Spanish and German)) are beams with an I- or H-shaped cross-section. The horizontal elements of the "I" are flanges, while the vertical element is the web. The web resists shear forces while the flanges resist most of the bending moment experienced by the beam. Beam theory shows that the I-shaped section is a very efficient form for carrying both bending and shear loads in the plane of the web. On the other hand, the cross-section has a reduced capacity in the transverse direction, and is also inefficient in carrying torsion, for which hollow structural sections are often preferred.

## OverviewEdit

There are two standard I-beam forms:

I-beams are commonly made of structural steel but may also be formed from aluminium or other materials. A common type of I-beam is the rolled steel joist (RSJ) - sometimes incorrectly rendered as reinforced steel joist. British and European standards also specify Universal Beams (UBs) and Universal Columns (UCs). These sections have parallel flanges, as opposed to the varying thickness of RSJ flanges. UCs have equal or near-equal width and depth, while UBs are significantly deeper than they are wide.

I-beams engineered from wood with fiberboard and/or laminated veneer lumber are also becoming increasingly popular in construction, especially residential, as they are both lighter and less prone to warping than solid wooden joists. However there has been some concern as to their rapid loss of strength in a fire if unprotected.

## DesignEdit

I-beams are widely used in the construction industry and are available in a variety of standard sizes. Tables are available to allow easy selection of a suitable steel I-beam size for a given applied load. I-beams may be used both as beams and as columns.

I-beams may be used both on their own, or acting compositely with another material, typically concrete. Design may be governed by any of the following criteria:

• deflection - the stiffness of the I-beam will be chosen to minimise deformation
• vibration - the stiffness and mass are chosen to prevent unacceptable vibrations, particularly in settings sensitive to vibrations, such as offices and libraries
• bending failure by yielding - where the stress in the cross section exceeds the yield stress
• bending failure by lateral torsional buckling - where a flange in compression tends to buckle sideways or the entire cross-section buckles torsionally
• bending failure by local buckling - where the flange or web is so slender as to buckle locally
• local yield - caused by concentrated loads, such as at the beam's point of support
• shear failure - where the web fails. Slender webs will fail by buckling, rippling in a phenomenon termed tension field action, but shear failure is also resisted by the stiffness of the flanges
• buckling or yielding of components - for example, of stiffeners used to provide stability to the I-beam's web.

### Design for bending Edit

A beam under bending sees high stresses along the axial fibers that are farthest from the neutral axis. To prevent failure, most of the material in the beam must be located in these regions. Comparatively little material is needed in the area close to the neutral axis. This observation is the basis of the I-beam cross-section; the neutral axis runs along the center of the web which can be relatively thin and most of the material can be concentrated in the flanges.

The ideal beam is the one with the least cross-sectional area (and hence requiring the least material) needed to achieve a given section modulus. Since the section modulus depends on value the moment of inertia , an efficient beam must have most of its material located as far from the neutral axis as possible. The farther a given amount of material is from the neutral axis, the larger is the section modulus and hence a larger bending moment can be resisted.

When designing a symmetric I-beam to resist stresses due to bending the usual starting point is the required section modulus. If the allowable stress is $\sigma_{\mathrm{max}}$ and the maximum expected bending moment is $M_{\mathrm{max}}$, then the required section modulus is given by[1]

$S = \cfrac{M_{\mathrm{max}}}{\sigma_{\mathrm{max}}} = \cfrac{I}{c}$

where $I$ is the moment of inertia of the beam cross-section and $c$ is the distance of the top of the beam from the neutral axis (see beam theory for more details).

For a beam of cross-sectional area $a$ and height $h$, the ideal cross-section would have half the area at a distance $h/2$ above the cross-section and the other half at a distance $h/2$ below the cross-section[1] For this cross-section

$I = \cfrac{ah^2}{4} ~;~~ S = 0.5 a h$

However, these ideal conditions can never be achieved because material is needed in the web for physical reasons, including buckling. For wide-flange beams, the section modulus is approximately

$S \approx 0.35 a h$

which is superior to that achieved by rectangular beams and circular beams.

### Issues Edit

Though I-beams are excellent for unidirectional bending in a plane parallel to the web, they do not perform as well in bidirectional bending. These beams also show little resistance to twisting and undergo sectional warping under torsional loading. For torsion dominated problems, box beams and other types of stiff sections perform better.

## Wide-flange steel materials and rolling processes (U.S.) Edit

In the United States, the most commonly mentioned I-Beam is the wide-flange (W) shape. These beams have flanges in which the planes are nearly parallel. Other I-Beams include American Standard (designated S) shapes, in which flange surfaces are not parallel, and H-piles (designated HP), which are typically used as pile foundations. Wide-flange shapes are available in grade ASTM A992,[2] which has generally replaced the older ASTM grades A572 and A36. Ranges of yield strength:

• A36: 36,000 psi (250 MPa)
• A572: 42,000–60,000 psi (290–410 MPa), but 50,000 psi (340 MPa) is the most common
• A588: Similar to A572
• A992: 50,000–65,000 psi (340–450 MPa)

Wide-flange shapes are produced by the electric arc furnace method.

Like most steel products, I-beams often contain some recycled content.

The American Institute of Steel Construction ("AISC") publishes the "Steel Construction Manual" for designing structures of various shapes. It documents the common approaches, ASD and LRFD, (as of 13th ed.) to creating such designs.

## Designation and terminology Edit

• In the United States, steel I-Beams are commonly specified using the depth and weight of the beam. For example, a "W10x22" beam is approximately 10 in (25 cm) in depth (height when the I-Beam is standing on its flanges) and weighs approximately 22 lb/ft (33 kg/m).
• In Canada, steel I-Beams are now commonly specified using the depth and weight of the beam in metric terms. For example, a "W250x33" beam is approximately 25 cm (10 in) in depth (height when the I-Beam is standing on its flanges) and weighs approximately 33 kg/m (22 lb/ft).[3] I-Beams are still available in U.S. sizes from many Canadian manufacturers.
• In India I-beams are designated as ISMB, ISJB, ISLB, ISWB. ISMB :Indian Standard Medium Weight Beam, ISJB : Indian Standard Junior Beams, ISLB : Indian Standard Light Weight Beams, ISWB : Indian Standard Wide Flange Beams. Beams are designted as per respective abbreviated reference followed by the depth of section such as for example ISMB 450, where 450 is the depth of section in millimetres (mm). The dimensions of these beams are classified as per IS:808. (as per BIS)
• In the United Kingdom, these steel sections are commonly specified with a code consisting of the major dimension (usually the depth)-x-the minor dimension-x-the mass per metre-ending with the section type, all measurements being metric. Therefore a 152x152x23UC would be a column section (UC = universal column) of approximately 152mm depth 152mm width and weighing 23kg per meter length.[4]

### European standard beams IPE Edit

Type
Beam
height
(mm)
Flange
width
(mm)
Web
thickness
(mm)
Flange
thickness
(mm)
Weight
(kg/m)
Cross-section
area
(cm2)
Moment of inertia
in torsion (J)
(cm4)
IPE 8080463.85.26.07.640.70
IPE 100100554.15.78.110.31.10
IPE 120120644.46.310.413.21.71
IPE 140140734.76.912.916.42.54
IPE 750 x 13775326311.517137175137.1
IPE 750 x 14775326513.217147188161.5
IPE 750 x 17376226714.421.6173221273.6
IPE 750 x 19677026815.625.4196251408.9

### European wide flange beams HEA and HEBEdit

Type
Beam
height
(mm)
Flange
width
(mm)
Web
thickness
(mm)
Flange
thickness
(mm)
Weight
(kg/m)
Cross-section
area
(cm2)
Moment of inertia
in torsion (J)
(cm4)
HE 100 A961005816.721.25.24
HE 120 A1141205819.925.35.99
HE 140 A1331405.58.524,731.48.13
HE 160 A1521606930.438.812.19
HE 1000 x 41510203042646415528.72714
HE 1000 x 438102630526.949437557.23200
HE 1000 x 49410363093154494629.14433
HE 1000 x 58410563143664584743.77230