Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

Width
Width
Width
Depth
X
Y
thickness
X
Web
Depth
Flange
Y
X X
Y thickness
Stem
X
Y
Y
X
Web
Depth
Y
Flange
Flange
(a) Wide-flange shape (W)
(b) Tee shape (WT)
(c) Channel shape (C)
Width
leg
thickness
Y
Y
long leg
Depth
X
X
X
X
Y
Wall
thickness
Y
Short
leg
FIGURE 8.9 Standard steel shapes.
(d) Hollow structural section (HSS)
(e) Angle shape (L)
plastics, and it is worthwhile to discuss some terminology associated with these standard
shapes. Since steel is perhaps the most common material used in structures, this discussion
will focus on the five standard rolled structural steel shapes shown in Figure 8.9.
The most commonly used steel shape for beams is called a wide-flange shape
(Figure 8.9a). The wide-flange shape is optimized for economy in bending applications. As
shown by Equation (8.10), the bending stress in a beam is inversely related to its section
modulus S. If a choice is given between two shapes having the same allowable stress, the
shape with the larger S is the better choice because it will be able to withstand more bending
moment than the one with the smaller S. The weight of a beam is proportional to its
cross-sectional area, and typically, the cost of a beam is directly related to its weight.
Therefore, a shape that is optimized for bending is configured so that it provides the largest
possible section modulus S for a given cross-sectional area of material. The area of a wideflange
shape is concentrated in its flanges. The area of the web, which connects the two
flanges, is relatively small. By increasing the distance between the centroid and each flange,
the shape’s moment of inertia (about the X–X axis) can be increased dramatically, roughly
in proportion to the square of this distance. Consequently, the section modulus of the shape
can be substantially increased with a minimal overall increase in area.
For a wide-flange shape, the moment of inertia I and the section modulus S about the
X–X centroidal axis (shown in Figure 8.9a) are much larger than I and S about the Y–Y
centroidal axis. As a result, a shape that is aligned so that bending occurs about the X–X
axis is said to be bending about its strong axis. Conversely, bending about the Y–Y axis is
termed bending about the weak axis.
In U.S. customary units, a wide-flange shape is designated by the letter W followed by
the nominal depth of the shape measured in inches and its weight per unit length measured
in pounds per foot. A typical U.S. customary designation is W12 × 50, which is spoken as
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