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Mechanics of Materials-Steel
Structural Steel
Structural steel considered one of the predominant materials for construction
of buildings, bridges, towers and other structures. The preferable physical
properties of steel makes it widely used for construction of steel bridges, high
rise buildings, and other structures. The high strength, ductility, toughness,
and uniformity are some of the desirable properties that made steel a leading
martial for structures. Despite steel desirable properties, disadvantages of
using steel include associated maintenance cost, fatigue, and susceptibility to
buckling
Stress-Strain Relationship
The stress-strain relationship of steel material as plotted by the results of a
tensile test is shown in Figure 1. The relationship is linear up to the
proportional limit; where the material follows the Hook’s law. The upper yield
point in the curve is the peak value reached after the linear part; the peak
value is followed by a lower yield point at which the curve levels off.
Elastic limit
Upper yield point
A
Proportional limit
Lower yield point
0
ε
B
Elastic
Plastic
Strain Hardening
Necking and failure
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As shown in the curve, the stress remains constant while the strain continues
to increase. At that stage the elongation continues as long as the load is not
removed. The constant stress region of the curve called the yield plateau, or
plastic range.
The strain hardening of the stress-strain curve begins at a strain of
approximately 12 times the strain at yield. At that stage, additional stress is
required to further extend the material until a maximum stress is reached,
after which the stress decreases with increasing the strain, and then fracture
occurs. This behavior as exhibited by the curve is called ductility, which allows
the steel material to largely deform before fracturing.
The elastic limit of the material is the stress on the curve that lies between
the proportional limit and the upper yield point. If the material is loaded to a
stress lower than this value, unloading will not induce any permanent
deformations. Unloading before elastic limit will follow the linear path
developed during loading the material. Unloading from a point beyond the
elastic limit will follow a path parallel to the linear part but it would produce a
permanent deformation.
Idealized Stress-Strain Relationship
In idealized stress strain curve as shown in Figure 2, the proportional limit,
elastic limit, and the upper and the lower yield point are represented by a
single point called yield point, defined by the stress Fy. The maximum stress in
the idealized curve represents the ultimate tensile strength Fu. It should be
noted that the shape of the curve below is typical for mild structural steels
which are different from each other in the values of Fy and Fu. The ratio of the
stress to strain within the elastic range called Young's modulus and denoted
by E. The modulus of elasticity, E, is the same for all structures steel and has
a value of 29,000,000 psi.
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Fu
Fy
E
1
ε
Figure 2
High Strength Steel
High strength steel is less ductile than mild structural steel discussed above. A
typical stress-strain curve is shown in Figure 3. It can be noted that there is no
well-defined yield point or yield plateau in the curve. To define the yield
strength, a stress at the point of unloading that corresponds to a strain of
0.002 is used. This method of determining the yield strength is called the
0.2% offset method. The two properties usually needed for steel design are Fu
and Fy regardless of the shape of the stress-strain curve and regardless of how
Fy was obtained.
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Fu
Tensile strength
Fy
Yield strength
Elastic limit
E
1
Residual strain
ε
Figure 3
Properties of Steel
The properties of structural steel are determined by the quantity of carbon
and other elements that are present in the chemical composition. Elements
such as Silicon; Nickel; Manganese; and Copper are normally added. Steel
having significant amount of these elements is referred to as an alloy steel.
Structural steels can be categorized according to their chemical composition
into plain carbon steels, low-alloy steels, and high-alloy steels.
Grades of Structural Steel
Structural steels are generally grouped into several ASTM classifications which
are identified by the designation assigned by the ASTM. Grade A36 steel with
Fy =36 ksi and Fu= 58 ksi is one of the most commonly mild structural steel
used. Other grades used are A572 Grade 50 and A992. More information is
available for each grade of steel in the AISC Steel Construction Manual. The
steel grades for the available structural shapes are shown in Table 2-3 of the
AISC Steel Construction Manual.
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Structural Shapes
One of the objectives of the design is to select the adequate section for the
individual member under consideration. Most frequently, the selection
involves choosing a standard section from the shapes that are available. Most
of the standard shapes are produced by hot-rolling manufacturing process.
Symbols for the structural shapes of some of the widely used hot-rolled
shapes are shown in Table 1.
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The dimensions and designations of the standard available shapes can be
found in the AISC Steel Construction Manual. Usually, the shapes with large
moments of inertia compared to their areas are preferable. The commonly
used I, T, and C shapes fall into this category. As shown in the AISC Steel
Construction Manual, the steel cross-sections are designated by their shapes,
for example there are angles, tees, and plates. One important distinction with
regard to defining the shapes, is the American standard beams (S beams) and
the wide-flange beams (W beams) as they are both I-shaped as shown in
Figure 4. The wide-flange shape is designated by the nominal depth and the
weight per foot, such as a W16X100 which has a nominal 16 in depth and
weighs 100 pounds per foot.
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W-shape Beam
Standard Beam
Figure 4
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Example Problem (1)
A structural shape of A588 Steel is to be used as a beam in a building
structure. What are the values of the yield stress Fy, ultimate tensile strength
Fu, and the modulus of elasticity E.
a.
b.
c.
d.
Fy= 36 ksi, Fu = 58 ksi, E = 29,000 ksi
Fy= 50 ksi, Fu = 58 ksi, E = 29,000 ksi
Fy= 50 ksi, Fu = 70 ksi, E = 29,000 ksi
Fy= 65 ksi, Fu = 80 ksi, E = 29,000 ksi
Referring to Table 2-3 of the AISC Steel Construction Manual, Fy= 50 ksi, Fu =
70 ksi, and E = 29,000 ksi for all grades of types of steel.
Answer: c
Example Problem (2)
A W18X97 is to be used as a beam in a building structure. What is the selfweight of the beam if a span of 50 ft is required?
a.
b.
c.
d.
6.25 kips
9.85 kips
4.85 kips
13.25 kips
A W18X97 weight 97 Ib/ft, so for a beam of 20 ft span:
Weight of beam = (97 Ib/ft)(50ft)=4,850 Ib = 4.85 kips
Answer c.
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