### The stress may be obtained from tensile tests

The
most important material properties which influence the behaviour of steel
tension and compression members are the modulus of elasticity, E, and the yield
stress, ay. Values for both the modulus of elasticity and the yield stress may
be obtained from tensile tests on coupon specimens or from compression tests (Parke, 1988).

Figure
2.4: Stress strain curve and its fracture

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The
slope of the line in a region where stress is proportional to strain and is
known as the modulus of elasticity or young’s modulus. The modulus of
elasticity (E) defines the properties of a material as it undergoes stress,
deforms, and then returns to its original form after the stress is removed. It
is a measure of the stiffness of a given material. To compute the modulus of
elastic, simply divide the stress by the strain in the material. This modulus
is of interest when it’s far essential to compute how much a rod or wire

The
stress applied to the material at which plastic deformation begins to arise in
called as the yield strength of a material. In ductile materials for instance,
at some point, the stress strain curve deviates from the straight line
relationship and law no longer applies as the strain increases faster than the
stress. In brittle materials, little or no plastic deformation occurs and the
material fractures close to the end of the linear elastic portion of the curve.

The
ultimate tensile strength (UTS) or the tensile strength, is the maximum stress
level reached in a tensile test. The strength of a material mean its ability to
withstand external forces without breaking. In brittle materials, the UTS will
be at the end of the linear elastic portion of the stress strain curve or close
to the elastic limit. While, in ductile materials, the UTS will be well outside
of the elastic portion into the plastic portion of the stress strain curve.

2.3.1
Measures
of Ductility (Elongation and Reduction of Area)

The ductility of a material IS defined as a measure of
the extent to which a material will deform before it fail due to fracture. Moreover,
the amount of ductility plays an important factor when considering forming
operations such as rolling and extrusion which provides an indication of how
visible overload damage to a component might become before the component
fractures. Besides that, ductility is also used as a quality control measure to
assess the level of impurities and proper processing of a material.

The common measures of ductility were the engineering
strain at fracture (elongation) and the reduction of area at fracture. These
two properties were obtained by fixing the specimen back together after
fracture thus, measuring the change in length and cross sectional area. The
change in axial length divided by the original length of the specimen or
portion of the specimen is called elongation which expressed as a percentage.
Percent elongation is defined simply as

%Elongation
= (Lf – Lo)/Lo / 100

Where, Lo is the initial gage length and Lf
is the length of the gage section at fracture. For most materials, the amount
of elastic elongation is so small that the two are equivalent. When this is not
so (as with brittle metals or rubber), the results should state whether or not
the elongation includes an elastic contribution. The other common measure of ductility
which is percent reduction of area is defined as,

%Reduction
area = (Ao _ Af)/Ao / 100

Where, Ao and Af are the initial
cross-sectional area and the cross-sectional area at fracture, respectively.
Figure 2.2 shows the stress strain curve comparing between brittle and ductile
fracture.

Figure 2.5:
Stress strain curve comparing between brittle and ductile fracture.

2.1
Structural
steel compression member

A
structural member which carries an axial compression load is known as a
compression member which are called as columns, trusses member and bracing
members. Columns, posts or stanchions are the vertical compression members in
buildings whereas struts is a compression member called in a roof trusses.

Therefore,
compression test is needed in order to determine the behavior or response of a
material or specimen while it experiences a compressive load by measuring the fundamental
variables, such as, strain, stress, and also deformation. Furthermore, only by
testing a material in compression, then the compressive strength, yield
strength, ultimate strength, elastic limit, and the elastic modulus among other
parameters may all be determined. Besides, with the understanding of these
different parameters and the values associated with a specific material then it
can be concluded whether or not the material or the specimen is suited for
specific applications or if it will fail under the specified stresses or

Even
though steel is a very strong material and very reliable in structural
construction of buildings but its effectiveness, however, is only guaranteed
the variety type of failures of steel structures. The most common cause of
failure is fatigues, whereas the most spectacular one is brittle fracture.

2.4.1
Buckling
of compression member

Buckling can occur
when long slender steel members are subjected to compressive loads and suddenly
undergoes bending as shown in the Figure 2.6 (b). Consider a long slender
compression member, as an axial load, P is applied and increased slowly, it
will ultimately reach a value of the critical buckling load of the column, Pcr,
which will cause buckling of the column. Buckling result in instability of
columns, and causes sudden failure. Buckling occurs when load, P is greater
that the critical load, Pcr. The most common failure modes in structural steel
member are local buckling, flexural buckling (Euler buckling) and torsional
buckling

Figure 2.6: Buckling of axially

Flexural buckling
(Euler Buckling) is a primary type of buckling which occurs when the members
are subjected to flexure or bending where they become unstable or when the
lateral loads on the members increase beyond its limit as shown in Figure 2.6.
However, these are one of the least occurring failures in steel structure.

Unlike flexural
buckling, local buckling occurs when a part or section of the column buckles
before other modes of failure occurs due to its small thickness at some parts
of its cross-section as shown in Figure 2.7. Local buckling depends on the slenderness
(width-to-thickness ratio) of the plate element and the yield stress (fy) of
the material.

In
addition, there is one more important failure of steel structure which known as
failure due to lateral torsional buckling as shown in Figure 2.8.This kind of
failure happens when the compression flange of the steel beam is unrestrained.
The loads are present on the floor and there always in an eccentricity of the
load, this eccentricity leads to a twisting moment. Therefore, as the flange of
the steel beam is not fixed, the beam twists as well as moves laterally.

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