If a steel member is subjected to a tensile load (P), the stress and strain of the member can be computed as (Ref. ASTM A370, Standard Test Methods and Definitions for Mechanical Testing of Steel Products):

• Stress, f = P/A

• Strain, ε = ΔL  / L

where, A     = cross sectional area

         ε      = Axial strain

         L      = Total Length of the steel member

         ΔL   = Change in length due to load P

The typical stress-strain curve of mild steel is shown in Figure 1. When the load is increased at a uniform rate, the elongation of the member will also increase linearly within certain limits, called the proportional limit. The material follows Hooke’s law, i.e., the relationship between stress and strain is linear upto the proportional limit. After that point, the elongation of the material increases at a greater rate while the stress remaining almost constant.

If the load is applied rapidly, the peak value, the upper yield point is reached. While the slow loading results in leveling off the value at a lower yield point. The highest stress that a steel material can withstand without permanent deformation is the elastic limit of that material which lies between proportional limit and upper yield point. In practice, the actual value of the elastic limit is rarely calculated since it is almost equal to the proportional limit. Thus, sometimes the term proportional elastic limit is also used. The elastic region of the material lies up to this point.

Young’s Modulus of Elasticity, E measures the ratio of stress to strain of the steel in the elastic region. According to AISC Specification, E = 29,000 ksi. has been used in practice.

After the yield point, if the load is still increased, the stresses in the material remain constant while the strain (or elongation of the material) continues to increase. This constant elongation region is called the plastic region. The starting point of this region gives us the yield stress, which is one of the most important property of steel for the design of steel structures.

Yield stress is the stress at which the steel material elongates significantly without an increase in stress. Yield Stress is commonly designated as Fy.  The yielding of steel members without any increase in stress prevents the steel structures from sudden failure.

Typically, the plastic region continues until the strain is 15 to 20 times the strain at the yield. At the end of this region, the material requires addition stress for elongation. This is called strain hardening. The stress after this point increases and reaches to the maximum value (peak of the stress-strain curve). This maximum value is the ultimate stress (tensile strength) of the steel member, which is denoted by Fu. Once the ultimate stress is reached, a sharp reduction in the cross-section of the member occurs (known as necking) and the steel rupture occurs.