Last Updated on September 12, 2026 by Maged kamel
Easy approach to stress-strain relationship.
The ensuing details will be covered as follows:
1-Steel’s stress-strain relationship.
2-The various regions observed from the Stress-strain relationship for steel.
3-How can the steel stress-strain relationship be used to calculate the yield stress?
4-The different steel grades and their graphs.
5-The various grades of steel and their graphs.
Stress-strain relationship for steel.
Today’s second lecture introduces structural steel. We’ll discuss the relationship between stress and strain in ductile structural steel when it is pulled taut.
That load will increase the piece’s length. Elongation grows linearly as long as the tensile force increases at a consistent rate.
For example, when the tension increases from 6000 psi to 12000 psi (pounds per square inch), the elongation will quadruple. The elongation rate increases faster without a corresponding increase in stress as the tensile stress approaches about 3/4 of the steel’s maximum strength.
The graph of stress versus strain.
We are discussing this piece of steel. The cross-section of the piece is A. f=P/A is the stress equation, while ε=ΔL/L is the elongation. f is the axial tensile stress. The Area of the cross-section is denoted by A.
ε stands for axial strain, L for specimen length, and ΔL for length change. A graph with stress on the vertical axis and strain on the horizontal axis shows the stress-strain relationship.
The stress f is estimated using the preceding equation: f = P/A. The elastic modulus of Elasticity, or E, is shown by the inclination of the line. The line stretches until stress increases with load.
As the load increases, stress and strain rise, starting with a slight increase. We have arrived at point A.
Later, until the ultimate tensile strength is reached, increasing load increases both stress and strain. Until the fracture point, the stress decreases while the strain increases. The proportional limit is the graph’s main point.
The Lower yield point is the other point.
The ultimate tensile strength point is the third point, and the fracture point is the last.
The various regions observed in the Stress-strain relationship for steel.
Four zones may be recognized on the graph. In the first region, the specimen returns to its initial length once the load is removed; in the other regions, it does not. A permanent elongation will occur. The plastic zone is the second region, stress hardening the third, and necking and failure the final regions.
This graph also shows the elastic data for the elastic modulus and the various regions.
How can you determine the yield stress for a specimen?
How can one find a specimen’s yield stress? There are two approaches. The first one involves choosing a strain of 0.20% or 0.002 in/in.
When the dotted line crosses the graph at a given point, the stress is taken as Fy at 0.2% strain. The dotted line is initially offset from the original straight line.
Building a vertical line at a strain of 0.005 inches/inch (0.5% of the inch) is the second technique—the point where the graph and the vertical line intersect. When the strain is 0.5% (0.005 in/in), it is considered Fy. For a high-strength steel specimen, we use this technique.
So Fy can be determined at either 0.20% or 0.50% strain. This is a typical tensile test plot.
The structural steel composition and the steel grades for structural steel.
The next slide shows the composition and steel grades of structural steel.
The composition of two well-known steel grades, ASTM A-572 and ASTM A-36, is as follows.
The table below illustrates the variations in carbon, manganese, phosphorus, sulfur, and silicon between the two structural steel classes.
The first column shows the different steel grades. The density of ASMA-A36 is 7800 kg/m3, or 0.028 lb/cu in. Young’s modulus of Elasticity for A36 is always calculated using a value of 200 GPA (29,000,000 psi). The Pascal is N /m^2, and the Giga is 10^9.
The lateral strain/longitudinal strain = 0.20 is Poisson’s ratio. A tensile force will cause elongation, but it will also cause compressive strain in the perpendicular direction, equal to 0.20.
The different structural steel grades.
The following graph, which starts with ASTM-A-36, indicates a yield stress of 36 ksi. The second curve shows ASTM A572 high-strength low-alloy carbon steel with a yield stress of 50 ksi.
For heat-treated construction alloy ASTM A514 and quenched-and-tempered alloy steel, an additional curve shows a yield stress of 100 ksi. Based on 0.20% inch/inch strain, the Fy is estimated. Strain of 0.20% inch/inch. The modulus of Elasticity shared by all prior steel grades is 29,000 ksi.
The lower table shows the relationship between the yield point and the various steel grades.
For A36, the yield point is 36 ksi, and the tensile strength ranges from 58-80 ksi. For A572, the yield point is 42- 65 ksi, and the tensile strength is 0.5-0.70%, 50 ksi-70 ksi.
For A514, the tensile strength ranges from 110 to 130 ksi. The slide image shows steel types. We are starting with ASTM A36 for structural shapes and plates. The High strength of alloy steel. The grade begins with A441 for structural shapes and plates, and then A572.
You can view or download the PDF for this post from the following link.
The following new subject covers the different structural steel shapes and their related weights, as discussed in post 3.
To see the major changes between Cm#14 and CM#15 regarding steel grades and their uses for steel elements and bars, refer to post 1A.
This is a link to a very good reference: Chapter 1 – Introduction–An Overview of the AISC Steel Construction Manual, 14th Edition.
This is a link to a very good reference: Chapter 1 – Introduction–An Overview of the AISC Steel Construction Manual, 15th Edition.
This is a link to a very good reference: Chapter 1 – Introduction–An Overview of the AISC Steel Construction Manual, 16th Edition.