 # 2- Easy approach to Stress strain relationship.

## Stress-strain relationship.

### Stress-strain relation video.

The video discusses the introduction of structural steel. We will discuss the stress-strain relationship between structural steel and structural steel decomposition. The video has a subtitle and a closed caption in English.

The following points will be included as follows:

1-Stress strain relationship for steel.

2-The various regions observed from the Stress-strain relationship for steel.

3-How to derive the yield stress from the Stress-strain relationship for steel?

4-Structural steel decomposition.

5-The various grades of steel and their graphs.

## Stress-strain relationship for steel.

This lecture is the second lecture on the introduction of structural steel. We will discuss the stress-strain relationship in structural steel. If a piece of ductile structural steel is subjected to a tensile force.

The length of the piece will increase due to that load. As the tensile force increases at a constant rate, then the elongation will increase linearly.

For instance, The elongation will double when the stress goes from 6000 psi to 12000 psi, pound per square inch. When the tensile stress reaches a value roughly =3/4 of the ultimate strength of steel, The elongation begins to increase at a greater rate without a corresponding increase in the stress.

### The graph between stress and strain.

This is a piece of steel for which we have a discussion. The piece has a cross-section A.  The stress equation is shown as f=P/A and the elongation ε=ΔL/L. Where f =axial tensile stress. A= cross-sectional area.

ε=axial strain, L= the length of the specimen, ΔL change in length. The stress-strain is represented by a graph where strain is drawn as an x-axis, and the stress is drawn as a vertical axis.

The previous equation f=P/A  is used for the estimation of the stress f. The slope line represents E or the elastic modulus of elasticity. Upon load increase, the line extends till with an increase in stress

With a little increase in strain, later when loads increase, any increase in stress will be accompanied by a Considerable increase in strain. Point A is reached.

Later Any increase in load will cause an increase in both stress and strain till the ultimate tensile strength is reached. The stress will decrease with a considerable increase in strain till the fracture point.

The major points in the graph are the proportional limits.

The other point is the Lower yield point.

The third point is the point of ultimate tensile strength, and the last point is the fracture point.

### The various regions observed from the Stress-strain relationship for steel.

The graph can be subdivided into four regions. The first region is the elastic region,  in which when the load is removed, the specimen will return to its original length. But for the other regions. There will be permenant elongation. The second region is the plastic region, the third is stress hardening, and the last is necking and failure.

The different data for the modules of Elasticity and the various regions are also shown in this graph.

## How to get the yield stress for a specimen?

How to get the yield stress for a specimen? There are two methods, the first method is to select a strain of 0.002 in/inch, or 0.20% inch/inch.
The dotted line is offset from the initial straight line till the dotted line will intersect with the graph at a point, for which the stress is considered as Fy at 0.2% strain.
The second method is to construct a vertical line at a strain of 0.005 inches/inch or 0.5% inch /inch. The intersection with the graph. The stress is considered to be Fy at 0.5% inch/inch. This procedure is done when we have a high-strength steel specimen.

So Fy can be determined either based on 0.20% strain or can be based on 0.50% strain. This is a typical plot for a tensile test.

## The structural steel composition and the steel grades for structural steel.

The following slide will give the structural steel composition and the steel grades for structural steel.

The following composition of two well-known grades of steel ASTM A-572 and ASTM A-36.

The differences between the two structural steel grades regarding carbon, Manganese, Phosphorous, Sulfur, and silicone are shown in the table below.

The first column shows the various grades of steel.ASMA-A36 has a density of 7800 kg/m3 or (0.028 lb/cu in). Young’s modulus of elasticity for A36, is always taken, as 29,000,000 psi or (200 GPA). The Giga is 10^9; the pascal is N /m^2.

Poisson’s ratio is the lateral strain/ longitudinal strain=0.20. The tensile force will create an elongation but accompanied by compressive strain in the perpendicular direction =0.20.

## The different curves for steel grades.

The next graph shows the different curves for steel grades starting with ASTM-A-36, which denotes yield stress of 36 ksi. The second curve is for high strength low-alloy carbon steel ASTM-A-572 with a yield stress of 50 ksi.

There is another curve for Heat treated constructional alloy ASTM-A-514, quenched and tempered alloy steel, where the yield stress reaches 100 ksi. The Fy is estimated based on 0.20% inch/inch strain. 0.20% inch / inch strain. All the previous steel grades have a common modulus of elasticity of 29,000 ksi.

The lower table shows the relation between the yield point and the different steel grades.

For A36 the yield point=36 ksi and the tensile point ranges from 58-80 ksi.  For A572 the yield point=42-65 ksi, the tensile point is from 0.5-0.70%, 50 ksi-70 ksi.

For A514  the tensile point is from 110-130 ksi. The carbon steel types are shown in the slide image. For the ASTM. We are starting with ASTM-A36 for structural shapes and plates. The High strength of alloy steel. The grade starts with A441 for structural shapes and plates and then A572.

This is a link for the Pdf data used for this post, you can view or download the data.

The next new subject will be the different structural steel shapes, and the related weights will be discussed.

if you want to see the major changes between Cm#14 and CM#15 regarding the different grades of steel and their uses for steel elements and bars please refer to post 1A.

A very good reference, A Beginner’s Guide to Structural Engineering. Scroll to Top
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