Calculating Cross Sectional Dimensions of Steel Bar Under Compression

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In summary, to calculate the cross sectional dimensions of a steel bar under compression, you need to know the applied load, the length of the bar, and the material properties of the steel. The yield strength of steel is an important factor in this calculation, as it determines the maximum load the bar can withstand without failing. The length of the bar directly affects its cross sectional dimensions, with longer bars requiring a larger cross sectional area to withstand the load. There is no standard cross sectional dimension for steel bars under compression, as it varies depending on the specific scenario. It is important to consider safety factors, with a recommended factor of at least 2, when calculating these dimensions.
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Stacyg
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A steel bar of rectangular cross section 120mm x 60mm is compressed along its longitudinal direction by a force of 1500kN. Do the cross sectional dimensions increase or decrease ? Calculate and write down the resulting dimensions for both sides for both sides of the cross section. Youngs modulus E=200GPa, and Poissons rato of v=0.3

I am not sure what equations to use to do this so I haven't showed any attempts.
Any help would be great.
 
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HINT: How is Poisson's ratio related to the transverse and longitudinal strains?
 
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I would approach this problem by using the principles of mechanics and material science. The cross sectional dimensions of the steel bar will change under compression due to the applied force. This change in dimensions is known as strain, which is a measure of the deformation of a material.

To calculate the resulting dimensions, we can use the formula for strain, which is defined as the change in length over the original length. In this case, the change in length is caused by the applied force, and the original length is the initial dimension of the steel bar.

First, we need to convert the force of 1500kN to Newtons (N) as the units used in the formula for strain are in SI units. 1kN is equal to 1000N, so 1500kN is equal to 1,500,000N.

Next, we can calculate the strain using the formula: strain = (change in length) / (original length). The change in length is equal to the force divided by the cross-sectional area and the original length is the length of the steel bar. The cross-sectional area can be calculated by multiplying the width (60mm) by the height (120mm), which gives us a cross-sectional area of 7200mm^2 or 0.0072m^2.

Strain = (1500000N) / (0.0072m^2 x 200GPa) = 0.104

Now, we can use the Poisson's ratio to calculate the change in dimensions. Poisson's ratio is a measure of the lateral strain (change in width) over the axial strain (change in length). In this case, since the force is applied along the length of the steel bar, the change in width will be negative.

Change in width = -0.3 x 0.104 x 120mm = -3.744mm

Therefore, the resulting width will be 60mm - 3.744mm = 56.256mm. The change in height can be calculated using the same formula, resulting in a change of 1.1232mm and a resulting height of 121.1232mm.

In summary, the cross-sectional dimensions of the steel bar will decrease under compression, with the resulting dimensions being 56.256mm x 121.1232mm. It is important to note that these calculations are based on ideal conditions and may
 

1. How do you calculate the cross sectional dimensions of a steel bar under compression?

To calculate the cross sectional dimensions of a steel bar under compression, you need to know the applied load, the length of the bar, and the material properties of the steel. Then, you can use the formula A = F/(σy*L) where A is the cross sectional area, F is the applied load, σy is the yield strength of the steel, and L is the length of the bar.

2. What is the yield strength of steel?

The yield strength of steel is the amount of stress that a steel material can withstand before it begins to deform permanently. It is an important factor in calculating the cross sectional dimensions of a steel bar under compression as it determines the maximum load the bar can withstand without failing.

3. How does the length of the steel bar affect its cross sectional dimensions under compression?

The length of the steel bar directly affects its cross sectional dimensions under compression. The longer the bar, the larger the cross sectional area needs to be in order to withstand the applied load. This is because longer bars have a higher tendency to buckle under compression.

4. Is there a standard cross sectional dimension for steel bars under compression?

No, there is no standard cross sectional dimension for steel bars under compression. The dimensions will vary depending on the applied load, material properties, and length of the bar. It is important to calculate the dimensions for each specific scenario to ensure the bar can withstand the intended load.

5. Are there any safety factors to consider when calculating the cross sectional dimensions of steel bars under compression?

Yes, it is important to consider safety factors when calculating the cross sectional dimensions of steel bars under compression. These factors take into account potential variations in material properties, manufacturing processes, and unforeseen loading conditions. It is recommended to use a safety factor of at least 2 to ensure the bar can safely withstand the applied load.

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