Calculating Extension & Stress in Machined Steel Bar

In summary, the problem is asking for the total extension and tensile stress of a steel bar with varying diameters when subjected to an axial tensile load. The solution involves treating the bar as three separate bars in series and using the equation \frac{A_{i}E}{L_i} to calculate the spring constant for each portion.
  • #1
wock
3
0

Homework Statement



1. A steel bar 375mm long is machined to give a diameter of 75mm for the first 175mm length, a diameter of 45mm for the next 100mm length and a diameter of 37mm for the final 100mm length. Determine:

(i) The total extension of the bar when it’s subjected to an axial tensile load of 84 kN.

(ii) The tensile stress in each portion of the bar.
Assume E = 200 GN/m2


Homework Equations





The Attempt at a Solution



can this be solved by working out each part as if it were 3 separate bars ?
 
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  • #2
The simple answer is yes. A bar with varing diameter as noted is nothing more that 3 springs in "series" with 3 different spring constants "k". An axial force applied to springs in series would be equal to the sums of the [itex] k_i \cdot x_i [/itex].

[tex] k_i [/tex] in this problem would be [itex] \frac{A_{i}E}{L_i} [/itex]
 
  • #3
thanks
 

Related to Calculating Extension & Stress in Machined Steel Bar

1. What is the formula for calculating extension in a machined steel bar?

The formula for calculating extension in a machined steel bar is: Extension = (Force x Length)/(Cross-Sectional Area x Young's Modulus).

2. How do I calculate stress in a machined steel bar?

To calculate stress in a machined steel bar, use the formula: Stress = Force/Cross-Sectional Area.

3. What is Young's Modulus and how does it relate to calculating extension and stress?

Young's Modulus, also known as the modulus of elasticity, is a measure of a material's stiffness or resistance to deformation under stress. It relates to calculating extension and stress by providing a constant value that is used in the formulas for both calculations.

4. Can I use the same formula for calculating extension and stress in any type of steel bar?

Yes, the same formulas can be used for calculating extension and stress in any type of steel bar as long as the material's Young's Modulus is known and the bar is under uniform stress.

5. Are there any factors that can affect the accuracy of these calculations?

Yes, there are several factors that can affect the accuracy of these calculations, such as temperature, material defects, and non-uniform stresses. It is important to ensure that all necessary variables are accounted for and that the material is under uniform stress in order to obtain an accurate result.

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