Calculating Extension & Stress in Machined Steel Bar

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SUMMARY

The discussion focuses on calculating the total extension and tensile stress in a machined steel bar subjected to an axial tensile load of 84 kN. The bar, measuring 375mm in length, features three distinct diameters: 75mm for the first 175mm, 45mm for the next 100mm, and 37mm for the final 100mm. The Young's modulus (E) is given as 200 GN/m². The solution approach involves treating the bar as three separate segments, each with its own spring constant, to determine the total extension and stress in each section.

PREREQUISITES
  • Understanding of axial tensile load calculations
  • Familiarity with Young's modulus and its application
  • Knowledge of stress and strain concepts in materials
  • Basic principles of mechanics of materials, specifically the concept of springs in series
NEXT STEPS
  • Study the calculation of tensile stress in varying cross-sectional areas
  • Learn about the mechanics of materials, focusing on axial loading
  • Explore the concept of spring constants in mechanical systems
  • Investigate the application of Young's modulus in real-world engineering problems
USEFUL FOR

Mechanical engineers, materials scientists, and students studying mechanics of materials will benefit from this discussion, particularly those involved in structural analysis and design of components subjected to axial loads.

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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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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 k_i \cdot x_i.

k_i in this problem would be \frac{A_{i}E}{L_i}
 
thanks
 

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