Calculating Cross Sectional Dimensions of Steel Bar Under Compression

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The discussion focuses on calculating the changes in cross-sectional dimensions of a steel bar under compression. Given a rectangular cross-section of 120mm x 60mm and a compressive force of 1500kN, the Young's modulus (E) is specified as 200GPa, and Poisson's ratio (v) is 0.3. The application of these parameters indicates that the cross-sectional dimensions will decrease due to the compressive force, with specific calculations required to determine the exact new dimensions based on longitudinal and transverse strains.

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  • Understanding of Young's modulus and its application in material deformation
  • Knowledge of Poisson's ratio and its effect on strain
  • Familiarity with basic mechanics of materials
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  • Calculate longitudinal strain using the formula: ε_long = σ / E
  • Determine transverse strain using Poisson's ratio: ε_trans = -v * ε_long
  • Apply the calculated strains to find the new dimensions of the steel bar
  • Explore the implications of material properties on structural integrity under compression
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Mechanical engineers, materials scientists, and students studying mechanics of materials who are interested in understanding the effects of compressive forces on structural components.

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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Yes, that is correct. Good job!
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