Effective area for compression versus tension of a link?

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SUMMARY

The analysis of link BD and link CE reveals that link BD is in tension while link CE is in compression, necessitating different calculations for normal stress. For link BD, the effective cross-sectional area for normal stress should be calculated as (Total Area - Pin Diameter), whereas for link CE, the Total Area is used. This distinction arises from the loading conditions: link BD experiences tensile forces at the outer ends, while link CE experiences compressive forces toward the center, affecting the distribution of stress across the links.

PREREQUISITES
  • Understanding of equilibrium equations in structural analysis
  • Knowledge of tensile and compressive forces in mechanics
  • Familiarity with normal stress calculations
  • Concept of effective cross-sectional area in structural components
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  • Study the principles of equilibrium in structural mechanics
  • Learn about normal stress and its calculation in tension and compression
  • Investigate the effects of pin diameter on effective cross-sectional area
  • Explore case studies involving tension and compression in structural links
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Structural engineers, mechanical engineers, and students studying mechanics of materials will benefit from this discussion, particularly those focused on analyzing forces in structural links.

joahe
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I solved the equilibrium equations and found that link BD is in tension while link CE is in compression, but my resulting answers for normal stress were wrong.

The solutions show that the cross area to be used for normal stress at links BD and CE should be different. Link BD should incorporate the (Total Area - Pin Diameter) while link CE incorporates the Total Area.

Why is this true?
 
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For the A & D link the loading of both pins are pulling toward the outer ends of the link with only the tensile strength of the two areas on each side of each pin resisting the load.

For the C & E link both pins are pushing toward the center of the link, so they are actually trying to compress the area between the C & E pins.
 
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The maximum value of the average normal stress doesn't occur in the pin for the link in compression like it does for the link in tension.
 
Would you mind explaining that what is the total area here being referred to?
 

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