Stress Distribution in Bent Beams: Compression vs Tension

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Discussion Overview

The discussion revolves around the stress distribution in bent beams, specifically addressing the concepts of compression and tension in relation to bending stress. Participants explore the mechanics of how stress varies across the beam's cross-section during bending, including the implications of axial strain and the neutral axis.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants question why the inner part of a bent beam, which undergoes compression, experiences minimum stress, while the outer part, under tension, has maximum stress.
  • One participant asserts that bending stress is not simply equal to force divided by area, indicating a need for a deeper understanding of stress distribution in bending scenarios.
  • Another participant explains that axial strain is positive on the outside of the bend (tension) and negative on the inside (compression), leading to corresponding positive and negative axial stresses.
  • There is a clarification that compression corresponds to negative (minimum) stress and tension corresponds to positive (maximum) stress, although the implications of this relationship are still being explored.

Areas of Agreement / Disagreement

Participants generally agree on the relationship between axial strain and stress in bent beams but continue to explore the implications and nuances of these concepts. Some points remain contested, particularly regarding the interpretation of stress values in relation to bending.

Contextual Notes

The discussion includes assumptions about the definitions of stress and strain, as well as the conditions under which these relationships hold true. There are unresolved aspects regarding the application of these concepts to specific beam geometries and loading conditions.

chetzread
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Homework Statement


I have the bent beam like this . The inner part of beam undergo compression , right , so it shortens. Why the stress is minimum at here ?
the outer part undergo tension , why the normal stress is maximum here ?
This is from my notes
http://imgur.com/a/H8fy4

Homework Equations

The Attempt at a Solution


since the outer part elongate , the surface area is max , so it should has min stress , right ? pressure = force / area [/B]
 
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chetzread said:

Homework Statement


I have the bent beam like this . The inner part of beam undergo compression , right , so it shortens. Why the stress is minimum at here ?
the outer part undergo tension , why the normal stress is maximum here ?
This is from my notes
http://imgur.com/a/H8fy4

Homework Equations

The Attempt at a Solution


since the outer part elongate , the surface area is max , so it should has min stress , right ? pressure = force / area [/B]
Bending stress is not equal to force / area.

The terms "minimum stress" and "maximum stress" are entirely relative in beam bending.
 
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SteamKing said:
Bending stress is not equal to force / area.

The terms "minimum stress" and "maximum stress" are entirely relative in beam bending.
can you explain why bending stress is min when the beam is compressed?
 
Analysis of the kinematics of deformation shows that on the outside of the bend (relative to the neutral axis), the axial strain is positive, and, on the inside of the bend (relative to the neutral axis), the axial strain is negative. At the neutral axis, the axial strain is zero. Along with these axial strains go axial stresses, which are proportional to the axial strains. So the axial stresses are positive on the outside of the bend (tension), and the axial stresses are negative on the inside of the bend (compression).
 
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Chestermiller said:
Analysis of the kinematics of deformation shows that on the outside of the bend (relative to the neutral axis), the axial strain is positive, and, on the inside of the bend (relative to the neutral axis), the axial strain is negative. At the neutral axis, the axial strain is zero. Along with these axial strains go axial stresses, which are proportional to the axial strains. So the axial stresses are positive on the outside of the bend (tension), and the axial stresses are negative on the inside of the bend (compression).
so compression correspnds to negative(minuimum stress) tension corresponds to positive(maximum stress) ??
 
chetzread said:
so compression correspnds to negative(minuimum stress) tension corresponds to positive(maximum stress) ??
Sure.
 

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