Stress Distribution in Bent Beams: Compression vs Tension

[chetzread]

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]

 

[SteamKing]

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.

 

[chetzread]

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?

 

[Chestermiller]

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).

 

[chetzread]

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) ??

 

[Chestermiller]

so compression correspnds to negative(minuimum stress) tension corresponds to positive(maximum stress) ??

Sure.