Stress Distribution in Bent Beams: Compression vs Tension

In summary: The stress at a point is always maximum when the force is directed perpendicular to the direction of the change in length.
  • #1
chetzread
801
1

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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  • #2
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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  • #3
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?
 
  • #4
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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  • #5
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) ??
 
  • #6
chetzread said:
so compression correspnds to negative(minuimum stress) tension corresponds to positive(maximum stress) ??
Sure.
 

FAQ: Stress Distribution in Bent Beams: Compression vs Tension

What is the difference between compression and tension in a beam?

Compression and tension are two types of forces that act on a beam. Compression is a force that pushes down on a beam, while tension is a force that pulls on the beam. In simple terms, compression compresses or shortens the beam, while tension elongates or stretches it.

How can compression or tension affect the strength of a beam?

Compression and tension can both weaken a beam, but in different ways. Too much compression can cause the beam to buckle or collapse, while too much tension can cause it to snap or break. It is important to design a beam to withstand the expected amount of compression or tension it will experience.

Which type of beam is better suited for handling compression?

Generally, a beam that is thicker and shorter will be better equipped to handle compression forces. This is because a thicker beam is able to distribute the force over a larger area, and a shorter beam is less likely to buckle under the force. However, the specific design of the beam will also play a significant role in its ability to handle compression.

How does the material of the beam affect its ability to withstand compression or tension?

The material of the beam is a crucial factor in its ability to handle compression and tension forces. Different materials have varying levels of strength and elasticity, which will affect how they respond to these forces. For example, a steel beam is stronger and more rigid than a wooden beam, making it better suited for handling compression forces.

What are some real-world applications of beams under compression or tension?

Beams under compression and tension are used in many different structures and machines. For example, bridges utilize beams to support the weight of vehicles and people, and skyscrapers use beams to withstand the forces of wind and gravity. In machines, beams are often used to transfer forces and loads, such as in cranes or vehicles.

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