Buckling: Formula to relate Temperature increase with axial Compression

In summary, buckling is a sudden failure of a structural member due to compressive stress and can lead to catastrophic consequences. Temperature increase can weaken a structural member and make it more susceptible to buckling. The formula for relating temperature increase with axial compression is known as the Euler's buckling formula. Engineers can prevent buckling by using design techniques and considering the effects of temperature during the design phase. Other factors that can cause buckling include material properties, cross-sectional shape, loading, and manufacturing imperfections. It is crucial for engineers to consider all of these factors to prevent buckling failures.
  • #1
socrates_1
26
0
hi, does anyone know how to find how much axial pre-compression is required so that buckling will occur after a temperature rise of 50 C°?

I know the cross section of the pinned at each end copper strip (4mm x 8mm)
length= 100mm
E= 100 GN/m^2
Coefficient of thermal expansion is 18 x 10^-6
 
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  • #2
any ideas??
 
  • #3
socrates_1 said:
any ideas??

Start out by determining the compressional stress required to cause buckling without a temperature rise. The formula is in most strength of materials books.
 

1. What is buckling and why is it important?

Buckling is a phenomenon in which a structural member, such as a column or beam, suddenly fails due to compressive stress. It is important because it can lead to catastrophic failure of structures, resulting in loss of life and property.

2. How does temperature increase affect buckling?

As temperature increases, the material properties of a structural member can change, causing it to become weaker and more susceptible to buckling. This is because higher temperatures can reduce the material's strength and stiffness, making it less able to resist compressive stress.

3. What is the formula for relating temperature increase with axial compression?

The formula for relating temperature increase with axial compression is known as the Euler's buckling formula. It is given by P = (π^2EI)/(l^2(1-αT)), where P is the critical axial load, E is the modulus of elasticity, I is the moment of inertia, l is the length of the structural member, α is the coefficient of thermal expansion, and T is the temperature increase.

4. How can engineers prevent buckling due to temperature increase?

To prevent buckling due to temperature increase, engineers can use design techniques such as increasing the size or thickness of the structural member, providing additional support, or using materials with higher strength and stiffness at elevated temperatures. Conducting thorough structural analysis and considering the effects of temperature during the design phase can also help prevent buckling.

5. Are there any other factors besides temperature that can cause buckling?

Yes, there are several other factors that can cause buckling, including the material properties of the structural member, its cross-sectional shape, and the type of loading it is subjected to. Additionally, imperfections in the manufacturing process or during construction can also contribute to buckling. It is important for engineers to consider all of these factors when designing structures to prevent buckling failures.

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