3 connected beams and stress

In summary, the conversation discusses finding the stress in each of three columns in a setup where a force of 100kN is applied to the top and the temperature is 70C colder. The area of each aluminum piece is 20mm^2 and the brass is 60mm^2. To find the stress, the force distributed to each column must be calculated using a simple beam equation, taking into account the different areas and the reaction forces at the top and bottom plates. The resulting stress in the aluminum is 400MPa and in the brass is 33.3MPa.
  • #1
ShawnD
Science Advisor
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Look at this picture
http://myfiles.dyndns.org/pictures/stress.jpg

The top and bottom bars do not bend at all. The setup is taken outside where the temperature is 70C colder then a force of 100kN is applied to the top. Find the stress in each of the 3 columns.
The area of each aluminum piece is 20mm^2, the brass is 60mm^2. These areas refers to the area that is touching the top (and bottom) plates.


I can find the stress in each bar caused by the temperature change but how do I add in the force applied to the top? The aluminum shrinks faster than the brass so the aluminum is in tension and the brass is in compression. When that force is applied to the top, it puts more stress on the brass and relieves stress in the aluminum... but how much?
 
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  • #2
To find the stress in each column, we need to calculate the force distributed to each column due to the applied load. This can be done using a simple beam equation. First, calculate the distance between the top and bottom plates: Distance = 100mm - (20mm + 60mm) = 20mm Next, calculate the reaction forces at the top and bottom plates: Top Force = 100kN Bottom Force = Top Force * (Distance / 2) = 10kN Then, calculate the force distributed to each column: Aluminum = Bottom Force * (Area Aluminum / Area Total) = 8kN Brass = Bottom Force * (Area Brass / Area Total) = 2kN Finally, calculate the stress in each column: Stress Aluminum = Force Aluminum / Area Aluminum = 400MPaStress Brass = Force Brass / Area Brass = 33.3MPa
 
  • #3


The stress in each of the 3 columns can be calculated using the formula: stress = force/area. In this case, the force applied to the top is 100kN and the area of each aluminum piece is 20mm^2, so the stress in the aluminum columns would be 100kN/20mm^2 = 5000kPa. The area of the brass piece is 60mm^2, so the stress in the brass column would be 100kN/60mm^2 = 1666.67kPa.

However, as you mentioned, the temperature difference also affects the stress in each column. The aluminum, being more sensitive to temperature changes, will experience a greater change in stress compared to the brass. To calculate this, we can use the formula: stress = E*alpha*deltaT, where E is the modulus of elasticity, alpha is the coefficient of thermal expansion, and deltaT is the change in temperature.

Assuming the temperature difference is 70C, and using the values for aluminum (E=70GPa, alpha=23.5x10^-6), the change in stress in the aluminum columns would be 70GPa*23.5x10^-6*70C = 115.5MPa. This means that the total stress in the aluminum columns would be 5000kPa + 115.5MPa = 115.505MPa.

For the brass column, using the values for brass (E=110GPa, alpha=19x10^-6), the change in stress would be 110GPa*19x10^-6*70C = 145.4MPa. Therefore, the total stress in the brass column would be 1666.67kPa + 145.4MPa = 147.0667MPa.

In summary, the stress in each column can be calculated by considering both the force applied to the top and the temperature difference. The aluminum columns experience a greater change in stress due to their higher coefficient of thermal expansion, while the brass column experiences a smaller change in stress. It is important to consider both factors in order to accurately determine the stress in each of the connected beams.
 

1. What is the concept of 3 connected beams?

The concept of 3 connected beams refers to a structural arrangement where three beams are connected to each other at their endpoints, forming a triangular shape. This type of structure is commonly used in construction to provide stability and support.

2. How does stress affect 3 connected beams?

Stress is a force that acts on a material and can cause it to deform or break. In the case of 3 connected beams, stress can cause the beams to bend, twist, or buckle, depending on the type and magnitude of the stress. This can lead to structural failure if the beams are not designed to withstand the applied stress.

3. What factors contribute to the stress on 3 connected beams?

There are several factors that can contribute to the stress on 3 connected beams, including the weight of the structure or load being supported, the material properties of the beams, and the design and construction of the beam connections. Other external factors such as wind, seismic activity, and temperature changes can also affect the stress on the beams.

4. How is stress calculated in 3 connected beams?

The calculation of stress in 3 connected beams involves analyzing the internal forces and moments acting on the beams, such as bending, shear, and axial forces. These forces can be calculated using mathematical equations and formulas, and the resulting stress can be determined by dividing the force by the cross-sectional area of the beam.

5. What are some common methods for reducing stress in 3 connected beams?

There are several methods for reducing stress in 3 connected beams, including increasing the size or strength of the beams, modifying the beam connections, and redistributing the loads on the structure. Other techniques such as adding additional supports or reinforcing the beams with materials like steel can also help to reduce stress and improve the overall stability of the structure.

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