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Question 7.3: A column 3 m high has a solid circular cross section and car...

A column 3 m high has a solid circular cross section and carries an axial load of 10 000 kN. If the direct stress in the column is limited to 150 N/mm² determine the minimum allowable diameter. Calculate also the shortening of the column due to this load and the increase in its diameter. Take E = 200 000 N/mm² and ν = 0.3.

Question Data is a breakdown of the data given in the question above.
  • Height of the column: 3 m
  • Axial load on the column: 10,000 kN
  • Limiting direct stress in the column: 150 N/mm²
  • Young’s modulus (E): 200,000 N/mm²
  • Poisson’s ratio (ν): 0.3
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Step 1:
The given equation (7.1) represents the stress, σ, in a...
Step 2:
In the given example, the stress is given as 150 MPa an...
Step 3:
By rearranging equation (7.1), we can solve for D: σ...
Step 4:
Simplifying the equation, we find that the required dia...
Step 5:
Next, the shortening of the column, δ, needs to be calc...
Step 6:
Using the given stress of 150 MPa and the modulus of el...
Step 7:
Additionally, equation (7.12) is used to calculate the ...
Step 8:
Finally, the increase in diameter is calculated by mult...
Step 9:
Therefore, in summary, the theoretical explanation for ...

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