Load Calculation Safely Supported

[sperrya]

Homework Statement

A mild steel column has a cross section of 100mm by 50mm. Assuming a safety factor of 6 calculate the load that it can safely support.

Homework Equations

Column material: mild steel
Column cross section: 100mm x 50mm
Safety factor: 6

On the basis that the tensile strength of steel is equivalent to its compressive strength and that there is no compressive stress value provided in the tables of my study module. I have used the average tensile stress value which is provided in my study material.
∴ Tensile stress of mild structural steel: 430 to 510 N/mm²
∴ Average tensile stress of mild structural steel: 470N/mm²

Is this correct?

The Attempt at a Solution

Area = 100mm x 50mm = 5,000mm²

σ = 470N/mm² x 0.167 = 78.49N/mm²

∴ Load = Aσ

∴Load = 5,000mm² x 78.49N/mm² = 392,450N

Therefore the safe load that the column can support is 392,450N.

Is this correct, any help on this would be much appreciated.

Thanks

 

[PhanthomJay]

That is the safe load if the column is in tension or if it is 'short' in compression. Long columns in compression are governed by buckling strength which requires knowledge of its length to solve. Safe buckling loads for long slender
columns are independent of
the material yield or ultimate stress

 

[sperrya]

Hi PhanthomJay,

Thanks for your reply.

Considering your advice, is it as simple as follows then:

P = AσK

Where:
P is safe working load - ?
A is sectional area - 100mm x 50mm = 5000mm²
σ is ultimate strength of material (mild steel) - 480N/mm²
K is fraction - 1/6 or 0.167

Therefore:

P = 5000 x 480 x 0.167 = 400,800N or 400.8kN

Can you confirm this is correct or am I missing something?

Thanks in advance

 

[PhanthomJay]

This is the safe load if the column is in tension (usually columns are in compression). This is also the safe load if the column is in compression but ONLY IF it is relatively 'fat and short'. If it is a long column, Euler Buckling may apply, that is, the allowable compressive load is (0.167) pi^2 E I /(kL)^2, where k is determined from the support conditions.. But since you do not state the value of L, the problem can't be solved unless you assume that the column is short enough so that buckling is not a factor.

 

[sperrya]

Hi again PhanthomJay,

the question is this:
"A mild steel column has a cross section of 100mm by 50mm. Assuming a safety factor of 6 calculate the load that it can safely support."

So with this in mind, the length is not stated. So assuming buckling is not required in the answer to this question have I correctly answered it? Or do I need to look at anything else?

Thanks again

 

[PhanthomJay]

If buckling is not a factor, your answer is correct...short solid steel rectangular sections have the same maximum compressive stress values as the max tensile stress, which you are assuming to be 480 MPa. Please round off your answer to 400 kN.

 

[sperrya]

Thank you very much PhanthomJay, your help is much appreciated!