Stress and Strain Factor of Safety

[nettie2311]

Homework Statement

Hello,

I've been given a question:

The ultimate strength of a round steel rod is 560MPa. If a factor of safety is 6 is required, what is the maximum permissible load for the rod if it has a diameter of 6.9cm?

If anyone can explain how to set up this calculation and how I go about solving this question it would be great.

 

[nettie2311]

Homework Statement

Hello,

I have been given the question:

What is the factor of safety of a steel hanger having an ultimate strength of 560MPa and supporting a load of 71000N. The steel hanger in question has a cross sectional area of 5 cm squared.

If anyone can help me set up the formula and explain how I go about solving this question that would be great.

 

[nettie2311]

Hello,

Thanks for the reply...I've tried calculating it and I'm pretty close but for some reason a few decimal places off.

I'm guessing I need to convert cm squared to metre squared? And MPa to Pa? I'm getting all confused.

 

[rock.freak667]

Start with the definition of the factor of safety, how does it relate the maximum stress to the ultimate stress?

 

[DeeNos]

I can provide a response to this question regarding stress and strain factor of safety. The factor of safety is a measure of how much a structure can withstand before it fails. In other words, it is the ratio of the ultimate strength of a material to the working stress applied to it.

To solve this question, we need to first calculate the cross-sectional area of the steel rod using the given diameter of 6.9cm. This can be done by using the formula A = πr^2, where r is the radius of the rod.

Next, we need to determine the maximum permissible stress that the rod can withstand by dividing the ultimate strength of 560MPa by the factor of safety of 6. This gives us a maximum permissible stress of 93.33MPa.

To calculate the maximum permissible load, we can use the formula F = σA, where F is the maximum permissible load, σ is the maximum permissible stress, and A is the cross-sectional area of the rod. Plugging in the values, we get F = 93.33MPa x π x (0.069m)^2 = 11.22 kN.

Therefore, the maximum permissible load for the round steel rod with a diameter of 6.9cm is 11.22 kN.

I hope this explanation helps in understanding the concept of stress and strain factor of safety and how to solve problems related to it. It is important to always consider the factor of safety in engineering designs to ensure the safety and reliability of structures.