An offset h must be introduced into a metal tube of 0.75-in. outer diameter and 0.08-in. wall thickness. Knowing that the maximum stress after the offset is introduced must not exceed 4 times the stress in the tube when it is straight, determine the largest offset that can be used

Complete Question

The diagram for this question is shown on the first uploaded image  

The largest offset that can be used is  

Explanation:

From the question we are told that

   The diameter of the metal tube is  

    The thickness of the wall is  

Generally the inner diameter is mathematically evaluated as

Generally the tube's cross-sectional area can be evaluated as

Generally the maximum stress of the metal is mathematically evaluated as

The diagram showing when the stress is been applied is shown on the second uploaded image  

        Since the internal forces in the cross section are the same with the force P and the bending couple M then  

Where h is the offset

       The maximum stress becomes

Where is the radius of the outer diameter  which is evaluated as

and I is the moment of inertia which is evaluated as

So the maximum stress becomes  

Now the question made us to understand that the maximum stress when the offset was introduced must not exceed the 4 times the original stress

So

=>    

  The P would cancel out  

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explanation:

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