Answered: An engineer determines that a 60 cm…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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An engineer determines that a 60 cm long rod of 1045 HR grade of steel will be subjected to a tension of 20kN. The following two designs requirements must be met: must remain below 145MPa and the rod must stretch less than 0.125mm. Determine an appropriate value for the rod's diameter to meet these two requirements. Round to the nearest milimeter

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Step 1

Given Data

Length of the rod is: $L = 60 cm = 600 mm$
Tensile load is: $P = 20 kN = 20000 N$
Maintained stress is: $σ_{m} = 145 MPa$
Stretched length of the rod is: $∆ L = 0.125 mm$

The modulus of elasticity is: $200 GPa$

The diameter of the rod to maintain the stress below 145 MPa is

$\begin{array}{rcl} σ & < & 145 \\ \frac{P}{A} & < & 145 \\ \frac{4 \times 20000}{π (d^{2})} & < & 145 \\ d^{2} & > & 175.61 \\ d & > & 13.25 mm \end{array}$

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