The mechanical properties of metal alloys depend on a lot of parameters:

1. Composition of the consitutents in the alloys, e.g. carbon content in steel.

2. The processes the material has undergone i.e. heat treatment, mechanical working, strain hardening etc. (It is the macroscopic picture).

The properties and arrangement of grains in the microstructure gives variation in the macroscopic properties of the metal alloys.

The relation between Shear Modulus and Elastic Modulus can be derived analytically, you can find it here:

https://nptel.ac.in/courses/Webcourse-contents/IIT-ROORKEE/strength%20of%20materials/lects%20&%20picts/image/lect10/lecture10.htm

however values of Shear Strength and Tensile Strength are arrived experimentally, and depend on a lot of factors as I have mentioned above. I do not know of any relation between them.

If you are looking for applications in structural design, and maximum allowable stresses, I would suggest you to read about principal stresses, Mohr's circle (an easy way to understand), and factors of safety. The following is a short guide for your reference:

https://nptel.ac.in/courses/112107146/lects%20&%20picts/image/lect4/lecture4.htm

Factor of safety will be different for different types of applications, but shall give you an understanding of the requirements for your application and the standards against which it will be tested, and from there you can get the strength requirements.

Well, it depends on various factors and loading conditions. However, using poison ratios and Mohr circle should possibly lead you to comment on any relationship between the shear and tensile strength of ferrous alloys. In my opinion, it would be quite difficult to predict any solid relationship between shear and tensile strength of the HSS.

Hi Mr. Jatin Chaudhary

below the relation in machine elements in mechanical design book.

best regard

Ali Hussein Afnan Haider Khan Ananyo Bhattacharya Thank you very much.