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The tensile (or ultimate) strength of materials are generally determined by pull testing of specific material samples in a material yield/tensile testing machine and then included in the material certs supplied with the material by the materials supplier. Alternatively, for some applications where specific code requirements must be met the accepted tensile strength of a material for that code will be published in a materials table included in the code documents. Also, if you can access a copy of the "Machinery's Handbook" (A reference that, in my opinion, every engineer should own) you will find a section that lists the generally accepted tensile strengths for a number of common steel alloys. I reality even if you use a generally published value for calculating the safe design stresses for any planned application the safest path is to ask for the certs on the actual materials you purchasefor your finished parts to verify the min tensile stregth used in your calculations.
As for the determination of the CG (center of gravity) there are specific equations for this calculation required depending upon the geometrical shape of the item in question. To find an extensive listing of these calculations for many differnt shapes again refer to the "Machinery's Handbook"; or, a number of these formulas can be found in the appropriate chapters of most text books used in Strength of Material engineering courses.
Just for information, the equation used for calculating the tensile strength of a pull test sample is the measured force at the point of the material sample breakage divided by the actual measured area of the reduced diameter of the sample at the breakage point.
Ultimate tensile strength (UTS), often shortened to tensile strength (TS) or ultimate strength, is the maximum stress that a material can withstand while being stretched or pulled before failing or breaking. Tensile strength is the opposite of compressive strength and the values can be quite different.
Some materials will break sharply, without deforming, in what is called a brittle failure. Others, which are more ductile, including most metals, will stretch some - and for rods or bars, shrink or neck at the point of maximum stress as that area is stretched out.
The UTS is usually found by performing a tensile test and recording the stress versus strain; the highest point of the stress-strain curve is the UTS. It is an intensive property; therefore its value does not depend on the size of the test specimen. However, it is dependent on other factors, such as the preparation of the specimen, the presence or otherwise of surface defects, and the temperature of the test environment and material.
Tensile strengths are rarely used in the design of ductile members, but they are important in brittle members. They are tabulated for common materials such as alloys, composite materials, ceramics, plastics, and wood.
Tensile strength is defined as a stress, which is measured as force per unit area. For some non-homogeneous materials (or for assembled components) it can be reported just as a force or as a force per unit width. In the SI system, the unit is the pascal (Pa) (or a multiple thereof, often megapascals (MPa), using the mega- prefix); or, equivalently to pascals, newtons per square metre (N/mē). The customary unit is pounds-force per square inch (lbf/inē or psi), or kilo-pounds per square inch (ksi, or sometimes kpsi), which is equal to 1000 psi; kilo-pounds per square inch are commonly used for convenience when measuring tensile strengths.
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