### How to Calculate Tensile Deformation

Materials science deals with the study of the properties of various materials and their individual characteristics. A good understanding of a material’s chemical make-up and physical properties is vital to good structural design. There are three primary modes of stress that are relevant in gauging a material’s suitability as a construction material – tensile, compressive, and shear.

Tensile deformation is deformation due to an object being pulled apart, as opposed to being pushed together (compression) or pushed in opposite parallel directions (shear). The tensile strength of a material is an intensive property, which means it is not related to the specimen’s size. However, when the material is used as a structural member, its cross section and second moment of area become important.

What this means is that when measuring a material’s tensile strength, it is expressed as the quotient of the tensile stress over tensile strain, a ratio. It is the portion of the stress-strain curve from the point of loading to the point of necking. The ultimate tensile strength (UTS) of a material is not to be confused with its Young’s modulus, which has the same units of force per unit area but doesn’t express when it will yield, only its stiffness.

It is often necessary to calculate tensile deformation of a structural member under a given load so as to determine its suitability for a particular task. Note that we are not talking about bending moments here, but pure tension. A bending moment is a rotational force (moment) caused by the bending of an element – which results in both tension and compression. An object in pure tension has no other forces acting on it but tension.

In order to calculate the tensile deformation in a sample member with uniform cross section and Young’s modulus, assuming complete homogeneity and freedom from prior stress, you need to know the following values:

• P = the applied force on the member that is causing it to deform in newtons (N)
• L = the length of the member
• A = the cross-sectional area of the member
• E = the material’s Young’s modulus (pascal = N/m2) – also known as the elastic modulus or modulus of elasticity

If all you want to know is the tensile deformation along a single elastic member, you can calculate it using this simple formula:

The image further above is an example of a weight-force placing two vertical steel rods into tension. The two rods are spaced evenly from the edges so as to support an equal amount of weight. They are both 1 meter long, are solid all the way through, have diameters of 20 millimeters, and are made of steel, with a Young’s modulus of 200 Gpa. The area for circular cross sections are found by the formula A = πr2. You can use the above equation with a slight tweak to account for 2 rods:

Remember that uniform units must be used for proper results. Depending on the magnitude of the individual values, it may be more convenient to use smaller unit-variations. For example, Young’s modulus (E) can be expressed in N/mm2 or kN/mm2 (kilo-newtons) if the cross-sectional area (A) is better defined in square millimeters instead of square meters – which is often the case.

• For conversion to N/mm2, bring the decimal of E in N/m2 left 6 digits
• For conversion to kN/mm2, bring the decimal of E in N/m2 left 9 digits

However, if you do this, you must convert all other units to millimeters as well – your answer will also naturally be in millimeters. Length (L) must be in millimeters, and the applied force (P) must be converted to kNs if you use kN/mm2 as Young’s modulus. This can be a source of confusion for beginners so be sure you understand this and get it right.
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