Calculating shear strengths and tensile strengths for screws

Basic knowledge Joining

Shear strength and tensile strength are two important parameters for selecting and using screws. Screws are used to connect components in a friction-locking manner and to withstand mechanical loads. In order to ensure that screws meet the required strength requirements in a given application, it is important to know what shear strength and tensile strength are and how they are calculated.

Strength of screws

Many different factors play a role in the selection of screws. In addition to the thickness and strength of the substrate, other important factors such as the material and diameter of the screw, the expected load, etc. must be observed. All of these factors affect the strength of a screw. The strength of the screw used is of great importance. This relates to the ability of the screws to withstand shear forces and tensile forces. Strength is specified by marking or by classification systems, which may vary depending on the standards system used and national standards. The strength class of a screw provides information about the tensile strength and yield strength. Steel screws are marked differently than stainless steel screws. Steel screws are marked with two numbers (for example 10.9), whereas stainless steel screws are marked with letters and numbers (for example A4-80).

Shear strength of screws

Shearing occurs when offset pairs of forces act on the screw. This results in shear forces that can lead to the elongation, distortion or torsion of the screw. Screws require a certain shear strength to counteract these shear forces. This shear strength indicates which load a screw can be subjected to without yielding or being destroyed. Shear forces of varying strength and direction can be exerted on a screw at the same time.

Shearing of the thread: This type of shear is also called stripping of the thread and is caused by axial loads, which is mainly caused by the preload force when tightening a screw.

Shearing of the screw shaft caused by transverse load

Shearing of the screw shaft caused by rotation or torsional moments around the screw axis

How to calculate the shear strength.

In general, there are different methods by which the shear strength of materials can be tested.. Standardized measurement methods are generally used, which are also referred to as shear tests. Shear tests subject the material sample is to a constantly increasing shear force. The force measured during shearing of the sample is the maximum shear force F_m from which the shear strength is derived.

\tau{_B} = \frac{F }{A} = N/mm^2

In practice, however, the materials are not fully exhausted up to the maximum load limit, but rather a certain safety margin is always taken into account. This safety margin ensures that the permissible shear stress (T_rated) is significantly lower than the actual shear strength (T_B). The rated shear stress is determined using this so-called safety factor (v):

\tau_{rated} = \frac{{\tau}{_B}}{v} = N/mm^2

The rated shearing force (F_rated) can then be determined by means of this rated shear stress (T_rated). The calculation is performed by multiplying the permissible shear force by the shear surface (S):

F_{rated} = \tau_{rated} \times S

However, it should be emphasized that it is preferred in practice to design a screwed connection such that only a tensile force, but not shearing force, is exerted on the screw in order to prevent a possible failure due to shear loads.

Tensile strength and yield strength of screws

Similar to shear strength, tensile strength is a stress that expresses the ratio of a force (F) to an area (A), wherein the force is a tensile force (longitudinal to the screw axis).

The tensile strength of screws indicates how much the material of the screw can be exposed to tensile stress. It indicates the maximum tensile stress that the material can withstand per square millimeter of its cross-sectional area.

Figure: tensile force (longitudinal to the screw axis)

The strength specification on screws not only provides information about the tensile strength, but also about the yield strength. The yield strength refers to the stress at which a material experiences the transition from elastic to plastic deformation. Or in other words: It is the maximum stress that a material can absorb before the material invariablydeforms. If the material cannot return to its original shape after elongation, the yield strength is exceeded.

Determination of tensile strength using tensile tests

The tensile strength (_Rm) is determined using tensile tests. A tensile test is a standardized procedure by which a material sample is stretched in the longitudinal direction until it tears. During the test, the force and the length change (= elongation) of the material sample are measured. The tensile strength is calculated from the maximum tensile force achieved and the cross-sectional area of the material sample. The tensile strength is specified in N/mm².

R_m = \frac{F }{A}

Calculating the tensile strength and yield strength of steel screws

As already mentioned, screws are labeled with a strength class. This strength class provides information about their tensile strength, i.e. the tensile force that a screw can withstand. The tensile strength of a screw can therefore be easily calculated based on the strength class and the cross-sectional area of the screw.

In order to determine the tensile strength for steel screws, the first number of the strength specification is multiplied by a factor of 100. In the following example illustration, the following calculation would result:

R_m = 10 \times 100 N/mm^2 = 1000 N/mm^2

In order to calculate the yield strength or elongation limit (R_p-0.2) of steel screws, both numbers of the strength specification are first multiplied together, followed by multiplying with a factor of 10. Based on the above-mentioned example (10.9), the following calculation is obtained:

R{_p}{_-}{_0}{_,}{_2} = 10 \times 9 \times 10 N/mm^2 = 900 N/mm^2

Calculating the tensile strength and yield strength of stainless steel screws

For stainless steel screws, the specification of the strength differs in that screws made of stainless steel are marked with a letter-number combination (e.g. A4-80). The entry to the left of the hyphen refers to the stainless steel type of the screw used. In the following example, the designation A4 states that the stainless steel screw is made of austenitic stainless steel (V4A steel). To determine the tensile strength, the value to the right of the hyphen (80) is multiplied by a factor of 10:

R_m = 80 \times 10 N/mm^2 = 800 N/mm^2

The elongation limit of stainless steel screws is often not clearly determined in the tensile test. For this reason, the 0.2% expansion limit determined in the tensile test is used for stainless steel. This depends on the raw material and is provided by the manufacturer or must be referenced from a standard. DIN EN ISO 3506- 1 contains information on the elongation limit determined for A1 to A5 in conjunction with strength classes 50-80 and the defined diameter ranges.

Conversion from MPa to N/mm^2

Tensile strength and shear strength can be specified in different units, namely in Megapascal (MPa) and Newton per square millimeter (N/mm²⁾. However, both units are equivalent, because 1 MPa corresponds to 1 N/mm². Megapascal is part of the international system of units (SI) and is thus widely used in many technical and scientific fields. Newton per square millimeter is based more on older conventions and is still widespread in mechanical engineering in particular. In many technical applications, especially in strength theory, forces are measured in Newton (N) and surface areas in square millimeters (mm²). Therefore, the unit N/mm² is a natural choice for calculating tensile strength and shear strength.

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Screws are basic components in the world of mechanical engineering and custom machine construction. MISUMI supplies a comprehensive range of screws with different strength classes and made of different materials. MISUMI also offers additional accessories depending on the screw connection requirements, such as washers, nuts, brackets or thread lockers.

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