# How to Calculate Shear Stress on Bolts

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Loading and unloading structures applies force to bolts and other types of connectors. Shear stress is one of the forces that affect bolts. When a bolt connects two or more parts, each of the parts can impart separate forces on the bolt, often in different directions. The result is shear stress at the plane through the bolt between the two connected components. If the shear stress in the bolt is too high, the bolt can break. An extreme example of shear stress is the use of bolt cutters on a bolt. The two blades of the cutters impart opposite forces on a single plane of the bolt, resulting in a cut bolt. Determining the shear stress in a bolt is a straightforward calculation using only a few inputs.

1. ## Measure Thickness of Parts

2. Use a ruler or digital calipers to measure the thickness of each part of the bolted assembly. Label each thickness t1, t2, t3, and so on.

3. ## Apply Formula for Two Plates

4. Calculate the shear stress using the formula F ÷ (d x (t1+t2)) if the bolt connects two plates where each plate is subjected to a force (F) in opposite directions. This load case is called single shear. For example, if two plates each 1 inch thick are connected by a bolt with a diameter (d) of 1 inch, and each plate is subjected to a force of 100 lb, shear stress is 100 lb ÷ (1 inch x (1 inch + 1 inch)), or 50 psi.

5. ## Apply Formula for Three Plates

6. Calculate the shear stress using the formula F ÷ (2d x (t1+t2+t3)) if the bolt connects three plates, where the center plate experiences a force in one direction and the other two plates experience a force in the other direction. This load case is considered double shear because shear occurs in two different planes in the bolt. For example, if three plates each 1 inch thick are connected by a bolt with a diameter (d) of 1 inch, and the plates are subjected to a force of 100 lb, shear stress is 100 lb ÷ (21inch x (1 inch + 1 inch + 1 inch)), or 16.7 psi.

#### About the Author

Susan Kristoff has been writing engineering content for 13 years. Her articles have appeared on eHow.com, Suite101, her personal websites, and the websites of many ghostwriting clients. Kristoff's expertise includes design, structures, sensors, data acquisition, and fabrication.

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