Shear Strength of Structural Bolts

Bolted connections are fundamental to steel construction. When two steel plates are joined, the bolts transfer forces either in tension, shear, or a combination of both. This calculator focuses on shear, the action that tends to slide one plate relative to the other. In a typical double-lap joint the bolt shank is sheared along one or more planes. If the applied shear exceeds the bolt's capacity, the bolt may fail by sudden shearing across the cross section. Engineers therefore evaluate the nominal shear strength of bolts and then apply safety factors to determine an allowable or design load. The calculator automates these computations using formulas consistent with the American Institute of Steel Construction (AISC) specifications.

The basic nominal strength is proportional to the bolt's tensile strength and its net area. A widely used expression is $Vn=0.6F{u}_{}A{n}_{}N$, where $F_u$ is the ultimate tensile strength in megapascals, $A_n$ is the area resisting shear on one plane, and $N$ is the number of shear planes. The factor 0.6 reflects experimental observations that the shear yield stress of steel is approximately 60% of its tensile strength. If a bolt is subjected to double shear, such as in a connection with two exterior plates and one interior plate, $N$ equals 2 because there are two planes where shear can occur.

The area term must consider whether the threads cross the shear plane. Threads create stress concentrations and reduce the effective area compared to the smooth shank. When the threaded portion lies within the shear plane, AISC recommends using the stress area, roughly 0.78 times the full shank area. If the threads are excluded from the shear plane, the full area $A_b=\frac{\pi }{4}{d}^2$ can be used. This calculator applies a simple multiplier of 0.78 when the user indicates that threads are included, providing a conservative estimate that matches common practice for standard coarse threads. For customized fasteners the exact stress area may vary slightly, but the approximation captures the essential reduction.

Once the nominal strength is known, design codes require a strength reduction factor φ for limit state design or a safety factor Ω for allowable stress design. This tool employs φ, which is typically 0.75 for bolt shear in LRFD methodology. Multiplying φ by the nominal shear strength produces the design shear strength that must exceed the factored applied shear. Users may adjust φ to explore how stricter or looser safety margins influence allowable loads.

To use the calculator, input the bolt diameter, the ultimate tensile strength of the bolt material, the number of shear planes, whether threads are in the shear plane, and the desired strength reduction factor. The output reports both the nominal shear capacity and the design capacity in kilonewtons. The procedure is summarized below:

Step	Computation
1	Determine bolt area $A_b=\frac{\pi }{4}{d}^2$
2	Adjust to stress area if threads are present (×0.78)
3	Compute nominal shear $Vn=0.6F_u{A}_{n}N$
4	Apply φ to get design shear $\phi Vn$

Consider a 20 mm diameter ASTM A325 bolt with ultimate tensile strength F_u ≈ 825 MPa. In a single-shear lap joint with threads excluded, the area resisting shear is the full circular area: 314 mm². The nominal shear strength is 0.6 × 825 × 314 = 155,418 N. Applying φ = 0.75 gives a design strength of 116 kN. If the connection uses a double-lap configuration, doubling the shear planes raises the nominal strength to 311 kN and the design strength to 233 kN. Conversely, if the threads fall within the shear plane, the effective area drops to about 245 mm², lowering the design strength to roughly 181 kN even with two shear planes. These simple adjustments show why detailing bolts so the unthreaded shank bears the load is advantageous.

Engineers frequently choose bolt grades based on required strength. Common structural bolt types and their typical tensile strengths are listed below. Values can vary slightly depending on the standard and manufacturing tolerances.

Bolt Grade	Ultimate Tensile Strength Fu (MPa)	Notes
ASTM A307	415	Low strength for light connections
ASTM A325	825	High-strength structural bolt
ASTM A490	1040	Highest strength for demanding joints

While high-strength bolts provide greater shear capacity, they also require careful handling to ensure proper tensioning. Slip-critical joints, which rely on friction rather than bearing, are sensitive to installation torque and surface preparation. The present calculator assumes a bearing-type connection where shear is transferred through direct bearing of the bolt on the plate. In slip-critical design the shear capacity depends on clamping force and surface condition, which are beyond the scope of this tool.

Another nuance concerns combined shear and tension. Bolts often experience both actions, such as in beam seat connections where vertical reaction induces shear while prying action induces tension. Interaction equations are used to ensure the combined effect does not exceed the bolt's capacity. Although this calculator does not evaluate combined loading, knowing the pure shear strength is the first step in that process.

Bolted joints also involve deformation considerations. Under shear, a bolt may deform elastically before reaching its limit state. Excessive deformation could compromise serviceability even if ultimate capacity is not reached. For example, oversized holes or slippage in bearing connections can lead to lateral movement. Engineers sometimes specify slip-critical bolts or add dowels to control deformation. The calculator focuses on ultimate strength and does not predict displacement.

Historically, rivets performed a similar role to structural bolts. Rivets are hot-driven and rely on forming a head after insertion, whereas bolts are pre-formed and tightened with a nut. Modern construction overwhelmingly favors high-strength bolts due to ease of installation and consistent material properties. Nevertheless, the mechanics governing shear resistance are analogous: both depend on material strength and area, and both benefit from multiple shear planes and avoidance of stress concentrations at threads.

The concept of shear planes is sometimes confusing. Imagine two plates overlapped and joined by a bolt. If the plates are pulled apart parallel to their interface, the bolt experiences shear along the interface plane. In a single-lap joint there is one interface and thus one shear plane. In a double-lap joint, an interior plate is sandwiched between two exterior plates; the bolt passes through all three, creating two planes where relative sliding can occur. Each plane effectively shares the shear load, so the bolt's nominal strength doubles. Connections with more than two planes are rare but the formula is general and will accommodate any integer input.

For design verification, the applied factored shear on a bolt, V_u, must not exceed φV_n. If several bolts share the load, the design strength per bolt can be multiplied by the number of bolts to obtain the total connection capacity, provided load distribution is reasonably uniform. Unequal spacing, eccentric loading, or prying forces may increase demand on certain bolts, calling for a more detailed analysis. As with any structural calculation, judgment is essential.

This calculator serves as an educational aid and a quick preliminary sizing tool. It is not a substitute for the comprehensive requirements of AISC or other design standards, which include additional considerations such as bearing strength of connected materials, bolt spacing and edge distance limits, fatigue resistance, and installation procedures. Users should confirm that the assumptions inherent in this simplified model align with their specific application.