Bolted Connections

Common structural bolts are classified by ASTM specifications. The standard grades in steel design include:

• A307: Low-carbon steel bolts, similar to regular machine bolts. Used for light structures, secondary members, and temporary connections. $F_u = 60$ ksi.
• Group A (F3125 Grade A325): High-strength carbon-manganese steel bolts. The primary standard for structural work. $F_u = 120$ ksi for $d \le 1$ in, and $105$ ksi for $d > 1$ in.
• Group B (F3125 Grade A490): Higher-strength alloy steel bolts. Used when Group A capacity is insufficient. $F_u = 150$ ksi. Because they are harder and less ductile, they must not be galvanized.

Bolted joints are categorized by how they transmit forces and the required level of bolt pretension.

• Snug-Tight (Bearing-Type): Bolts are tightened to bring connected plies into firm contact, usually using the full effort of an ironworker with an ordinary spud wrench. The connection transfers force by bearing against the bolt. Appropriate for static loads where slip is acceptable.
• Pretensioned: Bolts are tightened beyond snug-tight to a minimum of 70% of their tensile strength. Required for connections with significant load reversal or tension fatigue.
• Slip-Critical: A pretensioned connection designed to resist shear solely through friction between the faying (contact) surfaces. Used when joint slip would impair the structure's performance (e.g., severe vibration, oversized holes, or fatigue loading).

Geometric constraints ensure proper installation, prevent material tearing, and provide space for tightening tools.

• Minimum Spacing ($s$): The center-to-center distance between standard holes must not be less than $2.67d$, but $3d$ is preferred to allow clearance for impact wrenches, where $d$ is the nominal bolt diameter.
• Minimum Edge Distance ($L_e$): The distance from the center of a standard hole to any edge of a connected part depends on the bolt diameter and edge manufacturing process. AISC Table J3.4 provides exact values, typically ranging from $1 \frac{1}{4}$ to $1 \frac{3}{4}$ times the bolt diameter.

The shear strength of a single bolt depends on its grade, its cross-sectional area, and whether the unthreaded shank or threaded portion intersects the shear plane.

• N (Threads Included): Threads are included in the shear plane. The actual resisting area is reduced by thread roots, yielding a lower $F_{nv}$.
• X (Threads Excluded): Threads are excluded from the shear plane. The full, smooth shank resists shear, yielding a higher $F_{nv}$.

Resistance Factors: $\phi = 0.75$ (LRFD), $\Omega = 2.00$ (ASD).

For bolts subjected to direct tension, such as in hanger connections or end-plate moment connections:

Resistance Factors: $\phi = 0.75$ (LRFD), $\Omega = 2.00$ (ASD).

Bearing failure occurs in the connected steel material, not the bolt itself. It can manifest as tear-out (the bolt rips through the plate edge) or excessive hole deformation.

Resistance Factors: $\phi = 0.75$ (LRFD), $\Omega = 2.00$ (ASD).

For connections that must not slip under service loads, clamping friction must exceed applied shear.

Resistance Factors (LRFD): $\phi = 1.00$ (standard holes), $0.85$ (oversized/short-slotted parallel), $0.70$ (long-slotted). ASD $\Omega$ factors are $1.50, 1.76, 2.14$ respectively.

When a bolt is subjected to simultaneous shear and tension, its nominal tensile capacity must be reduced based on the applied shear stress. The modified nominal tensile stress ($F_{nt}'$) is computed and then applied to the tensile area.

When the line of action of an applied load does not pass through the center of gravity of a bolt group, the connection experiences both direct shear and a torsional moment.

• Elastic Method: Assumes bolts are elastic and forces are proportional to their distance from the center of rotation. A conservative, traditional approach.
• Instantaneous Center of Rotation (ICR) Method: The AISC preferred ultimate strength method. It assumes rigid body rotation about an instantaneous center, incorporating load-deformation curves of individual bolts. Design aids (AISC Tables 7-6 to 7-13) use this method.

When flexible connection fittings (e.g., WT hangers or angle legs) are subjected to tension, they bend. Their tips bear against the rigid support acting as a fulcrum, inducing an additional tensile force in the bolts known as prying force ($q$).

The total tension force per bolt is $B_c = T_{applied} + q$. To safely resist this, engineers must either thicken the connection plate (preventing bending and prying) or use stronger/more bolts. AISC Part 9 provides procedures to calculate the required thickness ($t_{req}$).

A critical tearing failure mode at the ends of coped beams, gusset plates, or tension members. It involves simultaneous shear failure along a line of bolts parallel to the force and tension rupture along a line perpendicular to the force.

The governing equation limits the nominal strength to the sum of shear yielding and tension rupture, or shear rupture and tension rupture:

$R_n = 0.60 F_u A_{nv} + U_{bs} F_u A_{nt} \le 0.60 F_y A_{gv} + U_{bs} F_u A_{nt}$