Bolt Torque vs Tension: K-Factor, Preload & Lubrication Effects

The Torque-Tension Equation

The fundamental equation relating torque to bolt tension is: T = K × d × F, where T is the applied torque (in-lb or ft-lb), K is the dimensionless nut factor (K-factor), d is the nominal bolt diameter (inches), and F is the bolt tension or preload (pounds). This is sometimes called the short-form torque equation, and it captures the entire friction picture in a single coefficient.

Rearranging for tension: F = T / (K × d). For a 3/4-inch Grade 8 bolt torqued to 185 ft-lb (2,220 in-lb) with K = 0.20 (dry steel on steel): F = 2,220 / (0.20 × 0.75) = 14,800 lb. Change that to K = 0.15 (oiled threads): F = 2,220 / (0.15 × 0.75) = 19,733 lb. Same torque wrench setting, same bolt, 33% more clamping force. That is the core problem with torque-based tightening: you are not controlling tension directly. You are controlling torque and hoping the friction is what you assumed.

The target preload for most structural and pressure applications is 60% to 75% of the bolt's proof load. Proof load is the maximum tensile load the bolt can sustain without permanent deformation. For a Grade 8 bolt, the proof strength is 120,000 psi. For a 3/4-10 bolt with a tensile stress area of 0.3340 square inches, the proof load is 120,000 × 0.3340 = 40,080 lb. A 70% preload target means 28,056 lb of clamping force. Getting there accurately requires knowing K within a tight range.

The scatter in torque-tension relationships is the reason critical applications use direct tension indicators (DTI washers), ultrasonic bolt stretch measurement, or hydraulic tensioning. These methods bypass the friction variable entirely and measure or control the actual stretch of the fastener. For routine plant maintenance, torque control with a calibrated wrench and known lubrication condition is the practical standard.

K-Factor Values for Common Conditions

The K-factor is not a property of the bolt. It is a property of the entire system: bolt material, nut material, surface finish, thread condition, lubrication, washer (or no washer), and bearing surface roughness. Published K-factor tables are empirical averages with significant scatter. A K-factor listed as 0.20 might actually range from 0.17 to 0.23 in practice, which translates to a 30% variation in achieved tension at constant torque.

Common K-factor values for steel bolts:

• Dry, as-received (black oxide or plain): K = 0.20 (range 0.17 to 0.24)
• Zinc plated, dry: K = 0.20 (range 0.17 to 0.22)
• Cadmium plated, dry: K = 0.16 (range 0.13 to 0.18)
• Machine oil on threads: K = 0.15 (range 0.13 to 0.17)
• Moly paste (MoS2): K = 0.13 (range 0.11 to 0.15)
• Copper-based anti-seize: K = 0.14 (range 0.12 to 0.16)
• Nickel-based anti-seize: K = 0.13 (range 0.11 to 0.15)
• Teflon/PTFE coating: K = 0.12 (range 0.10 to 0.14)
• Waxed (as in DTI bolts): K = 0.12 (range 0.10 to 0.13)

The critical takeaway: if you look up a torque value in a chart and it says "dry," applying that torque to a lubricated bolt will over-tension it. The most common version of this mistake is using published dry torque values on bolts coated with anti-seize. The preload can exceed 90% of proof load, putting the bolt in the yield zone where it permanently stretches and loses clamping force on the next thermal cycle.

Always match your torque value to the actual lubrication condition. If you change lubricants, you must change the torque specification. Many ASME and API torque tables specify the lubrication condition alongside the torque value. If the table does not state the assumed K-factor, it is not a reliable reference.

Preload Targets and Joint Design

The purpose of bolt preload is to clamp the joint members together tightly enough that external loads do not separate them. In a properly preloaded joint, external tension loads are carried almost entirely by a slight reduction in the clamping force, not by additional stretching of the bolt. The bolt acts like a stiff spring, and the clamped members act like a stiffer spring. The ratio of these stiffnesses determines how much of any external load the bolt actually sees.

This stiffness ratio is quantified by the load introduction factor, sometimes called the load ratio: n = k_b / (k_b + k_c), where k_b is the bolt stiffness and k_c is the clamp stiffness. For a typical steel-on-steel joint, n is around 0.1 to 0.2. This means if you have 20,000 lb of preload and apply 5,000 lb of external tension, the bolt tension increases by only 500 to 1,000 lb (n × external load), while the clamping force decreases by 4,000 to 4,500 lb. The joint remains clamped. If the preload were only 3,000 lb, the external load would fully separate the joint, and the bolt would see the entire 5,000 lb plus cyclic fatigue loading.

Recommended preload targets by application:

• General structural connections (AISC): 70% of minimum tensile strength for slip-critical
• ASME PCC-1 pressure joints: 50% to 60% of bolt yield for controlled tightening
• Automotive (VDI 2230 method): 75% to 90% of proof load depending on tightening method
• Non-critical general purpose: 60% to 75% of proof load

Under-preloading is far more common than over-preloading in plant maintenance. Mechanics who are afraid of breaking bolts frequently under-torque them, which leads to joint separation, fretting, fatigue cracking, and leaks. A bolt that is properly preloaded to 70% of proof load has a very long fatigue life because it barely sees the cyclic component of external loads. A bolt at 30% preload sees the full cyclic load and fails in weeks or months.

Why Lubrication Changes Everything

Bolt lubrication is not optional. It is a design variable. The difference between a dry bolt and a moly-lubricated bolt is not subtle: at the same applied torque, the lubricated bolt develops roughly 50% to 70% more tension. This is because lubrication reduces the friction coefficient in the threads and under the nut face, allowing more of the applied torque to be converted into useful bolt stretch.

The danger of lubrication comes when it is applied inconsistently or without adjusting the torque value. The most common field error is applying anti-seize compound to bolts and then using a torque specification that was developed for dry conditions. The result is systematic over-tensioning. In flange applications, this can crush gaskets beyond their recovery range, creating a leak path that shows up on the next thermal cycle. In structural connections, it can yield fasteners in the elastic-to-plastic transition zone, reducing the effective clamping force.

The second common error is inconsistent lubrication within a bolt pattern. If half the bolts in a flange have anti-seize and half are dry, the lubricated bolts carry more than their share of the clamping force. The dry bolts are under-loaded. This creates an uneven gasket stress distribution and is one of the leading causes of flange leaks, especially on heat exchangers and valve bonnets where the bolts are accessible from only one side and the mechanic may apply anti-seize unevenly.

Best practice: lubricate all bolts in a joint identically, use a K-factor appropriate for the lubricant, and adjust the torque specification accordingly. If you are using anti-seize with K = 0.13 but the torque spec assumes K = 0.20, multiply the published torque by 0.13/0.20 = 0.65. Apply 65% of the published dry torque value. This is the single most important torque adjustment most plant mechanics never make.

Torque Sequence and Multi-Pass Tightening

Torquing bolts in a circular pattern (going around the flange clockwise) is one of the most common assembly errors in maintenance. When you tighten bolt #1, it elastically deforms the flange. When you tighten bolt #2 next to it, the deformation changes and bolt #1 partially relaxes. By the time you get back to bolt #1, it may have lost 20% to 40% of its preload due to elastic interaction.

The correct approach for flanged joints is a star (cross) pattern with multiple passes at increasing torque levels. ASME PCC-1 recommends a minimum of three passes: the first at 30% of target torque, the second at 60%, and the third at 100%. A fourth "check pass" at 100% in a circular pattern catches any residual relaxation. For large flanges (24 inches and up), four to five passes may be necessary because the elastic interaction effects are more pronounced on larger bolt circles.

The star pattern ensures that load is distributed as evenly as possible across the gasket. For a typical 8-bolt flange, the sequence is: 1, 5, 3, 7, 2, 6, 4, 8 (assuming bolts numbered sequentially around the circle). For 12-bolt and larger patterns, the same principle applies: tighten opposing bolts in sequence, never adjacent bolts.

After the final pass, allow the joint to sit for at least 4 hours if possible (or one thermal cycle) and re-torque. Gasket creep and embedment relaxation can reduce bolt preload by 5% to 15% during the first thermal cycle. This "hot retorque" or "post-assembly check" is especially important for spiral-wound and flexible graphite gaskets that experience significant creep under initial compression.

Common Torque-Tension Mistakes

The field is full of recurring torque errors. The most damaging ones:

• Using an impact wrench for final torque: Impact wrenches deliver torque in short pulses that generate high instantaneous friction heat. The dynamic K-factor during impact tightening is different from static tightening. Impact wrenches are for run-down (getting the nut snug). Final torque must be applied with a calibrated torque wrench at a steady, smooth pull.
• Reusing torque-to-yield (TTY) bolts: TTY bolts are intentionally stretched past their yield point during installation for maximum preload accuracy. They cannot be reused because the bolt has permanently elongated. Common on modern diesel engines and some ASME pressure connections.
• Ignoring thread damage: A bolt with damaged or corroded threads has a much higher effective K-factor. Running a die over the threads or replacing the bolt is cheaper than dealing with a failed joint.
• Calibration neglect: Torque wrenches drift. A click-type wrench should be calibrated annually, or more frequently in heavy industrial use. A wrench stored at its maximum setting loses calibration faster than one stored at the lowest setting because the spring is always under tension.
• Using extensions without correction: A crow-foot adapter or extension changes the effective lever arm. The torque correction factor is: T_actual = T_set × (L / (L + E)), where L is the wrench handle length and E is the extension length. Forgetting this correction means under-torquing every bolt.

The single most effective improvement most plants can make is standardizing the lubrication condition and adjusting torque tables accordingly. Post the K-factor next to the torque value on every work order. If the bolt gets anti-seize, the torque value must reflect that. This one change eliminates the most common source of bolted joint failures in plant maintenance.