Structural / connections

Bolt torque and preload

A structural bolt works by being stretched: the tension in the shank clamps the joint, and the torque is only the means of getting there. This converts the RCSC minimum pretension into a tightening torque and checks the resulting stress, with the friction coefficient exposed because it is where the uncertainty lives.

Stress area0.3345 in²Threads/in10Preload scatter±8.4 kip

Tightening torque

350 ft·lb

K = 0.20, 0.750 in

Target preload

28.0 kip

RCSC minimum 28 kip at 100%

Pretension stress

83.7 ksi

70% of the 120 ksi tensile strength

Service load

20.0 kip

50% of tensile capacity

Bolt working

The preload is the specification; the torque is only how you get there.

350 ft·lb

Bolt working
Quantity	Value	Note
Bolt	3/4 in A325	high-strength carbon
Nominal diameter	0.750 in
Threads per inch	10	coarse series
Tensile stress area	0.3345 in²	π/4(d − 0.9743/n)²
Minimum pretension	28 kip	RCSC Table J3.1
Target pretension	28.0 kip	100% of minimum
Torque coefficient K	0.200	0.20 dry, 0.15 lubricated
Tightening torque	350 ft·lb	T = K·F·d / 12
Pretension stress	83.7 ksi	70% of Fu
Service stress	59.8 ksi	applied load over stress area
Service utilisation	50%	of 120 ksi
Turn-of-nut	90°	after snugging, RCSC Table 8.1

Torque is a poor control method because K varies with lubrication, plating and thread condition — the same torque can produce 30% more or less preload. That is why the specification prefers turn-of-nut or a direct tension indicator for critical connections.

Torque against the friction coefficient

The same preload needs almost four times the torque from K = 0.08 to K = 0.30.

Torque by diameter

At the same grade and coefficient, torque rises faster than diameter because the stress area does.

Canonical equations

The exact relationships implemented by this engine.

T = K·F·d · K about 0.20 dry, 0.15 lubricated.

A_t = π/4(d − 0.9743/n)² · The thread root, not the shank.

σ = F/A_t · About 70% of Fu at the RCSC minimum.

60° to 120° past snug · Depending on length-to-diameter ratio.

Show model notation and computationOpen the symbolic form, the variable definitions, and the step-by-step derivation when you need the detail.

A clear path from inputs to results.

Step-by-step methodWorked exampleAssumptions explained

The formula

T = K\,F\,d \;;\; A_t = \frac{\pi}{4}\left(d - \frac{0.9743}{n}\right)^2

Reference: RCSC Specification for Structural Joints, Table J3.1 for minimum pretension and §8.2 for turn-of-nut; AISC 360 Table J3.2 for tensile strength.

Worked example

3/4 inch A325 at the minimum pretension

Inputs

3/4 inch A325 bolt, 10 threads per inch.
Torque coefficient 0.20 (as-received).
Target 100% of the RCSC minimum pretension.

Calculation path

1
The tensile stress area is π/4 × (0.75 − 0.9743/10)² = 0.3345 in².
2
RCSC Table J3.1 gives a minimum pretension of 28 kip for a 3/4 inch A325 bolt.
3
Torque is K·F·d/12 = 0.20 × 28,000 × 0.75 / 12 = 350 ft·lb.
4
The pretension stress is 28 / 0.3345 = 83.7 ksi.
5
That is 70% of the 120 ksi tensile strength, which is where the specification intends the bolt to sit.
6
The scatter on torque control is roughly ±30%, so the achieved preload could be anywhere from 20 to 36 kip.

Result

350 ft·lb · 28 kip preload · 83.7 ksi · 70% of Fu.

Interpreting the result

Torque is a proxy and a poor one: the same torque on a dry, a lubricated and a galvanised bolt produces three different preloads. That is why the specification controls critical connections by turn-of-nut or a direct tension indicator, and why a torque value should always be quoted with the K factor it assumes.

Assumptions & limitations

Pretension values are the RCSC Table J3.1 minima for A325 and A490 bolts.

The torque coefficient K is a single value; in reality it varies with lubrication, plating and thread condition.

Tensile stress area uses the coarse thread series.

The joint is assumed to be a bearing connection with no prying action.

Embedment, relaxation and temperature effects on long-term preload are not modelled.

Frequently asked questions

What is the torque coefficient K?

It lumps together the thread friction and the under-head friction into one number, which is why it is sometimes called the nut factor. It is about 0.20 for as-received fasteners, 0.15 for lubricated ones and 0.12 for waxed, and it is the largest single source of error in torque-controlled tightening.

What is the tensile stress area?

The effective area at the thread root, which is smaller than the nominal shank area. It is calculated from the nominal diameter and the thread count, and it is the area the preload and the service stress are divided by.

What is turn-of-nut?

Tighten to snug, then rotate the nut a specified fraction of a turn — typically 60° for short bolts and 120° for long ones. Because the thread pitch is known, the rotation directly controls the stretch, and therefore the preload, regardless of friction.

Why not just tighten to a torque?

Because the preload you get for a given torque varies by ±30% with friction. For ordinary connections that is acceptable; for slip-critical or seismic connections the specification requires turn-of-nut or a direct tension indicator, which control the preload rather than the torque.

How much preload should I target?

The RCSC minimum, which is about 70% of the bolt's tensile strength. Higher preloads improve fatigue and slip resistance but risk yielding during tightening; lower ones let the joint slip and the bolt see the load as shear.