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Thread Tensile Stress Area and Bolt Preload

Guide · Updated October 28, 2026

A threaded fastener is weakest through the threads, so strength calculations use the tensile stress area rather than the full shank area. Multiply the stress area by the proof strength of the bolt grade to get the proof load, take a percentage of that as the target clamp load (preload), and estimate the tightening torque with the short-form equation T = K × D × F. The torque estimate is approximate because friction varies, but it is the standard starting point.

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Step by step

  1. Identify the thread: Nominal diameter D and threads per inch n, or metric diameter d and pitch P.
  2. Calculate stress area: Inch: As = 0.7854 × (D − 0.9743 ÷ n)². Metric: As = 0.7854 × (d − 0.9382 × P)².
  3. Find proof strength: From the bolt grade or property class marking on the head.
  4. Pick a preload: A common target is about 75 percent of proof load for reusable joints.
  5. Estimate torque: T = K × D × F, with K about 0.20 for plain dry steel and lower for lubricated or plated bolts.
  6. Verify: Use the fastener or equipment maker torque spec when one exists, and a calibrated torque wrench.

Stress areas

These match the tensile stress areas in ASME B1.1 and ISO 898-1 tables:

Check one: for 3/8-16, 0.9743 ÷ 16 = 0.0609, 0.375 − 0.0609 = 0.3141, and 0.7854 × 0.3141² = 0.0775 in².

Proof strengths

Grade 5 heads have three radial lines and Grade 8 heads have six. Metric heads are stamped 8.8, 10.9 or 12.9.

Worked example: 3/8-16 Grade 8

Proof load = 0.0775 × 120,000 = 9,300 lb. At 75 percent, target preload F = 6,975 lb. Dry torque estimate T = 0.20 × 0.375 × 6,975 = 523 in-lb, or about 44 ft-lb. If the threads are oiled and K drops to about 0.15, the same torque would give about 9,300 lb, right at proof load, so a lubricated bolt needs about 0.15 × 0.375 × 6,975 = 392 in-lb (33 ft-lb) for the same clamp load.

Worked example: M10 × 1.5 class 8.8

Proof load = 58.0 mm² × 580 N/mm² = 33,640 N. At 75 percent, F = 25,230 N. T = 0.20 × 0.010 m × 25,230 N ≈ 50 N·m dry. Compare with your fastener supplier chart before using it on a real joint.

Into tapped holes

When a steel bolt goes into a tapped hole, especially in aluminum or cast iron, the internal threads may strip before the bolt yields. A common rule is engagement of at least 1 × D in steel and 1.5 to 2 × D in aluminum, or use thread inserts. Drill deep enough for the tap and the bolt; see the tap drill and drill point guides.

Common problems

Using the shank area instead of stress area, using dry K values on oiled or plated bolts, reusing torque-to-yield bolts, and trusting a torque wrench that is out of calibration.

FAQ

What is tensile stress area?

An effective area through the threads used for bolt strength, from As = 0.7854(D − 0.9743/n)².

What is K in T = K D F?

The nut factor, which lumps together thread and under-head friction. About 0.20 is a typical dry steel value.

How much preload should I use?

Often about 75 percent of proof load for reusable joints; follow the design or manufacturer spec.

How do I check thread size?

Use thread wires or a thread mic, set on gage blocks; build stacks free at gageblockcalc.com.

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General shop information only — follow your drawing, tool maker's data and your quality system.