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### Bolt Elongation by Turn Formulas and Calculator

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**Bolt Preload Equations**

Bolt Elongation by Turn Formulas and Calculator per. MIL-HDBH-60

Bolt Elongation by turn of bolt and nut in that the lead of the thread is related to elongation.

Preview Bolt Elongation by Turn Calculator

Note: Variations due to rounding

The following formula applies:

Equation 1

*σ _{B} = θ L / 360*

By substitution Bolt Elongation and Stress Formula and Calculator thus

*Equation 2
θ = 360 _{}f_{t}*

*L*/ ( E L )

_{B}

Where:

*θ *= Turn of nut, degrees *
σ _{B}* = Bolt elongation, in (mm)

*f*= Axial stress based on thread stress area, psi (MPa)

_{t}*L*= Lead of the thread helix, in (mm)

*L*= Effective bolt length, in (mm), see Figure 1

_{B}*E*= Modulus of elasticity, psi (MPa)

Accuracy is affected by elastic deformation of the threads, by roughness of baring surfaces and by difficulty in determining the starting point for measuring the angle. Generally, the nut is then loosened to just release the bolt tension and twisting; this is the starting point. Nut turn angle will be different for each bolt size, length, material and thread lead and will vary with the properties of the clamped materials. Unless the deformation of the nut and significant portion of the nut rotation will be absorbed other than in elongation of the bolt. In such case, the above formulas will not apply so nut turn angle would have to be determined empirically using a simulated joint and tension measuring device as a standard.

Equation 3

*L _{B}* = ( d

_{ts}/ d )

^{2}( L

_{S}+ 0.5 H

_{B}) + L

_{J}- L

_{S}+ 0.5 H

_{N}

Elongation length application in elongation formula Figure 1

Military Handbook, Threaded Fasteners - Tightening to Proper Tension MIL-HDBK-60

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