**Scott Sauer****Empire Engineering****Sunnyvale, Calif.**

Most engineers who deal with bolted joints are familiar with torque tables for SAE-grade bolts, but these are all too often used without regard for the yield strength of internal threads or the bolt’s length of engagement.

In some instances that can be a serious mistake. That’s because in static-bolting applications — assuming sufficient thread engagement — there are three cases to consider in determining maximum torque.

The first is when yield strength of the internal thread equals or exceeds the proof strength of the bolt, *S _{i}* ≈ St

*S*in which case the bolt may be fully torqued.

_{t}
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The second is when the yield strength of the internal thread is less than the bolt proof strength, *S _{i}*<

*S*, but because of the greater shear area of the internal thread the bolt can still be fully torqued. The final case has an internal-thread yield strength less than the bolt proof strength,

_{t}*S*<

_{i}*S*, and even with the added shear area the internal threads have insufficient strength to support full torque.

_{t}In the first case, when the internal thread is as strong as the bolt and the length of engagement is at least 1.5 times the nominal bolt diameter, designers can use standard torque tables.

For the other two cases, where the internal thread material has a lower yield strength than the bolt’s proof strength, maximum allowable torque must be based on the length of engagement, bolt proof strength, and yield strength of the internal thread. Here’s a method for calculating maximum bolt torque for all three cases.

**FAILURE MODES**

For a typical static bolted joint, engineers should evaluate three failure modes to determine the highest load that the bolted joint can withstand. These are:

• Tensile failure of the bolt body.

• Shear failure of the bolt threads.

• Shear failure of the internal threads.

The lowest load that leads to failure determines the limiting torque. In the first instance, calculate the tensile-stress area of a bolt from *ASME B1.1-1989 Appendix B* using

In this equation,*D _{pb}*=

*D*– (2 3 3⁄8H), where

_{b}*D*= basic bolt diameter. Also,

_{b}*H*= tan 60°(

*P*/2), where 60° is the basic angle of the ASME thread form and pitch

*P*= 1/threads per in.

The calculated value At is not based on the minimum root diameter. This value is slightly larger than the area defined by the root diameter to account for the added strength of the actual thread in the bolt cross section. A more conservative value would be the minimum root diameter of the bolt which disregards the area of the spiraling thread. For hollow threaded parts, use the minimum root diameter.

The allowable tensile load in the bolt based only on the tensile area is determined from *P _{t} = S_{t} A_{t} ⁄F_{s}*. For a typical static application, the factor of safety

*F*= 1.25.

_{s}Next, evaluate shear stress in the bolt. Unlike the tensile area, length of engagement affects the bolt’s shear area. The shear area of the bolt is the effective area at the maximum minor diameter of the internal thread multiplied by the number of engaged threads. This is calculated as

The allowable tensile load in the bolt, based only on the shear area of the bolt threads, is then found from *P _{s} = 0.5S_{t} A_{s} ⁄F_{s}*.

An option is to calculate shear area using a 1-in. length of engagement. This gives shear area per unit length, and minimizes recalculation if the length of engagement changes. Multiplying the shear area per unit length by the length of engagement gives the actual shear area.

The final stress to evaluate is shear stress in the internal thread. As in a bolt, shear area of an internal thread is a function of the bolt’s length of engagement. The shear area of the internal thread is the effective area at the minimum major diameter of the external thread multiplied by the number of engaged threads. This is found from

The maximum tensile load in the bolt, based on the shear area of the internal threads, is calculated using *P _{i} = 0.5S_{i} A_{i} ⁄F_{s}*. The lowest calculated allowable tensile load of

*P*,

_{t}*P*, and

_{s}*P*should be used to determine maximum torque.

_{i}**DETERMINING TORQUE**

The general equation for bolt load based on applied torque is *T = KF _{i}D_{b}* where

*K*= torque coefficient.

*K*is a function of the coefficients of friction and collar friction in the joint, and these are based on variables such as surface finish, coatings, and so on. Accepted coefficient values for both types of friction for steel-on-steel bolts is 0.15. With a coefficient of friction = 0.15,

*K*≈ 0.20 for all ranges of bolt sizes in both coarse and fine threads. For materials other than clean steel on steel, determine appropriate values from similar applications or by testing actual bolt and joint configurations. Typical

*K*values are shown in the table.

When calculating loads and torques, the female thread always has a greater shear area than that of the bolt. This means there is a range where the base material yield strength is lower than the bolt’s, but the bolt can still be torqued to the maximum. In fact, with a length of engagement of 1.5*D _{b}*, the range where full torque can be applied to lower-strength base material is quite large.

Specialized torque charts are a better option for taking advantage of this range without going through a series of calculations for each application. They also determine the correct torque and bolt load under derated conditions.

For instance, the accompanying chart for Grade 5 and 8 bolts was developed from a computer program that calculates thread dimensions and stress areas from the previous equations. However, the program differs from the calculations in two areas. One is that a stress concentration factor of 1.2 adjusts for unequal load distribution on the first engaged thread. The other is that external minor diameters are calculated by nontypical formulas provided in *ASME B1.1-1989*.

1. Select the correct bolt size and type. 2. Move to the fourth (for Grade 5) or eighth (Grade 8) column. This is the maximum applied torque based solely on the bolt’s proof strength. This is also the maximum torque the bolt can withstand without yielding. Multiplying actual 3. Column five or nine lists the minimum yield strength of the internal thread material that will withstand the bolt’s fullload capability. When the material’s minimum yield is equal to or greater than this value, the torque calculated in step 2 is correct for the application. Otherwise, move to step 4. 4. Where the material’s yield strength is less than the value in the table, calculate the reduced torque. Move to the third column for Grade 5 bolts (seventh column for Grade 8) to determine torque per 10,000-psi yield of the internal thread material. Multiply this value by the yield strength of the internal thread material and the actual K value, and then divide by 10,000. This is the maximum torque that can be applied to the bolt without stripping the internal threads, using a safety factor of 1.25. Note that columns five and nine use a 1.375 safety factor. This necessitates confirming that bolt torque does not exceed the maximum calculated in step 2. Use the smaller of the torques calculated in steps 2 and 4. 5. Convert torque from lb-ft to lb-in. and calculate the resulting clamp load using |