Let’s start this discussion by introducing a term used in hydraulic bolt tensioning called elastic recovery, or more commonly just called relaxation; which is the difference between force applied by a hydraulic bolt tensioner and the residual preload left in the bolted joint after the nut is turned down and hydraulic pressure is released. As the load is transferred from the tensioner to the bolt the following happens:

• Elastic embedment of previously non-loaded joint members
• Strain between the threads of the bolt and nut as they take the load
• Localized plastic deformation of machining crests. This can occur between thread surfaces as well as under the nut against the flange or any metal contact areas.

The amount of relaxation is directly correlated to the stiffness (geometry) of the joint. Stiffer joint elements will have less relaxation than those in which joint elements are allowed to flex. The opposite is true for the bolt, with long slender bolts having less effect on joint relaxation when compared with short bolts with high stiffness. In the most common bolted joint arraignments, the bolt effective length has the largest impact on the relaxation ratio and is used to estimate the amount of relaxation during the bolt tensioning assembly process.

So, what is the effective length of a bolted joint and how is it measured? Let’s start with clamp length or what is sometimes called grip length. This refers to the combined thickness of all members which are clamped together. This typically means, the length between the surfaces of the bolt head and nut. Note: any washers or spacer lengths would be included in the clamp length.

Effective length is the length of the bolt effected by the tension load and is used to calculate joint stiffness and bolt stretch. This is commonly equal to the clamp length plus ½ of the thread engagement length with the nut(s) or flange.

-In the Figure below, “C” represents clamp length and “L” represents the effective length.

As shown in the table, as the effective stud length to diameter ratio increases, the relaxation factor dramatically decreases until a ratio of 12 is reached. After such relaxation is not affected immensely and any further affect is neglected while estimating relaxation.

For example; a 2.00” stud with an effective length of 12.00” would have and L/D ratio of 6 (12.00/2.00=6). Following the chart above would have a relaxation factor of 1.175. Therefore, if a preload force of 83,000 lbf is needed, 83,000 lbf would be multiplied by 1.175 to find a load of 97,525 lbf which must be applied by the bolt tensioner to the stud in, order to achieve the in-service preload of 83,000-lbf.

±5% Accuracy can typically be achieved in bolts loaded with hydraulic bolt tension tools. So, the above load of 83,000 lbf could very well be between 78850-89640 lbf. If more precision is needed to control the load, stretch measurements can be used to accurately measure the load applied. A ±1-2% accuracy can be achieved when applying accurate stretch controls in conjunction with hydraulic bolt tensioning.  Once bolt stretch is verified during the initial installation, repeatability is very good for subsequent studs / assemblies using hydraulic pressure alone.

The same target load achieved by simple torquing typically could see a range of ±25-30% (Ref: An Introduction to the Design and Behavior of Bolted Joints, 3^rd Edition, John H. Bickford), So that load of 83,000 lbf could see a spread between 62,250-103,750 lbf (25%). Again, if more precision is needed to control said load, stretch measurements can be used to accurately measure the load applied, but unlike the tensioning instance, the stretch would need to be measured on all bolts.

It is worth noting Relaxation happens during service; as well as during installation but is a whole another discussion.