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There are bolted connections throughout a ski area, and it’s important to understand the mechanics. Tightening a bolt too much or too little—that is, applying too much or too little torque—significantly effects how well the bolt will do its job, and for how long it will do it.

Nuts and bolts are manufactured and specified to various standards and measures: metric (made to the ISO 898-1 standard) and ASTM structural fasteners, for example. This discussion focuses on SAE J429 fasteners. i.e., the familiar Grade 2, 5 and 8 fasteners, measured in inches, but the principles are the same for all.

Bolted Connections, Clamping Force and Friction
Torqueing a nut stretches a bolt, creating a clamping force so that friction can hold a bolted joint together. The bolt acts like a very stiff spring. Friction, created by the clamping force that results from tightening a nut on a bolt, holds the joint together. The thread on nuts and bolts is an inclined plane, so rotating the nut moves the nut up the plane. That stretches the bolt and creates the clamping force. This also increases the friction between the parts being connected, and that friction holds the parts together.

Figure 1: Basic bolted joint with fastener in tension.

Torque
Torque is a measure of the effort it takes to twist something, like a nut or bolt or bottlecap. Numerically, it is the product of a force and the distance (moment arm) it acts through to create the twist (see Figure 2). For a given force, the longer the moment arm, the greater the torque.

Foot-pounds (ftlb) are the commonly-used units to measure torque, but inch-pounds (inlb) and newton-meters (Nm) are also used. Converting from one to another is only a matter of multiplying by conversion factors. For example, 36 pounds applied to a nut with a four-inch-long wrench produces a torque of 144 inch-pounds (36 lb x 4 in = 144 inlb). To convert this figure to ftlb, divide the inches by 12. This can be expressed as 36 lb x 4/12 ft = 12 ftlb.

Figure 2: Torque and Clamping Force

Steel Bolts
Steel has an elastic range in which it acts like a spring. In this range, the steel returns to its original shape when a load is removed. The more a bolt is stretched, the harder it pulls back, to return to its original length. This spring action is what holds connected parts together.

For steel in general, this spring action is described with a stress-strain diagram (Figure 3). The essential points are:

Strain (stretch). The horizontal axis is a measure of stretch. It is the elongation divided by the original length.

Stress (load). The vertical axis is stress, which is a measure of load. Its units are pounds per square inch (psi), like pressure.

Stress Area. This is the area at the root of the threads. For the 1/4-20 Grade 5 fastener, the stress area is 0.032 sqin.

Tensile Stress. For a bolt in tension, this is the load (pounds) divided by its cross-sectional area (square inches, “sqin”).

Yield Point. The upper limit of a bolt’s elastic range is the yield point—Point 2 in Figure 3. If we exceed the yield point, the bolt will be permanently stretched. This is why it’s very important to follow the torque recommendations of suppliers and manufacturers.

Proof Load. This is the load that we can safely put on the bolt without exceeding its yield point. The proof load is set by the manufacturer, and is typically 85-95 percent of the yield point.
For example, for a 1/4-20 SAE Grade 5 bolt, or any grade 5 bolt, the minimum proof stress is 85,000 psi. The proof load for this fastener is the proof stress (85,000 psi) multiplied by the stress area (0.032 sqin), from which we get the commonly tabulated value of 2,700 lb.

Ultimate Tensile Strength. If we exceed the yield point of the bolt—by overtightening its nut, or by putting too much load on the joint—we pass the “kink” in the stress-strain graph, Point 2 of Figure 3. Beyond this point, as we tighten a nut, far less force (torque on the wrench) is required than in the elastic range. This is what we feel when we overtighten a nut. This new range, between points 2 and 3 in Figure 3, is the “plastic range” of the stress-strain graph. In this range, the bolt is permanently deformed, and breakage is usually next.

The maximum strength of a material is called its Ultimate Tensile Strength, Point 3 in the stress-strain graph, Figure 3. Beyond this point, the load-carrying ability of the material falls off until it ultimately fails at Point 4.

This helps explain the recommendation against reusing bolts. It is possible that the elastic limit of the bolt has been exceeded and the bolt has been weakened, even though it has not yet failed.

Figure 3: As steel bolts stretch, they act like a spring to hold connected parts together. The spring action increases up to the yield point. This is the bolt’s elastic range (between points 1 and 2). Beyond that load, the bolt becomes permanently stretched, and can begin to weaken. Beyond a certain point, the bolt can fracture. This is the bolt’s plastic range.

Torque Specs and K-Factors
The more a nut is tightened, the more the bolt is stretched. That increases the clamping force and the friction in the joint, reducing the tendency for the joint to loosen—until the bolt stretches beyond its elastic range and clamping force is lost.

How much tightening is best? A good compromise is 75 percent of the bolt’s proof load. To determine that point, we most often use a torque wrench. But there’s more to the story: the clamping force for a given torque depends on the friction in the threads and between the faces and the bearing surfaces.

The Torque Requirement is usually estimated with the following formula:

T=k d F

Torque (T) is the product of clamping load (F), the diameter of the bolt (d) and a “k-factor” (k).

The clamp load (F)—which keeps the joint tight without over-stressing the bolt—is 75 percent of the bolt’s proof load, or 65 to 70 percent of its yield strength.

The k-factor is an experimentally derived “nut-factor” that accounts for the torque lost due to friction between the nut and the bolt, and the nut face and the surface being clamped. In fact, barely 10 percent of the torque on a nut goes to creating clamping force.

A nut factor of k = 0.2 is commonly used, but the Fastenal Bolted Joint Design paper gives a summary of values for a number of bolt conditions:

Here is how to calculate the recommended torque for our 1/4-20 Grade 5 bolt:

…which is commonly found in torque specifications for this fastener.
For reliable clamping forces, it is generally wise to lubricate fasteners before setting their torques.