7.1 Two-Leg Tension and Angle Reference

Separate vertical support from leg tension

For a symmetrical two-leg bridle, each leg provides half the vertical support when the load is balanced, the picks are at the same elevation and the geometry is symmetrical. The leg itself is inclined, so its tension is greater than that vertical component unless it is vertical. This distinction is central to sling and hardware selection.

Let the total supported load be W and each leg’s tension be T. Let θ be the angle between the sling and a horizontal reference through the picks. The vertical component of each tension is T sin θ. Summing both components gives W, so:

$$T=\frac{W}{2\sin\theta}$$

The load angle factor is 1/sin θ. It multiplies the vertical load share, not the total weight in every case. A factor greater than one means the sling has to carry a larger force to provide the required upward component.

Identify the angle before calculating

An angle measured from vertical is complementary to the horizontal angle in this simple model. If a sling is 30 degrees from vertical, it is 60 degrees from horizontal. Using sin 30 when the given 30-degree angle is vertical would produce a different and incorrect tension. Draw the reference line and label it before entering a factor.

At 30 degrees from horizontal, each leg’s tension equals the entire supported weight even though each supplies only half its vertical support. Adding the two tensions does not give the vertical weight; their components must be resolved in the correct directions.

For a simple numerical check, a 12,000-lb balanced load at 60 degrees needs approximately 6,000 × 1.1547 = 6,928 lb per leg. The two vertical components are each approximately 6,000 lb, totaling the weight. A proposed 6,000-lb vertical-rated sling is not adequate for that calculated leg tension merely because there are two slings.

Recognize the assumptions

The formula applies to the defined symmetrical model. An off-center CG, unequal pick elevations, different sling geometry or additional supports can invalidate equal division. A load that appears level is not necessarily symmetrical. Determine vertical reactions first when the CG is offset; then apply each leg’s own angle factor.

The supported weight for this model includes the masses carried below the two legs. A heavy lower beam or other carried gear can increase W. The crane block above those legs does not become part of their lower supported weight simply because it appears in crane capacity accounting. Trace the force path to decide which mass belongs in each calculation.

This is a static calculation. It does not approve shock loading or quantify all acceleration, wind and motion effects. The selected components and operating procedure must address those conditions separately. A design factor is not permission to add an unplanned bounce because the calculated tension appears below breaking strength.

Understand shallow angles

As the horizontal angle decreases, sine decreases and tension increases nonlinearly. The relationship is reciprocal-sine, not exponential. Small geometry changes at shallow angles can materially change demand and horizontal forces. Follow the manufacturer’s permitted minimum angle and the applicable standard or qualified-person conditions.

Do not cite OSHA 1926.251 as imposing a blanket engineer-signed prohibition at every angle below 30 degrees. The practical examination has its own 30-degree instruction, and sling standards and manufacturers have applicable angle conditions. The field selection must use the correct source for the actual assembly.

Selection example

A given sling is rated 8,000 lb for the applicable single-leg loading, and a balanced 12,000-lb load is proposed at 60 degrees. The calculated 6,928-lb tension is below that rating. This establishes only the tension comparison. The sling material, hitch, bend conditions, eye seating, attachments, temperature and movement controls must also be suitable.

If the same load is changed to 45 degrees, tension becomes approximately 6,000 × 1.4142 = 8,485 lb. The proposed sling no longer satisfies the numerical demand. The weight has not changed; the geometry has. The correct response is an approved change in component or arrangement, followed by the relevant checks, rather than relying on the unused breaking-strength margin.

Keep adequate precision during calculation, then choose equipment with applicable WLL at least equal to the demand. If an examination supplies a rounded factor, use its stated rounding consistently. Do not round a computed demand down simply to make it fit the available gear.

Use the provided calculator effectively

The on-screen four-function calculator can multiply a supplied angle factor by a vertical share. It does not require a trigonometric function when the factor is given. If a question supplies a factor of 1.414 for a balanced 10,000-lb load, first calculate 10,000/2 = 5,000 lb, then 5,000 × 1.414 = 7,070 lb. Record the factor's stated precision rather than claiming an exact trigonometric result.

Read a multi-leg assembly table differently from a single-leg rating. If the table already gives the complete two-leg assembly capacity at the stated angle, the manufacturer has incorporated that configuration. Do not apply the angle factor again to that assembly rating. Verify which quantity the table describes before comparing it with the supported weight.

Source: CCO rigging reference materials and capacity booklet.