Rigging Math

(Made Simple)

A Primer by

Delbert L. Hall, Ph.D.

ETCP Certified Rigger

ETCP Recognized Trainer

Lesson 9: Distributed Load on a Beam

       In Lesson 8, you learned how to compute the tension on L1 and L2 when there was a single load on the beam (truss).  In this lesson you will learn how to compute the loads when you have multiple loads that are spread out along the truss. Here is a diagram of the problem:

As in Lesson 8, our desire is to find the vertical force on the two supporting Legs (L1 and L2).  The equations for solving this problem are:

L1 = ((Load1 x D1) + (Load2 x D2)) / Span

L2 = (Load1 + Load 2) – L1

Before we begin, it should be noted that unlike the problem in Lesson 8, D1 + D2 will NOT equal Span.  The equation for determining the tension on L1 uses L2 as the starting point for D1 and D2.

Example: If the Span is 20 feet, D1 is 17.5 feet, D2 is 5 feet, Load 1 is 100 lbs, and Load 2 is 200; what is the tension on L1 and L2?

L1 = ((Load1 x D1) + (Load2 x D2)) / Span     or

L1 = ((100 x 17.5) + (200 x 5)) / 20               or

L1 = (1750+ 1000) / 20                                or

L1 = 2750 / 20                                             or

L1 = 137.5 lbs.   

And because L1 + L2 must equal Load1 + Load 2 we can use the simple equation to determine L2.

L2 = (Load1 + Load 2) – L1         or

L2= (100 + 200)  - 137.5           or

L2= 300  - 137.5                       or

L2 = 162.5 lbs.

Although this may seem complicated at first, remember that you keep the 1’s together (Load1 x D1) and the 2’s together (Load2 x D2), then add them and divide the result by the Span.  If you have more that two loads, just add “(Load 3 x D3)” and so on to the first part of the equation, and divide the total by the Span.  Practice computing these problems before going to the next lesson, which will become even more complex.

Worksheet 

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