X 10-1 R

pounds, beam and weight

R, X 10-1,000 X 9-2,000 X 4-3,000 X 2-400 X 5=0. The first one reduces to 10 39,000, or R.= 3,900 pounds; and the second to 10 25,000, or 2,500 pounds.

4. What are the total reactions in example 2 if the beam weighs 42 pounds per foot I As in example 3, we might compute the reactions due to the weight and then add them to the corresponding reactions due to the loads (already found in example 2), but we shall determine the total reactions due. to load and weight directly.

The beam being 20 feet long, its weight is 42 x 20, or 840 pounds. unds Since the middle of the beam is 8 feet from the left and 6 feet from the right support, the moments of the weight with respect to the left and right supports are respectively: 840 X 8 = 6,720, and-840 X 6 = —5,040 foot-pounds.

The moment equations for all the forces applied to the beam for origins at B and D are like those in example 2, with an addi tional term, the moment of the weight; they are respectively: —2,100X 2+ 0+3,600 X 14+1,600 X 18+6,720 = 0, —2,100 x 16 +R, X 14-3,600 X 8 + 0 + 1,600 X 4-5,040 = 0.

The first equation reduces to 14 R„=-52,920, or pounds, and the second to 14 R,= 61,040, or 4,360 pounds.

The sum of the loads and weight of beam is 8,140 pounds; and since the sum of the reactions is the same, the computation checks.

1. AB (Fig. 11) represents a simple beam supported at its ends. Compute the reactions, neglecting the weight of the beam.

Ans. 5 Right reaction = 1,443.75 pounds. Left reaction = 1,556.25 pounds.

2. Solve example 1 taking into account the weight of the beam, which suppose to be 400 pounds.

Right reaction = 1,643.75 pounds. Ans. Left reaction = 1,756.25 pounds.

3. Fig. 12 represents a simple beam weighing 800 pounds supported at A and B, and sustaining three loads as shown. What are the reactions ? Fig. 12.

4. Suppose that in- example 3 the beam also sustains a uni formly distributed load (as a floor) over its entire length, of 500 pounds per foot. Compute the reactions due to all the loads and the weight of the beam.

S Right reaction,_—_ 4,871.43 pounds. Ans. Left reaction 11,928.57 pounds.