475. We assume that the chain hangs in the form of a parabola, and that the load is uniformly ranged along the bridge. The tension upon the chains is greatest at their highest points, and least at their lowest points, though the difference is small. The amount of the tension can be calculated when the load, span, and deflection are known. We cannot give the steps of the calculation, but we shall enunciate the result.
Fig. 65.
476. The magnitude of the tension at the lowest point c of each chain is found by multiplying the total weight (including chains, suspension rods, and roadway) by the span, and dividing the product by sixteen times the deflection.
The tension of the chain at the highest point a exceeds that at the lowest point c, by a weight found by multiplying the total load by the deflection, and dividing the product by twice the span.
477. The total weight of roadway, chains, and load in the model is 120 lbs.; the deflection is 10", the span 108"; the product of the weight and span is 12,960; sixteen times the deflection is 160; and, therefore, the tension at the point c is found, by dividing 12,960 by 160, to be 81 lbs.
To find the tension at the point a, we multiply 120 by 10, and divide the product by 216; the quotient is nearly 6. This added to 81 lbs. gives 87 lbs. for the tension on the chain at a.
478. One chain of the model is attached to a spring balance at a; by reference to the scale we see the tension indicated to be 90 lbs.: a sufficiently close approximation to the calculated tension of 87 lbs.
479. A large suspension bridge has its chains strained by an enormous force. It is therefore necessary that the ends of these chains be very firmly secured. A good attachment is obtained by anchoring the chain to a large iron anchor imbedded in solid rock.
480. In [Art. 45] we have pointed out how the dimensions of the tie rod could be determined when the tension was known. Similar considerations will enable us to calculate the size of the chain necessary for a suspension bridge when we have ascertained the tension to which it will be subjected.