Answer to Quiz No. 4

Given the sketch below:

For each sling, find the tension in pounds.

T1=_____________ T2=____________



The tension in the left sling T1 = 35,619 lbs.
The tension in the right sling T2 = 79,919 lbs.

The main purpose of the monthly quizzes is not to test the readers skill in algebra or trigonometry, although a good knowledge of both is required in today's construction world, but to see if the reader recognizes one or more concepts that are fundamental in solving the problem. The reader can then use various ways to solve it, including mathematics, laying it out to scale, etc.

In the number 4 quiz, one way to solve it would be to solve for all the angles at the hook and then sum the forces vertically for T1 & T2.

A second and recommended way, because the sketch is easy to lay out to scale, is to choose a horizontal reference line (HRL) that runs through the center of gravity (CG) and the attachment point of the right sling to the load. Extend the left sling down until it intersects the HRL. Scale off or solve the horizontal distances from the CG to the intersections of the HRL and the right sling and the extended line of the left sling. These distances are approximately 3.25' and 10.07' respectively.

Now solve for the vertical reactions at the intersection points. The vertical reaction at the intersection of the left sling R1 = 100,000 lbs*3.25'/ (10.07' + 3.25') = 24,400 lbs. The vertical reaction at the intersection of the right sling R2 = 100,000* 10.07'/13.32 = 100,000 - 24,400 = 75,600 lbs.

Solve for the vertical distance h from the CG to bearing on the hook mathematically or by scaling it off the sketch, h = 9.46'.. Solve for the total length of the left sling plus the extended length down to the point of intersection with the HRL = 13.81'. Therefore T1 = R1*13.81'/h = 35,619 lbs. T2 = R2*10'/h = 79,916 lbs.

If the sketch is laid out carefully and to as large a scale as possible, the accuracy of the results should be acceptable for this kind of problem where the safety factor of the slings is at a 5:1.

Lastly, it should be remembered that a HRL can be chosen at any vertical point on the sketch and the one chosen in this example was for convenience only.

    


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