Find tension in tower crane

In summary, the conversation discusses finding the tension in a cable for a beam with a given weight and center of mass. The torque equation is used to calculate the tension, but there is an additional torque from another part of the beam that was not initially accounted for. After including this torque, the final value matches the answer in the book. The conversation also touches on the concept of pulleys and how they affect tension.
  • #1

Homework Statement


The beam ABC is1000LBs and its center of mass is given as 6.5ft to right of B. B is a pin joint. A & D are frictionless rollers. Find tension in cable.

Homework Equations


Call the tension in the cable T.
Trig shows us that the left-hand triangle is 45 degrees at ABD and the right-hand triangle is 15.5 degrees at BCD.
Torque due to wt of load and mass of beam are clockwise and negative; torques due to T are ccw and positive.

The Attempt at a Solution


So the torque at B should be: -(6.5ft)(1000Lb) + -(12ft)(3000LB) + (18ft)(sin15.5)T + (5ft)(sin45)T=0
This yields a T of 5114; the book shows the answer as 6770.
What am I missing?
 

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  • #2
The part of the torque you calculated for (A) actually goes in the opposite direction, and there is a second part.

I can confirm the book's answer.
 
  • #3
Thank you for helping! I am trying to work through this statics course on my own, so the Internet is, um, my professor.:biggrin:

So the cable from CD pulls up and to the left, yielding ccw rotation. Shouldn't the tension from D to A pull down and push to the right, also yielding a ccw rotation?

Oh...is the second part that you reference the torque from AE? This yields an additional torque of 5T.
 
  • #4
SoylentBlue said:
Shouldn't the tension from D to A pull down and push to the right, also yielding a ccw rotation?
It pulls A up and to the right.
SoylentBlue said:
Oh...is the second part that you reference the torque from AE? This yields an additional torque of 5T.
Right.
 
  • #5
Oh, you can look at the pulley at the top of the crane the same way you'd look at a cable draped across the top of a suspension bridge's tower; so the tension on the right opposes the tension on the left. Now I see. I just needed to brush up on Pulleys 101.

If you add in the torque from AE, then the final value comes out almost exactly to the 6770 that the book shows.

Again, thank you for helping!
 

1. What is the purpose of finding the tension in a tower crane?

The purpose of finding the tension in a tower crane is to ensure that the crane is operating safely and efficiently. Knowing the tension in the crane allows engineers to determine the maximum weight that the crane can safely lift and make adjustments if necessary.

2. How is the tension in a tower crane measured?

The tension in a tower crane is measured using load cells, which are sensors that can accurately measure the weight placed on the crane's cables. These load cells are typically attached to the crane's cables and provide real-time data on the tension.

3. What factors affect the tension in a tower crane?

The tension in a tower crane is affected by several factors, including the weight of the load being lifted, the length and angle of the crane's boom, wind speed and direction, and the stability of the crane's foundation. Changes in any of these factors can impact the tension in the crane's cables.

4. How often should the tension of a tower crane be checked?

The tension of a tower crane should be checked regularly, especially before and after heavy use or if there are any changes in the crane's operating conditions. It is recommended to check the tension at least once a day to ensure safe operation.

5. What are the potential risks of not properly finding the tension in a tower crane?

Not properly finding the tension in a tower crane can result in serious safety hazards, such as the crane collapsing or losing control of the load being lifted. It can also cause damage to the crane itself and surrounding structures. Properly maintaining and monitoring the tension in a tower crane is crucial for the safety of workers and the success of construction projects.

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