Calculating Member Forces of a Crane Lifting a 125kg Motor

In summary: If you prefer, yes, you can draw the entire structure which includes members EFG and CDE, and solve sum of moments about joint C equal to zero. Or, if you prefer, you can draw just member CDE and solve sum of moments about joint C equal to zero.
  • #1
raymanmusic
31
1

Homework Statement


This crane lifts a 125 kg heavey motor. What is the member forces of BF and BD?
Use 10 m/s^2 as accleration of gravity.

https://dl.dropboxusercontent.com/u/11241083/problemtruss.png



Homework Equations


F=ma
Sum Fx=0
Sum Fy=0
Sum M=0

The Attempt at a Solution


Answers:
BF force: -1939 N
BD force: -2596 N
 
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  • #2
Drawing a free body diagram? Writing equations of equilibrium? Bueller? Bueller?
 
  • #3
Force in G is F=125 kg * 10 m/s^2=1250 N
I found reaction force in A: 1250 N and reaction force in C: 0 N
 
  • #4
Yeah, but that's not what the problem solution requires. It also ignores the weight of the lifting mechanism, which is not given, in any event. You are asked to find the forces in two members BD and BF while the motor is suspended.

Again, draw a FBD and write equations of equilibrium.
 
  • #5
At what joint do I sum moments? Do I sum x and y forces including the BD and BF forces? Can I use method of joints? I'm unable to solve this. https://dl.dropboxusercontent.com/u/11241083/New%20Document20140131230411543.pdf
 
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  • #6
You've got to split the hoist into several parts, and solve each individually.

For the force in member BF, start with isolating member BF and the top piece EFG. You know the load applied at point G and you know this member is supported by BF and member CDE. You can use the geometry of the hoist to supply the unknown reactions which keep EFG in equilibrium and then solve for their magnitudes.

Once you have worked the top member, take a similar approach to analyze the forces in member BD.
 
  • #7
I got the right answer for BF. How do I find BD? Do I isolate member EDC and BD and use equations of equilibrium? How do I calculate reaction force in C
 
  • #8
You repeat the process used to solve member EFG. Use the reactions from that member and isolate EDC. Draw its FBD and write a new set of equilibrium equations. Remember, the joint at C is pinned, so it can't support/resist a moment.
 
  • #9
Do I solve sum of moments about joint C is equal to zero?
https://dl.dropboxusercontent.com/u/11241083/New%20Document20140201213045922.pdf
 
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  • #10
Yes. The joint at C is pinned and therefore the moment there must be zero.
 
  • #11
I'm unable to find the force in member BD. Can you please help me draw a FBD?
 
  • #12
raymanmusic: I think your answers in post 1 currently look incorrect. Your reaction forces in post 3 currently look correct. Isolate member CDE, and draw all forces acting on member CDE, in a member CDE free-body diagram. Show us what your attempted member CDE free-body diagram looks like. List the value of any forces on member CDE you already know. Then, sum moments on member CDE, about point C, and show us your attempted solution for the force in member BD. Or alternately, post your answers for members BF and BD; if your answers are already correct, then you are done.
 
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  • #13
My answers:
BF = -1938.87 N
BD = -2601.27 N
My attempt at solution:https://dl.dropboxusercontent.com/u/11241083/New%20Document20140202212736894.pdf

Do I only draw member CDE or do I draw EFG and CDE and then solve sum of moments about joint C equal to zero?
 
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  • #14
Post 1 says use g = 10 m/s^2.
 
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  • #15
I'm sorry that is a mistake. Use g=9.81 m/s^2
 
  • #16
raymanmusic: Your answers in post 13 are correct.

raymanmusic said:
Do I only draw member CDE, or do I draw EFG and CDE, and then solve sum of moments about joint C equal to zero?
Either way is fine. Either way you prefer.
 
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1. How do you calculate the weight of the motor being lifted by the crane?

The weight of the motor is given as 125kg in the problem. In order to calculate the weight, we can use the formula W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity. In this case, the weight of the motor is simply 125kg multiplied by the acceleration due to gravity (9.8 m/s^2), giving us a weight of 1225 N.

2. What is the maximum force that the crane needs to exert to lift the motor?

The maximum force that the crane needs to exert is equal to the weight of the motor, which we calculated to be 1225 N. This is because according to Newton's Second Law, the force required to accelerate an object (in this case, the motor) is equal to its mass multiplied by its acceleration, which in this case is just the acceleration due to gravity.

3. How can we calculate the tension in the crane's cables while lifting the motor?

In order to calculate the tension in the crane's cables, we need to consider the forces acting on the motor. These include the weight of the motor (1225 N) and the tension in the cables. By using the principle of equilibrium, we can equate the sum of these forces to zero, and solve for the tension. This will give us the tension in the crane's cables while lifting the motor.

4. What other factors should be taken into account when calculating the member forces of the crane?

Aside from the weight of the motor, other factors that should be considered when calculating the member forces of the crane include the length and strength of the crane's arms, the angle at which the motor is being lifted, and any external forces such as wind or uneven terrain that may affect the stability of the crane.

5. How can we ensure the safety and stability of the crane when lifting such a heavy load?

To ensure the safety and stability of the crane, it is important to properly calculate and distribute the forces on the crane's members. This can be achieved by using appropriate materials and construction techniques, as well as regularly inspecting and maintaining the crane. It is also crucial to follow proper safety protocols and guidelines while operating the crane, and to take into account any external factors that may affect its stability.

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