3 dimension reactions problem - statics

In summary, the problem involves a 100-kg rectangular plate supported by hinges A and B and a cable DCE passing over a frictionless hook at C. The tension in the cable and the reactions at A and B are to be determined, assuming that the hinge at B does not exert any axial thrust. This means that there will be reaction forces in the y and z directions at hinge B, but no reaction moment about the x-axis to maintain static equilibrium.
  • #1
LeFerret
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Homework Statement


A 100-kg uniform rectangular plate is supported in the position shown by hinges A and B and by cable DCE that passes over a frictionless hook at C. Assuming that the tension is the same in both parts of the cable, determine (a) the tension in the cable, (b) the reactions at A and B. (assume that the hinge at B does not exert any axial thrust)


Homework Equations





The Attempt at a Solution


What does it mean when it says assume that the hinge at B does not exert any axial trust?
Everyone keeps telling me that it means that there's no reactions, yet in the free body diagram, I see reaction forces, just no reaction moments, is this what it means?
 

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  • #2
I don't know, but would guess (and proceed on the assumption that) it means no reaction component parallel to AB.
 
  • #3
It means at hinge B, there will be reaction forces in the direction of the y-axis and z-axis. It's a hinge, so it can't support a reaction moment about the x-axis.

I think the stipulation about hinge B not being able to support an axial reaction force is to ensure that the problem is statically determinant.
 
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FAQ: 3 dimension reactions problem - statics

1. What is a 3 dimension reaction problem in statics?

A 3 dimension reaction problem in statics is a type of problem that involves analyzing the forces and moments that act on a structure in three dimensions, taking into account the static equilibrium of the structure. This type of problem is commonly encountered in engineering and physics, and it requires the use of vector mathematics and the principles of statics to solve.

2. How do you approach solving a 3 dimension reaction problem in statics?

The first step in solving a 3 dimension reaction problem in statics is to draw a free body diagram of the structure, clearly showing all the external forces and moments acting on it. Then, using the principles of static equilibrium, such as the sum of forces and moments equaling zero, the unknown reactions at each support can be calculated using vector mathematics and trigonometry.

3. What are some common applications of 3 dimension reaction problems in statics?

3 dimension reaction problems in statics are commonly encountered in the analysis and design of structures such as bridges, buildings, and other load-bearing structures. They are also used in the design of mechanical systems, such as cranes and hydraulic systems, to ensure that they can withstand the forces and moments acting on them.

4. What are some challenges when solving 3 dimension reaction problems in statics?

One of the main challenges when solving 3 dimension reaction problems in statics is dealing with the complexity of the calculations involved, as they often require the use of vector mathematics and trigonometry. Another challenge is ensuring that all the forces and moments acting on the structure are correctly identified and accounted for in the analysis.

5. Are there any specific software or tools that can assist in solving 3 dimension reaction problems in statics?

Yes, there are many software programs and tools available that can assist in solving 3 dimension reaction problems in statics. These include CAD (Computer-Aided Design) software, FEA (Finite Element Analysis) software, and structural analysis software. These tools can help with the visualization of the structure and the calculation of reactions, making the solution process more efficient and accurate.

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