Statics in 3D, there must a be faster way to do this.

  • Thread starter goonking
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    3d Statics
In summary, to compute this problem faster, you can use the cross product of each term. However, this method may still be slow and complicated. Another approach is to break up the forces into their x, y, and z components and sum them separately. Then, for the sum of moments to equal 0, each force component should be multiplied by its perpendicular distance from the line of action to the axis. This method avoids determinants and vector equations, but requires dividing the 3D problem into 2D problems and ensuring equilibrium within each plane.
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goonking
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Given this, is there a faster way to compute this or must I do 3 separate 3x3 determinants?

I can probably use cross product of each term, for example , (2rk) X (Axi) = (-2rAx j) (not forgetting the negative sign for j)

next, (2rk) X (Ayj) = (2rAyi)

and so on... but that feels too slow as well and can get very messy.
 
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Break up each of the forces into their x y and z components and sum them separately equal to 0. Then for the sum of moments equals 0 for each force component about an axis, it's

[itex] M_x = F_yz + F_zy[/itex]

[itex]
M_y = F_xz + F_zx
[/itex]

[itex]M_z = F_xy + F_yx [/itex]

where x y and z are the perpendicular distances from the line of action of the component force to the axis about which moments are being summed.
I don't know if that's easier for you, but it avoids determinants and vector math equations .
 
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Divide your 3D problems into 2D problems. Just remember, the forces and moments in a plane must be in equilibrium.
 

Related to Statics in 3D, there must a be faster way to do this.

1. What is the purpose of studying Statics in 3D?

Studying Statics in 3D allows us to analyze the forces acting on objects in three-dimensional space. This is important for understanding the stability and balance of structures and systems, such as buildings, bridges, and machinery.

2. What is the difference between 2D and 3D statics?

In 2D statics, we only consider forces acting in two dimensions, whereas in 3D statics, we also consider forces acting in the third dimension. This allows for a more comprehensive analysis of complex systems.

3. How is 3D statics applied in real-world scenarios?

3D statics is used in various engineering fields, such as civil engineering, mechanical engineering, and aerospace engineering. It is applied in the design and construction of structures, vehicles, and machines, ensuring they can withstand the forces they will encounter.

4. What are some challenges in solving 3D statics problems?

The main challenge in 3D statics is visualizing and understanding the three-dimensional forces acting on an object. Additionally, solving equations in three dimensions can be more complex and time-consuming compared to 2D statics.

5. Are there any shortcuts or faster methods for solving 3D statics problems?

While there are no shortcuts in understanding and applying the principles of 3D statics, there are various software programs and tools available that can assist in solving complex problems more efficiently. However, a thorough understanding of the fundamentals is still necessary for accurate analysis and results.

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