Deriving Equation #3: (b/2)θ=L(2θ)

  • Thread starter Brit412
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In summary, using equations #1 and #2, the derived equation #3 can be obtained by dividing the right-hand sides and setting them equal to the ratio of the left-hand sides.
  • #1
Brit412
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Homework Statement


Using equations #1 and #2 to derive equation #3

Homework Equations


#1- ∆x = (b/2)theta
#2- ∆z= L (2theta)
#3- ∆x= ∆z b/4L


The Attempt at a Solution


Now I set equations #1 and #2 equal to each other, but I'm not sure how the thetas end up cancelling or if I'm even supposed to set them equal to each other in the first place. HELP please!
 
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  • #2
Just divide one equation by the other.
 
  • #3
Does that mean that I divide (b/2)theta by L(2theta)?
 
  • #4
Yes, you divide the right-hand sides of the two equations, and the result must equal the ratio of the left-hand sides of the same two equations.
 

1. What is the equation (b/2)θ=L(2θ) used for?

This equation is commonly used in physics and engineering to calculate the deflection angle (θ) of a beam or structure when subjected to a load (L) at a certain distance (b/2) from the support.

2. How is the equation (b/2)θ=L(2θ) derived?

This equation can be derived using the principles of statics and equilibrium, specifically the moment equation ΣM=0, where the sum of all moments acting on a system must equal zero for it to be in equilibrium.

3. What do the variables in the equation (b/2)θ=L(2θ) represent?

The variable b represents the distance between the load and the support, θ represents the deflection angle of the beam or structure, and L represents the magnitude of the load acting on the beam.

4. Can this equation be used for any type of beam or structure?

Yes, this equation can be used for any type of beam or structure, as long as the load is applied at a certain distance from the support and the beam is in equilibrium.

5. How accurate is this equation in predicting deflection?

This equation provides a good estimation of deflection for beams and structures under certain conditions. However, it may not be accurate for more complex systems or when the material properties of the beam are not taken into account.

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