Macaulay’s method & principle of superposition:

Question 1

What are the key steps for the Macaulay Method?

Answer 1

1. Express M as a function of x
2. Integrate M/EI once to find θ
3. Integrate M/EI twice to find u
4. Apply boundary conditions

Question 2

Where do the Macaulay’s Bracket go?

Answer 2

Macaulay’s Bracket in the subsequent term not first term in the momentum equation

Question 3

What do you do when you have a UDL that doesn’t go to the end of the beam?

Answer 3

Introduce a dummy load

Question 4

What is the distance for the moment in a linear load (triangular shape)?

Answer 4

1/3 of the distance away

Question 5

How can the principle of superposition be applied?

Answer 5

Resulting deflection is equal to the sum of the deflection which is individually caused by the different loads

Question 6

How can the constants in the integration be found?

Answer 6

Determined from boundary conditions