Question 1

Question 1

Discontinuity Functions (Macaulay’s Method) question 1

Obtain the elastic curve expression for the beam. Use the Macaulay function.

Obtain the elastic curve expression for the beam. Use the Macaulay function.

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Step 1:
Section cut to get moment equation (with Macaulay brackets)

Step 1:
Section cut to get moment equation (with Macaulay brackets)

Discontinuity Functions (Macaulay’s Method) solution step 1

Step 2:
Integrate twice

Step 2:
Integrate twice

Discontinuity Functions (Macaulay’s Method) solution step 2

Step 3:
Apply boundary conditions (BCs) to get C₁ and C₂

Step 3:
Apply boundary conditions (BCs) to get C₁ and C₂

Discontinuity Functions (Macaulay’s Method) solution step 3

Step 4:
Final elastic curve equation

Step 4:
Final elastic curve equation

Discontinuity Functions (Macaulay’s Method) solution step 4

Useful formula:

Useful formula:

Discontinuity Functions (Macaulay’s Method) formula

Now that you've mastered this question, you can try Question 2.