Example Question

Same question as Question 2 of Chapter 9.1. Obtain a single elastic curve expression for the whole beam, using the Macaulay function. Also obtain the expression for the deflection at x = L/2.

Click below to show answer. X

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, find ν at x = L/2

Step 4:
Final elastic curve equation, find ν at x = L/2

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 1.

Example Question

Example Question

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

Step 2: Integrate twice Step 2: Integrate twice

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

Step 4: Final elastic curve equation, find ν at x = L/2 Step 4: Final elastic curve equation, find ν at x = L/2

Useful formula: Useful formula:

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

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

Step 2:
Integrate twice

Step 2:
Integrate twice

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

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

Step 4:
Final elastic curve equation, find ν at x = L/2

Step 4:
Final elastic curve equation, find ν at x = L/2

Useful formula:

Useful formula: