Question 2

Question 2

Integration Method question 2

Obtain the elastic curve expression for the beam. Also obtain an expression for the deflection of the beam at x = L/2.

Obtain the elastic curve expression for the beam. Also obtain an expression for the deflection of the beam at x = L/2.

Click below to show answer. X

Step 1:
Section cut to get moment equation

Step 1:
Section cut to get moment equation

Integration Method solution step 1

Step 2:
Integrate twice

Step 2:
Integrate twice

Integration Method solution step 2

Step 3:
Apply boundary conditions (BCs) to get C₁, C₂, C₃, C₄

Step 3:
Apply boundary conditions (BCs) to get C₁, C₂, C₃, C₄

Integration 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

Integration Method solution step 4

Useful formula:

Useful formula:

Integration Method formula

Congratulations! You've completed all the questions in this topic. Let's look at C9.2: Discontinuity Functions (Macaulay's Method) now.