10.6.2. Application: Beam Deflection with One Fixed End

Try these first

1. 1.

   Define beam deflection in your own words.

   Hint

   Think about what happens to a ruler when you push down in the middle.

2. 2.

   What is the Fourier Cosine Transform used for?

   Hint

   Recall how it deals with specific boundary conditions.

3. 3.

   What does the Euler-Bernoulli equation relate?

   • Deflection to material density
   • Load to beam deflection
   • Speed to load application

   Hint

   Focus on the primary relationship expressed in the equation.

4. 4.

   True or False: The Fourier Cosine Transform is suitable for periodic signals.

   • True
   • False

   Hint

   Consider the domain type for each transform.

5. 5.

   A cantilever beam of length L is subjected to a triangular load. Determine the deflection at the free end using Fourier Cosine Transform.

   Hint

   Analyze how the load shape affects the function form.

6. 6.

   Given a uniform load q(x) = q_0 on a cantilever beam, derive the expression for maximum deflection at the free end.

   Hint

   Ensure the load function is consistent with beam theory assumptions.