3. Double Integration Method

Try these first

1. 1.

   Define the term 'deflection' in the context of beam theory.

   Hint

   Think about what happens to a straight line when you apply a load.

2. 2.

   What are boundary conditions?

   Hint

   Consider the constraints you put on the ends of the beam.

3. 3.

   What is the first step in the Double Integration Method?

   • Integrate the deflection equation
   • Write the bending moment equation
   • Apply boundary conditions

   Hint

   Think about what defines the curvature of the beam.

4. 4.

   True or False: The maximum deflection for a cantilever beam with a point load is given by $\delta_{max} = \frac{PL^3}{3EI}$.

   • True
   • False

   Hint

   Recall the basic formulas derived during our discussions.

5. 5.

   Calculate the maximum deflection of a cantilever beam of length 2m with a point load of 50N at the free end. Given: E = 200 GPa, I = 5 × 10^-6 m^4.

   Hint

   Ensure to convert units appropriately.

6. 6.

   For a simply supported beam of length 4m with a load of 80N at the center, calculate the maximum deflection. Given: E = 150 GPa, I = 2 × 10^-5 m^4.

   Hint

   Check your calculations for accuracy.