3.1. First Theorem (For linearly elastic structures)

Try these first

1. 1.

   What is deflection?

   Hint

   Think about how a beam bends under weight.

2. 2.

   What does the First Theorem express?

   Hint

   Recall the formula from our session.

3. 3.

   What does the First Theorem allow us to calculate?

   • Force
   • Deflection
   • Stress

   Hint

   Consider what quantities are related to load in structural analysis.

4. 4.

   True or False: The total strain energy is used to find the maximum deflection in a structure.

   • True
   • False

   Hint

   Remember how energy relates to deformation.

5. 5.

   A cantilever beam of length 4 m is subjected to a point load of 500 N at its free end. Calculate the deflection using the First Theorem.

   Hint

   Remember the relationship between bending moment and strain energy.

6. 6.

   Discuss the implications of ignoring the First Theorem when designing a multi-story building.

   Hint

   Consider both immediate effects and long-term stability.