6.1. Theorem I

Try these first

1. 1.

   What does EI stand for in the context of beam analysis?

   Hint

   Consider the properties affecting the beam's stiffness.

2. 2.

   State the relationship outlined in Theorem I.

   Hint

   Think of how changes in slope relate to the diagram.

3. 3.

   What does Theorem I state?

   • Slope change equals area under moment diagram
   • Deflection equals area under moment diagram
   • Both are the same

   Hint

   Remember what relates slope to moment diagrams.

4. 4.

   The Moment Area Method is primarily used for what purpose?

   • True
   • False

   Hint

   Think about the advantages of this method.

5. 5.

   For a cantilever beam of length 5m subjected to a triangular load tapering from the fixed end, find the change in slope between the free end and the fixed support using Theorem I.

   Hint

   First calculate the total load then derive the moment equation.

6. 6.

   Evaluate the maximum deflection of a simply supported beam with a uniformly distributed load using Theorem I and compare it with the standard formula.

   Hint

   Break the problem into steps by calculating load and distance first.