A fixed beam of uniform section is carrying a point load at its mid-span. If moment of inertia of the middle half-length is now reduced to half of its previous value, then the fixed end moments will
- AIncreaseCorrect
- BDecrease
- CRemains constant
- DChange their directions
Solution
Concept
Fixed end moments with a non-uniform EI
Step-by-step solution
1. When the middle half becomes more flexible (I reduced to half), the stiffness of the end quarters is relatively higher. 2. A stiffer end region attracts more moment. 3. So the fixed end moments increase.
Explanation
Fixed end moments depend on the relative stiffness along the beam. If the middle portion is made less stiff, the end portions carry proportionally more of the load and their fixing moments increase, while the mid-span moment decreases.
Shortcut
Make the middle weaker → ends take more moment.
Common mistake
Assuming that FEM = WL/8 does not change.
Correct answer: A) Increase