The correct answer is A. (i) and (iii).
When an intermediate support of a continuous beam sinks, the beam will deflect downward at that support. This will cause the negative moment at that support to increase. The positive moment at the center of the span will decrease, because the beam will deflect upward at that point.
Here is a diagram to illustrate the effect of sinking an intermediate support:
[Diagram of a continuous beam with an intermediate support that has sunk]
The red arrows show the direction of the bending moments in the beam. The blue arrows show the direction of the deflections of the beam.
As you can see, the negative moment at the support that has sunk has increased, and the positive moment at the center of the span has decreased.
Here is a more detailed explanation of each option:
- Option (i): Sinking of an intermediate support of a continuous beam reduces the negative moment at support.
This is because the sinking of the support causes the beam to deflect downward at that support. This increases the lever arm of the negative moment, which in turn reduces the magnitude of the negative moment.
- Option (ii): Sinking of an intermediate support of a continuous beam increases the negative moment at support.
This is incorrect, as explained above.
- Option (iii): Sinking of an intermediate support of a continuous beam reduces the positive moment at center of span.
This is because the sinking of the support causes the beam to deflect upward at the center of the span. This decreases the lever arm of the positive moment, which in turn reduces the magnitude of the positive moment.
- Option (iv): Sinking of an intermediate support of a continuous beam increases the positive moment at center of span.
This is incorrect, as explained above.