This is a statics problem that asks for the calculation of the support reactions $A$ and $B$ for a simply supported beam under a set of point loads. The task has three parts:

1. Part a): Compute the reactions at supports $A$ and $B$ under the given loading conditions.

2. Part b): Recompute the reactions when the point load $F_5$ (4 kN) is removed.

3. Part c): Recompute the reactions when the point loads $F_1$ and $F_2$ are reduced by 10%.

Details from the problem:

• Beam length = 9.60 m
• Load values and positions:
  • $F_1 = 2.5 \, \text{kN}$ at 1.00 m from $A$
  • $F_2 = 1.8 \, \text{kN}$ at 3.50 m from $A$
  • $F_3 = 3 \, \text{kN}$ at 6.10 m from $A$
  • $F_4 = 2 \, \text{kN}$ at 8.60 m from $A$
  • $F_5 = 4 \, \text{kN}$ at 9.60 m from $A$

Steps to solve:

1. Equilibrium Equations:
   • Sum of vertical forces: $\sum F_y = 0$ (no net vertical force).
   • Sum of moments around $A$: $\sum M_A = 0$ (no net moment at point $A$).

Let me calculate the reactions for part (a) first, with the given loads.For part (a), the reactions at the supports under the given loading conditions are:

• Reaction at support $A$ = 4.69 kN
• Reaction at support $B$ = 8.61 kN

Next, let's solve part (b) by removing the load $F_5$.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can still ask any questions or request further details.

In the meantime, here are some follow-up questions related to this problem:

1. Would you like me to walk through the manual steps to solve part (b) without calculating the specific numbers?
2. Do you need clarification on how the moment equilibrium is set up around point $A$?
3. Are you familiar with the principle of superposition in beam problems like this?
4. Should I explain how support reactions change when loads are modified or removed?
5. Would you like help with finding the centroid of distributed loads, if that ever applies?

Tip: Always use a free-body diagram to visualize forces and reactions when solving statics problems.