This problem involves determining the support reactions and internal shear force distribution for a beam subjected to a uniformly distributed load.

From the image, I can see that the beam is subjected to a distributed load $q^0$ which varies linearly along the beam's length. The length of the beam is denoted by $L$, and the distributed load is given as $q^0 = 2 \, \text{kN/m}$. The goal is to find the reactions at the supports and the shear force distribution along the beam.

To solve this:

Steps:

1. Determine the reactions at the supports:

   • Start by calculating the total load applied on the beam, which is the area under the load curve.
   • For a triangular load, the area is $\frac{1}{2} \times L \times q^0$. Then, compute the reaction forces at both supports using equilibrium equations (sum of vertical forces and moments).

2. Shear Force Distribution:

   • Once the reactions are found, use them to calculate the internal shear force at different points along the beam.
   • For a linearly distributed load, the internal shear force will vary linearly along the length of the beam.

Let me know if you would like me to go into more detail on each calculation or if you'd like to proceed with any specific part of the problem!

Do you want further explanation or step-by-step calculations for this?