The image you uploaded contains a statics problem involving a steel beam (Stahlträger 3.17) under the effect of two forces:

• $F_1 = 6 \, \text{kN}$, which is inclined at $60^\circ$ to the beam's axis.
• $F_2 = 8 \, \text{kN}$, which acts vertically.

The beam is supported at two points, $A$ and $B$, with the following questions:

1. Sum of all vertical forces, $F_v$.
2. The vertical reaction forces at the supports $A$ and $B$.
3. The horizontal force at support $B$.

Step-by-step approach:

1. Resolve forces:

   • For $F_1$, we need to break it into its horizontal ($F_{1x}$) and vertical ($F_{1y}$) components: $F_{1x} = F_1 \cdot \cos(60^\circ), \quad F_{1y} = F_1 \cdot \sin(60^\circ)$
   • $F_2$ acts directly vertically, so it only contributes to the vertical forces.

2. Sum of vertical forces $F_v$: $F_v = F_{1y} + F_2$

3. Calculate reaction forces at $A$ and $B$:

   • Use equilibrium equations for the beam. The sum of forces in both vertical and horizontal directions must be zero, as well as the sum of moments around any point (we will use point $A$ for moments).

4. Horizontal force at $B$:

   • The horizontal component of $F_1$ must be balanced by the reaction at support $B$.

Let me calculate these values for you.Here are the calculations for the steel beam problem:

1. Resolved components of $F_1$:

   • Horizontal component $F_{1x} = 3 \, \text{kN}$
   • Vertical component $F_{1y} = 5.20 \, \text{kN}$

2. Sum of all vertical forces $F_v$: $F_v = F_{1y} + F_2 = 5.20 \, \text{kN} + 8 \, \text{kN} = 13.20 \, \text{kN}$

3. Vertical reaction forces:

   • At support $A$, $R_A = 7.87 \, \text{kN}$
   • At support $B$, $R_B = 5.33 \, \text{kN}$

4. Horizontal force at support $B$:

   • $R_{B_{horizontal}} = F_{1x} = 3 \, \text{kN}$

Would you like any further details or explanations?

Related Questions:

1. How would the reaction forces change if $F_1$ had a different angle?
2. What happens if we move the position of $F_1$ further away from point $A$?
3. How does the moment equilibrium affect the distribution of forces?
4. Can you calculate the total moment about point $B$?
5. What if there was an additional horizontal force acting on the beam?

Tip: Always resolve inclined forces into horizontal and vertical components for ease of calculation.