The image contains a beam with three forces acting on it, along with a problem asking for the moments about points $A$ and $B$. Here’s a breakdown of the key points and approach for determining the moments:

Given Information:

• $F_1 = 375 \, \text{lb}$ acting vertically downward at 8 ft from point $A$,
• $F_2 = 500 \, \text{lb}$ acting at an angle with the horizontal (with components calculated from the 3-4-5 triangle), positioned 6 ft from point $A$,
• $F_3 = 160 \, \text{lb}$ acting downward at a 30° angle from the beam, applied at 5 ft from point $A$, and 0.5 ft horizontally from point $B$.

4-4: Determine the Moment About Point A

1. For $F_1$: $M_{F_1/A} = F_1 \times d_1 = 375 \, \text{lb} \times 8 \, \text{ft} = 3000 \, \text{lb} \cdot \text{ft}$ (Counterclockwise).

2. For $F_2$: Resolve $F_2$ into horizontal and vertical components: $F_{2x} = 500 \times \frac{4}{5} = 400 \, \text{lb} \quad \text{(horizontal)}$ $F_{2y} = 500 \times \frac{3}{5} = 300 \, \text{lb} \quad \text{(vertical)}$ Moment arm from point $A$ for both components is 6 ft:

   • Horizontal component $F_{2x}$ does not contribute to moment about $A$.
   • Vertical component $F_{2y}$ moment: $M_{F_2/A} = 300 \, \text{lb} \times 6 \, \text{ft} = 1800 \, \text{lb} \cdot \text{ft}$ (Counterclockwise).

3. For $F_3$: Resolve $F_3$ into components: $F_{3x} = 160 \times \cos(30^\circ) = 138.56 \, \text{lb}$ $F_{3y} = 160 \times \sin(30^\circ) = 80 \, \text{lb}$ The moment arm for the vertical component is 11 ft (from $A$): $M_{F_3/A} = 80 \, \text{lb} \times 11 \, \text{ft} = 880 \, \text{lb} \cdot \text{ft}$ (Counterclockwise).

4-5: Moment About Point B

To compute the moments around point $B$, we use similar reasoning, but we change the distances and some forces might not produce a moment. The moments around point $B$ are already given in the image.

Would you like the moment about point $A$ to be calculated in more detail? Here are a few related questions:

1. How are moments affected by forces at angles?
2. Why does the horizontal component of force $F_2$ not contribute to the moment around point $A$?
3. How does the sign convention (clockwise or counterclockwise) affect moment calculations?
4. What would happen if the direction of one of the forces was reversed?
5. How do you determine which forces contribute to the moment about a given point?

Tip: When calculating moments, always check both horizontal and vertical force components and their respective perpendicular distances from the point of interest.