Answer:
Please find attached the diagram end result of the truss with the member reaction forces labelled with the amount of forces as required, created with Microsoft Visio
Explanation:
To answer the question, we note that the sum of the forces in the Truss is zero
Therefore, we have, ∑Fₓ = [tex]\Sigma F_y[/tex] = 0 N
The forces on the members CD and AD are therefore as follows;
Horizontal forces;
[tex]F_{CD}[/tex] × cos(45°) - [tex]F_{AD}[/tex] × cos(30.964°) = 100.0 N...(1)
[tex]F_{CD}[/tex] × sin(45°) + [tex]F_{AD}[/tex] × sin(30.964°) = 750.0 N...(2)
Solving the above system of equations using a graphing calculator gives;
[tex]F_{CD}[/tex] ≈ 715.94 N (Tension)
[tex]F_{AD}[/tex] ≈ 473.76 N (Compression)
[tex]F_{Cy}[/tex] + [tex]F_{Ay}[/tex] = 750.0 N
[tex]F_{Ax}[/tex] = 100.0 N
From ∑M[tex]_c[/tex] = 0, we have;
[tex]F_{Ay}[/tex] × 8 = 750 × 3 + 100 × 3
[tex]F_{Ay}[/tex] = 2550/8 = 318.75 N
∴ [tex]F_{Cy}[/tex] = 750.0 N - [tex]F_{Ay}[/tex] = 750.0 N - 318.75 N = 431.25 N
