Solve the Truss. Your end result should be
a diagram with all member and reaction
forces labeled with the amount of force and
either the direction indicated with an arrow
or whether it is under Tension(positive) or
compression(negative).
​

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  

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