Question

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 1

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

Step-by-step explanation:

To answer the question, we note that the sum of the forces in the Truss is zero

Therefore, we have, ∑Fₓ =
`\Sigma F_y` = 0 N

The forces on the members CD and AD are therefore as follows;

Horizontal forces;

`F_(CD)` × cos(45°) -
`F_(AD)` × cos(30.964°) = 100.0 N...(1)

`F_(CD)` × sin(45°) +
`F_(AD)` × sin(30.964°) = 750.0 N...(2)

Solving the above system of equations using a graphing calculator gives;

`F_(CD)` ≈ 715.94 N (Tension)

`F_(AD)` ≈ 473.76 N (Compression)

`F_(Cy)` +
`F_(Ay)` = 750.0 N

`F_(Ax)` = 100.0 N

From ∑M
`_c` = 0, we have;

`F_(Ay)` × 8 = 750 × 3 + 100 × 3

`F_(Ay)` = 2550/8 = 318.75 N

∴
`F_(Cy)` = 750.0 N -
`F_(Ay)` = 750.0 N - 318.75 N = 431.25 N