Consider a truss PQR loaded at P with a force F as shown in the figure. The tension in the member QR is

Concept:

To find the tension in a member of a truss, we can use either Lami’s Theorem or the Method of Joints. At joint P, three forces act in equilibrium: vertical load F, force in member PQ (45°), and force in member PR (30°). Since PR and QR are collinear, the force in PR is the same as the tension in QR.

Calculation:

Using Lami’s Theorem at joint P:

The angles between the forces are:

• Between PQ and PR: 45° + 30° = 75°
• Between F and PR: 60°
• Between F and PQ: 45°

Apply Lami's Theorem:

We are interested in:

Now, plug in the values:

Alternate Method (Method of Joints):

Let T₁ be force in PQ (at 45°), and T₂ be force in PR (at 30°):

Vertical equilibrium:

Horizontal equilibrium:

Substitute into vertical equation: