# Procedure of Joints for Analysis of Pin-Jointed Plane Truss

In this article we are going to provide a solution about a civil engineering problem. This will be beneficial for civil engineering students and civil engineers.

**The problem is as follows:**

**Solution:**

In the above truss A is supported by roller and C is supported by hinged. First of all, we have to find out this truss’s type whether it is determinate or indeterminate.

Condition of determinacy of plane truss: m=2j – 3

In this truss j=6 which needs 2x6-3 members for the truss to be determinate. It is clearly visible in the above figure that the truss has 9 members.

Thus the truss here is invariably determinate.

**Reactions at the support:**

As the support A is on the roller, so that it has no horizontal reactions except vertical reactions. On the other hand, support C is on the hinged therefore it will have both vertical and horizontal reactions.

Assuming horizontal reaction at C to be in the +ve x direction and using the conditions of static equilibrium, we obtain;

(1) ∑ Fx =0; so Cx – 15 = 0 equation (1)

Solving the equation we acquire Cx = 15 kN.

(2) ∑ Fy = 0; yields Ay + Cy - 25 - 10 – 20 = 0;

Ay + Cy = 55 equation (2)

(3) ∑ Mz = 0; considering z-axis perpendicular to the plane and passing through joint A.

Ay x 0 + Cy x 4 - CX x 0 – 20 x 2 + 15 x 2 – 10 x 2 + 25 x 0 = 0;

We get, **Cy** =7.5 kN;

Consequently **Ay** = 47.5 kN;

To get the complete equation solution, visit **civilengineer.webinfolist.com**