17.1 INTRODUCTION

An articulated structure or a truss is composed of a number of bars or members connected by frictionless pins, forming geometrical fi gures which are usually triangles. A truss is said to be statically determinate internally if the number of members

in which m is the total number of members, j is the total number of joints, and r is the total number of equilibrium equations.

In the above equation, the value of r is usually 3 but if there is an additional hinge separating the structure in two parts, r = 3 + 1 = 4, and if there is a link somewhere in the structure, r = 3 + 2 = 5. The frame is said to be perfect if the number m is equal to right side of the equation.

When external loads are applied on the truss, at the joints, the members carry internal forces, usually called the stresses, which may be either tensile or compressive. According to Hook's law, if any axial member of length L carries a force P, it will be deformed by an amount PL/AE, in which A is the area of cross section of the members. In the truss, therefore, the members carrying tension will be elongated, whereas those carrying compression will be shortened. Thus, all the joints will move from their initial position and will occupy their fi nal equilibrium position. The axial deformation in the members of the truss may also be due to temperature changes or due to errors in fabrication or lack of fi t of some members, and the joints may move from their original position. This movement of each joint is defi ned as the defl ection of the joint in the direction of movement. The resolved part of the movement in the vertical direction is called vertical defl ection of the joint, and that in the horizontal direction is known as the horizontal defl ection of the joint. In general, each joint has both vertical as well as horizontal defl ection, unless constrained to move in a given direction.