3: Forces in Statically Determinate Trusses

3.1: Introduction

The mathematical model of a truss makes the following assumptions and simplifications:

  • All members are straight and connected at each of their two ends using small, frictionless pins. The pins are incapable of transmitting any moment to the members.
  • All external forces are applied to the structure through the pins at the joints.
  • If self weight of the members is to be included, the weight of a member can be applied equally to the pin at either end.

Figure

Figure 3.1.1: Forces imparted by pins on members

With these assumptions, equilibrium will require that every member is subjected to two forces – one at each end transmitted by the pin. The forces must be equal and opposite at the ends, directed along the axis joining the pins, and will subject the member to either a pure tensile or pure compressive force. There will no shears or bending moments in the members.

All this leads to the ability to use a very special analysis technique to determine the internal forces in trusses.

3.1.1 Real World Trusses

Real world trusses are not built like the assumptions in the model. However, if care is taken in detailing a real structure to approximate some of these conditions, internal shears and bending moments in the truss members may indeed by very small - almost negligible. Under these conditions, the truss assumptions may be used and a truss analysis may be performed.

It is the responsibility of the design engineer to know when the truss assumptions and simplifications are valid, and when they are not.