Internal Force for Various Systems

We have discussed the general procedure for obtaining internal force variations in a planer system. We can
apply that procedure for various types of structural system. Here, we discuss the significance of internal
forces (and internal force diagrams) for different structural system types.
Truss : A truss members carries only axial force (tension or compression) and no shear force or bending
moment. The axial force comes from loads applied only at the two ends of a member. Therefore, the axial
force remains constant along the length of a single truss member. So, we do not really need to plot
diagrams or express axial force as function of length ( x ) in case of a truss member.


Cable : A cable is similar to a truss member except for that it carries only axial tension. For further detail
on internal forces in cables, see chapter 3.


Axially Loaded Bar : Only axial force exists in these members (such as columns ). However, unlike a truss
member a bar may be acted upon by external forces along its length. Hence, it is important to study the
variation of axial force through diagrams/mathematical expressions.
Beam and Beam-Column : A beam carries shear force and bending moment and if it carries axial force as
well, then we call it a beam-column. It is for these structural members that internal force diagrams are most
important, because deformation and failure behaviour of these members can be directly linked to these
diagrams.


Frame : Frames are two/three-dimensional structural systems made of beams and columns. A frame
member, in general, carries internal forces similar to a beam-column. Therefore, it is equally important to
obtain internal force diagrams for these systems. Note that for a frame, we may need to specify sign
convention for each member individually, as these members may have different orientations.


Arch : Arches can be treated as curved beams (or beam-columns).
How to deal with a curved centroidal axis, and with orientations of axial and shear forces.

In the next few sections we will discuss specific cases of determining forces in different types of statically
determinate systems, such as trusses, beams, arches, etc.