by external forces (including support reactions and other contact forces as well). To illustrate how internal
forces are generated or why they exist, let us consider a three-dimensional solid body (Figure 2.1a),
supported at points A and B. , and are external loads applied on the system. To study the
equilibrium of the whole body, we draw its free body diagram (Figure 2.1b). The supports are replaced by
reactions and in the free body diagram. We consider an internal surface by taking an arbitrary cut
through the system (Figure 2.1c). For equilibrium of the part at the right of the section, there has to be
forces acting on the internal surface which balance the external loads and (Figure 2.1d). and
are internal forces acting on the surface of the cut.
It is important to know the internal forces acting at different sections of a system. The material, of which
the body is made, should be strong enough to carry these forces. Otherwise the system fails (by crushing,
breaking, etc.) under the loading condition.
The general procedure of obtaining internal forces includes these following steps:
Obtain the system configuration (dimension and support conditions) and external loadings applied on it.
1. Draw a free body diagram of the whole system.
2. Find the support reactions by using equations of (static) equilibrium.
3. Take a cut through the body where internal forces have to be obtained.
4. Consider equilibrium of the part of the system at any one side of the cut by drawing a free body
diagram of that part.
5. Obtain the unknown internal forces acting on the cut surface by solving these equilibrium equations.
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transfer mechanisms. To elaborate, a system (or a structural member) is identified based on the
predominant types of internal forces carried by it. Thus we have: bars , cables , beams , columns , arches ,
etc. Below is a list of such members along with the predominant internal forces that they carry. Cable : A
cable or wire can carry axial tension only. Internal forces in cables are not discussed in this chapter
because cables are very different from all other systems due to their flexible geometry. Internal forces and
geometry of cable systems are discussed in detail in another post.
1. Cable : A cable or wire can carry axial tension only. Internal forces in cables are not discussed in this
chapter because cables are very different from all other systems due to their flexible geometry.Internal
forces and geometry of cable systems are discussed in detail in another post.
2.Bar : A bar carries only axial forces – tension and compression both. That is why it is also known as
axially loaded bar .
3.Beam : A beam's primary function is to transfer lateral loads applied externally on the beam. These loads
produce bending moments and shear forces on beam a cross-section.
4.Column : The predominant internal force in a column is axial compression.
5.Beam-Column : A beam-column, as the name suggests, carries all kinds of internal forces that are
produced in a beam or a column, which include: bending moment, shear force and axial force.
6.Arch: An arch is a curved member which carries primarily axial compression under lateral loads applied
externally.
There is no difference in the shapes of a beam, a column, a beam-column or a bar. All are straight
longitudinal members (one dimension is much larger than the other two) and we will not be able to
distinguish one from the other unless we know the load transfer mechanism. Figure illustrates this
issue.
All the members discussed above are primarily one-dimensional geometrically. Two-dimensional members
are also categorized similarly, such as: plates , shells ( thin & thick ), slabs , etc. We also have specific
names for systems formed by combination of members, such as a truss or a frame . A frame is a
combination of beams and columns, whereas all the members in a truss are axially loaded bars.
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