Module 2 :
Analysis of Statically Determinate Structures
Lecture
7 : Internal Force as a Function of x
Figure 2.14 Free body diagrams upto a distance x from the origin
Similarly, we can find out the internal forces in the portions x = 6 m
→ 10m (Figure 2.14b) and x = 10 m
→ 12 m (Figure 2.14c). For x = 6 m
→ 10 m :
and for x = 10 m
→ 12 m :
If we look at these expressions carefully, we see that:
We measure x always from the same origin and in the same direction. As noted earlier, it is not absolutely necessary to
follow this convention, but it is easier this way.
The internal force expressions change at points where concentrated forces/moments (including support reactions) act.
We will see later that these forces also change if a distributed force changes its distribution. Using singularity functions , we can combine different expressions for different segments of the beam together into a single expression, which we will discuss later.
We need to obtain mathematical expressions of internal forces first in order to plot the force variation diagrams. Although
these expressions provide adequate information on variation of internal forces, a pictorial representation is alwaysvery useful.
