Diagrams of internal forces

Before calculating the internal forces, one must remember about the principles that prevail when creating graphs of internal forces. Fortunately, there are many dependencies, for example, from the type of force applied or the structure scheme.

In this guide, in theory, almost all such “facilitations” are presented. The use of these facilities on examples, in practice, you will find in the next guides.

Starting the SW calculation, divide our element into individual parts. It can be said that this is an analogous assumption, like when calculating the support reactions, where we divided our element into shields. In this case, this division is more extensive, because we divide ours, for example beam in all characteristic points. I will use the beam, whose internal forces will be calculated in the next guide. Now he will show on it how this division into segments works.

The characteristic points are:

  1. Beginning and end of the element
  2. Supports
  3. Joints
  4. External forces acting on the element
  5. Fracture of the bar (for example: connection of a horizontal bar with a vertical bar in the frame)

In summary, the division takes place where we encounter some “obstacle”. In this case, our entire structure consists of six parts. From the right:

  1. Roller support – Moment
  2. Moment – Joint
  3. Joint – Support
  4. Support – Joint
  5. Joint – Consolidated force
  6. Consolidated force – Fixed support

The same applies to frames and arcs. We do not take into account the truss, as only normal forces appear in lattice constructions and they are counted a bit differently. The cutting forces and bending moments are zero.

The time has come for a few principles, which are during calculations and then drawing internal forces. Please also remember that internal forces are calculated only at the beginning of the road to the engineer. In further stages, such things must be performed in memory, the so-called engineering method. Of course, at the study stage, because it is normally used for computational programs.

Here are the rules on how the internal forces diagram should look like:

  1. In the place where the joint is, the bending moment diagram should be zero (exception of point 2).
  2. In the place where the bending moment (force) is applied, the bending moment diagram should have a jump by the value of this force.
  3. In the place of supports, where we have support reactions different from zero, in the graphs are jumps by the value of these reactions.
  4. At the free ends of the beam, the bending moment diagram should reset (exception point 2).
  5. The diagram of the shearing forces is a derivative of the moment, so when the moment diagram is a parabola, then the cutting forces diagram has the shape of a triangle. While the moment diagram has the shape of a triangle, then the cutting forces diagram has a rectangular plot, and when the moment has the shape of a rectangle, then the cutting forces diagram does not exist.
  6. The bending moment diagram is drawn on the side of stretched fibers.
  7. Graphs of shear and normal forces are drawn on any side, but we take into account the sign (+ or -). When we make calculations of shearing forces, it is obvious whether the force is positive or negative, whereas when we draw graphs from memory, then it is not so obvious. That is why in further guides this is described in detail.
  8. Graphs of normal forces are independent of the bending moments and shear forces diagrams.
  9. Values in the normal forces diagram are negative when the bar is compressed, and positive when the bar is stretched.
  10. In the place where the cutting forces diagram cuts the bar axis, in this place there will be an extreme value (the smallest or the largest) at the bending moment.

This is where the rules end, what a well-calculated and drawn graph should look like. When I learn something new (a man learns all his life) or I remember, there will be more points immediately. We will need more detailed rules when drawing graphs of internal forces from memory. They will be found in a guide called Drawing graphs of internal forces from memory.

You have learned the theoretical side of calculating internal forces now it’s time for practice.
For this purpose, I invite you to the next guides.