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Qualitative Structural Analysis of Beams and Frames

Structural engineers may be unfamiliar with qualitative structural analysis. The most common form of structural analysis is the numerical (quantitative) method, in which structural designers must identify dimensions and loads, as well as compute bending moments and reactions.

However, preliminary analysis is a critical phase that comes before numerical structural analysis. Before performing analysis, dimensions of elements should be assumed at this stage.

Naturally, the purpose of the extensive numerical analysis is to double-check the numbers used in the preliminary analysis. As a result, unless the structural pieces are properly proportioned, the analysis must be done multiple times, whether by computer or by hand computation. This can be time-consuming and expensive, therefore the designer should endeavour to avoid it.

In general, it is assumed that the essential information and skills to conduct appropriate and proper preliminary analysis come from researching and learning numerical analysis methodologies, although this may not be the case.

Qualitative structural analysis equips you with the skills and information you’ll need to conduct preliminary research. Understanding or recognising relationships between loads and subsequent structural behaviours is the cornerstone of these abilities.

For instance, basic skills in simple elements include recognising correlations between loads, deflected shape, and subsequent responses. The qualitative method differs significantly from the quantitative method. It not only lacks a specific solution process, but it also relies on a variety of diagrams.

In qualitative analysis, the procedure varies depending on the problem. For example, starting a solution from a deflected shape may be appropriate in some cases, while starting from a bending moment diagram may be more effective in others. To use qualitative structural analysis accurately and avoid misunderstanding, it takes time and a lot of practise.

Conditions of Structural Behavior in Qualitative Structural Analysis

There are a variety of structural behaviours that structural analysis relies on in order to perform qualitative structural analysis, some of which are visible while others aren’t:

1. Support types and restraints: a fully fixed support has two reactions and one moment, a pinned support has two reactions, and a roller support has one vertical reaction.

2. The moment at the hinge is zero.

3. Keep in mind that the moment is equal to the force multiplied by the distance.

4. To keep consistent answers, draw a bending moment diagram on the tension side of the beam.

5. The structure remains in the elastic ranges of material behaviour under all loading conditions. Deflections are directly proportional to loads, and stress is proportional to strain (first assumption of elastic analysis of structures).

6. Load-induced deflections do not result in the development of secondary bending moments. ABC is a cantilever that carries two loads W1 and W2 as indicated in Figure 1.

figure 1

7. In qualitative analysis, axial loads in members that cause axial strains are ignored when determining the bending moment.

8. The principle of superposition, which aids in the simplification of complex structures and the examination of loads in different ways, is considered to apply as long as the structure remains elastic.

Figure 2 illustrates two span beams ABC with deflected shape, responses, and bending moment diagram. The indeterminate beam can be simply solved using the superposition concept.

To begin, remove support C, which will result in a simple support and cantilever beam, and then create the bending moment diagram as shown in Figure 3 on the left side. Second, as shown on the right side of Figure 3, apply force Vc at C and draw BMD.

Figure 2
Figure 3

9. The part of the structure that remains straight after loading has no bending moment, but it may move

10. If the applied loads are point loads, the bending moment diagrams will be straight lines.

11. If the applied loads are dispersed, the bending moment diagrams will be curved.

12. The bending moment is zero at simple supports.Cross elements in bending moment diagrams at sites of counter flexure.

14. If the frame is symmetrical and symmetrically loaded, it will not sway.

15. Because qualitative analysis is only performed on visible loads, self-weight is ignored.

16. The shapes of deflected elements are extremely smooth, except at hinges.

17. After loadings, the angles of rigid joints in frames should maintain their original angles, as shown in figure 4.

Figure 4

18. Rigid joints in frames may only close or open as shown in.

Figure 5

Qualitative Analysis of Open and Closed Rigid Joints

Figure 5: Bending moment diagrams used to open and close rigid joints following loading.

19. The rigid joints that connect two elements have only one moment value.

20. At the right angle rigid connect, shear forces become axial forces and axial forces become shear forces in the alternate parts. To check this statement, use sum(fx) = 0 and sum(fy) = 0. Figure 6 illustrates this.

Figure 6

Figure 6: In the alternate part, shear force becomes axial and axial force becomes shear force.

This is not the case, however, in the oblique angle connection depicted in Figure 7.

figure 7

Figure 7: Joint with an oblique angle21. The joint must be in equilibrium when there are more than two members in a rigid joint. MA = MB+MC in the joint MA = MB+MC in the joint MA = MB+MC in the joint MA = MB+MC in the joint MA

Figure 8

Figure 8: Three components meet in an equilibrium rigid joint.

The following items make for a complete qualitative structural analysis solution: Deflected form Reactions Diagrams of bending moments.

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