**Conditions of Structural Behavior in Qualitative Structural Analysis **

There are numbers of certain structural behaviors that structural analysis depends on to carry out qualitative structural analysis and some of them are clear and obvious while others might not be:
1. Types of support and their restraints: the fully fixed support provide two reactions and one moment, pinned support has two reactions and roller support provide one reaction that is vertical as shown in **Table 1**:

**Table ****1 Types of supports and their reactions**

**Figure 1**ABC is a cantilever that carries two loads W1 & W2. The W2 develop bending moment at BC that leads to a horizontal deflection at B, which is called

Figure 1: Cantilever member ABC with loads, deflection and bending moment diagram

7. In qualitative analysis, axial loads in members which create axial strains are neglected in bending moment determination. 8. Principle of superposition, which helps to simplify complex structure and examine loads differently, is considered to apply provided that the structure remains in elastic range. For example: Two span beams ABC is shown**Figure 2**

**with deflected shape, reactions and bending moment diagram. Using principle of superposition, the indeterminate beam can be solved easily. Firstly, remove support C that lead to simply support and cantilever beam then draw the bending moment diagram as shown in left side of**

**Figure 3**.Secondly, apply force Vc at C and draw BMD as shown in right side of

**Figure 3**. These two diagrams provide the solution of the original two span beams. Similarly, deflections could be treated in the same manner.

Figure 2 Beam ABC with deflected shape, reactions, and bending moment diagram

Figure 3: Remove reaction at C (left side), remove W and recall reaction C right side, and solve both to get the original solution

9. There is no bending moment in the part of the structure that remains straight after loading, however it could move. 10. Bending moment diagrams will be straight lines if applied loads were point loads. 11. Bending moment diagrams will be curved if applied loads were distributed loads. 12. At simply supports, bending moment is equal to zero. 13. Bending moment diagrams cross elements at points of contra flexure. 14. Unbraced frames will not sway if it is symmetrical and symmetrically loaded. 15. Qualitative analysis is carried out for visible loads, therefore self weight is neglected. 16. Apart from at hinges, shapes of deflected elements are extremely smooth. 17. In frames, angles of rigid joints should maintain the original angles after loadings as shown in**Figure 4**

**.**

Figure 4: Angle of rigid joint frame keep the same angle after loading

18. In frames, rigid joints might close or open only as shown in .Figure 5: Open and close rigid joints after loading with bending moment diagrams

19. There is only one moment value in the rigid joints that connects two elements. 20. Shear forces become axial force and axial force become shear force in the alternate members at the right angle rigid join. sum(fx) = 0 , sum(fy) = 0 can be employed to check this statement. See**Figure 6**

Figure 6: Right angle rigid join in which shear force become axial and axial force become shear force in the alternate member.

However, this is not the case in the oblique angle join as shown in**Figure 7**

**Figure 8**

**, in the following joint MA = MB+MC**

**Figure ****8: Equilibrium rigid joint in which three members are meet.**

**A complete solution of qualitative structural analysis is composed of:**

- Deflected shape
- Reactions
- Bending moment diagrams