Influence Lines Dr. Abdulkhaliq A. Jaafer

1. Influence LinesDr. Abdulkhaliq A. Jaafer

2. Influence Lines • As applied loads on a structure changes location, the reactions, the member axial forces, shear forces, and bending moments change value correspondingly. • Typically, a single concentrated load (usually has the value of unity) is positioned at every possible load application point on the structure, and the various forces are calculated. Hence, a particular force response the structure can be expressed in terms of the location of the applied loading. The graph with the abscissa represented the distance along the structure and the ordinate represented the value of the force in referred as an influence line.

3. Example: Draw the influence lines for the reactions of the beam shown in figure below. Solution:

5. Example: Draw the influence lines for the reactions of the beam shown in Fig. Solution:

6. Example: Draw I. L. for S. F. at c • Solution: • For P=1 between A and c (Fig. 1) • 0≤x1≤c The shear force at c

7. The shear force at c

8. For P=1 between c and B (Fig. 2) 0≤x2≤L-c Shear at c

10. Example: draw the I. L. for reaction at A, shear at d and moment at d Solution: For P=1 between a and d The shear force at d

11. The shear force at d

12. The shear force at d

13. The moment at d For P=1 between a and 2a

14. The shear force at d

15. The moment at d For P=1 between 2a and 4a

16. The shear force at d The moment at d

18. Thank u