1. CE 203 Structural Mechanics Bending moment & Shearing force diagrams Lecture 23-24

2. What is a beam Members that are loaded in a direction perpendicular to their longitudinal axis Length is more significant than lengths in cross-section We could have: Simply supported, Cantilevered, Overhanging or Continuous beams

3. Find the internal forces at C.

4. Make section at C & Indicate internal forces

5. Sign Convention

6. Draw shear & bending moment diagrams

7. Draw shear & bending moment diagrams

9. Load-shear-moment relations dV/dx = -w(x) dM/dx = V(x)

10. Notes No load constant shear & linear moment variation Uniform load linear shear & quadratic moment variation

11. Notes Concentrated load causes jump in shear Concentrated moment causes jump in moment

12. 40 kips 1 kip/ ft 2 kip/ ft 15 ft 15 ft 5 ft 5 ft 10 ft 5 ft Draw shear force and bending moment diagrams

13. 40 kips 1 kip/ ft 2 kip/ ft 15 ft 15 ft 5 ft 5 ft 10 ft 5 ft 27.5 kips 37.5 kips Reactions

14. 40 kips 1 kip/ ft 2 kip/ ft 15 ft 15 ft 5 ft 5 ft 10 ft 5 ft 27.5 kips 37.5 kips 12.5 k 10 k -15 k -27.5 k

15. 37.5 k.ft 12.5 k 10 k -50 k.ft -15 k -150 k.ft -100 k.ft -27.5 k SFD BMD