1. ME221Lecture 261 ME 221 Statics Lecture #26 Section 7.4

2. ME221Lecture 262 Homework #9 Chapter 5 problems: –53, 54, 56, 62, 64, 69, 71 & 73 Due Today

3. ME221Lecture 263 Homework #10 Chapter 7 problems: –2, 5, 6, 8, 19, 21, 24, 26 & 35 Due Friday, November 7

4. ME221Lecture 264 Last Lecture: Internal Forces in Structures Reviewed internal/external forces Found internal forces Started shear & moment diagrams

5. ME221Lecture 265 Generate a shear / bending diagram as follows: 2. Take a section on each side of an applied force or moment and inside a distributed load (take a new section whenever there is a change in the load or shape of the beam) - draw a FBD and sum forces / moments 3. Repeat 2 along the length of the beam 1. Find reaction forces w(x) distributed load V(x) shear force M(x) moment Shear and Moment Diagrams using Sectioning Method

6. ME221Lecture 266 V M V M Sign Convention Positive Shear and Positive Moment

7. ME221Lecture 267 Positive Shear M M Positive Moment Effect of External Forces

8. ME221Lecture 268 Relations Between w, V, and M In balancing forces, we can come up with differential equations relating w, V, and M. These are as follows: This means you can integrate the shear diagram to obtain the moment diagram. dx M+dM M V V+dV w(x)w(x) Thus,

9. ME221Lecture 269 dx M+dM M V V+dV w(x)w(x) Shear and Moment Diagrams Using Integration Method x j x j+1 Area under the load intensity diagram between x j and x j+1 1 - Distributed Load:

10. ME221Lecture 2610 Area under the shear diagram between x j and x j+1 Similarly:

11. ME221Lecture 2611 2 - Concentrated Load: P M+dM M V V+dV P 3 - Concentrated Moment: C M+dM M V V+dV C

12. ME221Lecture 2612 Notes Concentrated force will cause a jump in the shear diagram by an amount equal to the applied load Concentrated moment will cause a jump in the moment diagram by an amount equal to the negative of the applied moment Connecting points in the shear and moment diagrams x j+1 xjxj xjxj Negative decreasing slope xjxj x j+1 xjxj Negative increasing slope Positive decreasing slope Positive increasing slope

13. ME221Lecture 2613 Developing Shear and Bending Diagrams 1. Show FBD and statics for each section 2. Determine equation for V(x) and M(x) 3. Draw shear and bending diagrams indicating linear or parabolic 4. Label end points of diagram as well as every region endpoint

14. ME221Lecture 2614 20 lb/in 125 lb 9 in. 12 in. 12 in. 12in. V x M x