1. ME221Lecture 151 ME 221 Statics Lecture #15a Sections 7.3 - 7.4

2. ME221Lecture 152 Homework #6 Chapter 7 problems: –6, 19 & 26 Chapter 6 problems –3 & 6 –Due Monday, June 28 MatLab Group Problems –7.19, 7.26 & 6.15 –Due Monday, June 28

3. ME221Lecture 153 Last Lecture: Internal Forces in Structures Reviewed internal/external forces Found internal forces Started shear & moment diagrams

4. ME221Lecture 154 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

5. ME221Lecture 155 V M V M Sign Convention Positive Shear and Positive Moment

6. ME221Lecture 156 Positive Shear M M Positive Moment Effect of External Forces

7. ME221Lecture 157 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,

8. ME221Lecture 158 Shear Forces Area under load curve

9. ME221Lecture 159 Bending Moments Area under shear force curve