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ME 221 Statics Lecture #15a Sections 7.3 - 7.4

ME 221 Statics Lecture #15a Sections 7.3 - 7.4. 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. Last Lecture: Internal Forces in Structures. Reviewed internal/external forces.

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ME 221 Statics Lecture #15a Sections 7.3 - 7.4

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  1. ME 221 StaticsLecture #15aSections 7.3 - 7.4 Lecture 15

  2. 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 Lecture 15

  3. Last Lecture:Internal Forces in Structures • Reviewed internal/external forces • Found internal forces • Started shear & moment diagrams Lecture 15

  4. Shear and Moment Diagrams using SectioningMethod 1. Find reaction forces 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 w(x) distributed load V(x) shear force M(x) moment Lecture 15

  5. M V M V Sign Convention Positive Shear and Positive Moment Lecture 15

  6. M M Effect of External Forces Positive Shear Positive Moment Lecture 15

  7. 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: w(x) M+dM V M Thus, V+dV dx This means you can integrate the shear diagram to obtain the moment diagram. Lecture 15

  8. Shear Forces • Area under load curve Lecture 15

  9. Bending Moments • Area under shear force curve Lecture 15

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