1. ENGR 225 Section

2. Mechanics of Materials
Mechanics of Solids
Mechanics of Deformable Bodies
Solid Mechanics
Strength of Materials.

3. Statics
Forces
Rigid Bodies
Dynamics
Motion
Particles, Rigid Bodies
Mechanics of Materials
Forces
External
Internal
Material Properties

4. Mechanics of Materials
Area of mechanics that studies the relationships between external loads applied to a deformable body and the intensity of internal forces within a body
An understanding of material behavior will play an important role in developing the necessary equations used in mechanics of materials.

5. Support Reactions

6. Internal Forces

7. Method of Sections

8. Internal Forces in 2-D

9. Determine the internal forces (normal force, shear force and bending moment) on a section passing through the beam at point C.

10. Internal Forces in 3-D

11. Internal Forces in 3-D Find the internal forces at the base

12. Mass = 650 kg and Wind Load = 900 N/m2

13. Internal Forces at a point – method of Sections
Internal forces at all points along length
Internal forces – a function of distance along length of beam.

14. Shear and Moment Diagrams
For beams we can calculate the shear and moment diagrams as a function of position along the beam.
Internal normal force will not be considered in that most loadings are vertical on a beam and we are primarily concerned about shear and bending failures.

15. Sign Convention
Shear ~ positive direction is denoted by an internal force that causes a clockwise rotation on which it acts.
Moment ~ positive direction is denoted by an internal moment that causes a compression or pushing on the upper part of the member

16. Relations between Distributed Load, Shear, and Moment.
Slope of the Shear Diagram = Negative of distributed load intensity
Slope of the bending moment diagram = Shear

17. Graph the internal forces shear force and bending moment along the axis of the beam.