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6 internal forces and moment
- 1. Bending: Internal Forces and Moments Better to bend than break. ~Scottish Proverb BIOE 3200 - Fall 2015
- 2. Learning Objectives Define shear forces and bending moment s for a structure in bending Draw a FBD and determine reaction forces and moments for a structure in bending Define the “method of sections” to determine shear forces and bending moments within a structure in bending Define the appropriate sign conventions for shear forces and bending moments BIOE 3200 - Fall 2015
- 3. What are shear forces and bending moments? Forces and moments within a material (internal forces and moments) are those that keep the material from being pulled apart under load. When designing a structure or device to resist applied loads, internal forces and moments must be determined. BIOE 3200 - Fall 2015
- 4. What is bending? BIOE 3200 - Fall 2015
- 5. Axial loads in structures create bending BIOE 3200 - Fall 2015
- 6. How do we determine internal forces and moments for beams in bending? The first step is to construct a free body diagram (FBD) for the structure under load BIOE 3200 - Fall 2015 If you need to review how to create FBDs for different loading configurations, check out this concise explanation with example problems: http://www.etcs.ipfw.edu/~dupenb/ET_200/Shear%20and%20moment%20diagrams.pdf
- 7. How to know what is happening inside the beam? Make imaginary “cuts” along the beam. BIOE 3200 - Fall 2015
- 8. Next: Each section becomes a FBD, with its own forces and moments. BIOE 3200 - Fall 2015
- 9. Other resources for FBD, support reactions and explanations of shear forces and bending moments: MIT Open Course (See lectures #5 & #6) http://ocw.mit.edu/courses/mechanical- engineering/2-001-mechanics-materials-i-fall- 2006/lecture-notes/ Drexel University MEM202 Slides http://www.pages.drexel.edu/~cac542/L20.pdf IPFW ET200 Handout http://www.etcs.ipfw.edu/~dupenb/ET_200/Sh ear%20and%20moment%20diagrams.pdf BIOE 3200 - Fall 2015
Editor's Notes
- Note that the second learning objective requires one to be able to Determine the types of supports and where the reaction forces are for different loading configurations Draw a Free Body Diagram Write out Equations of Equilibrium
- What are internal forces and bending moments, and why are they important? If you want to design something so that it will not fail, you have to know how the design will behave under load. This involves knowing what the shear forces and bending moments are within the structure.
- Structures are called “beams” if they are subjected to bending
- How do we determine internal forces and moments for these different configurations, or even combinations of different loadings? FBDs! From the diagram and equilibrium equations (sum forces and moments), we can determine reaction forces, for example at A and B in the diagram above. Don’t forget to include appropriate axes!
- Now were going to figure out what is going on inside the beam. The internal forces are what we are trying to find. So we’ll make a cut in our beam such that we have two separate pieces. Where do you make the cuts, and how many cuts are needed? Cuts are made wherever there are changes in loading, material or geometry along the length of the beam; you need a new section starting at each location where loading, material or geometry changes. For a beam made of a single material and with uniform geometry, there should be as many sections as there are different loads acting at different locations. So, a simply supported beam with a point load would need 2 sections. A beam with a uniform distributed load along its length would also need only 2 because you’re going to model the distributed load as a point load. We will discuss what this will look like forother configurations such as a cantilever beam, a wedge or triangular distributed load, a load over only half of the span between the supports, or some combination of these in the next part of this lesson (Part 2).
- Now we can see where those shear forces and moments come into play: they balance the support reactions. They are what stop the support reactions from tearing the structure apart. Sign convention governing shear and bending moment (LO2,LO5) - Shear What: Positive shear makes the section rotate CW Why: B/c the common approach to analysis of a beam is left to right, positive up, so a shear in the upward direction at the origin of a section would cause it to rotate CW. - Bending Moment What: Positive makes a smile, negative makes a frown. Why: What sort of bending moment would the upward shear located at the origin make? (Upward shear would be a positive shear force b/c it would make the section rotate CW; this makes the sign conventions for shear force and bending moment agree).