ENSC1002StaticsLectureNotes.pdf

# Unknown vertical reaction forces unknown horizontal

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unknown vertical reaction forces unknown horizontal reaction forces unknown reaction moments We have already applied our understanding of distributed load to represent the weight of the board as a point load. Now apply equilibrium to solve for the unknown reactions Ra and Rb

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Week 9 Lecture 1 11 Apply Equilibrium equations Consider horizontal equilibrium Now consider vertical equilibrium One equation, two unknowns. Can't solve!! But we still have moment equilibrium To apply moment equilibrium, choose a point to take moments about. The point you choose will not influence our answer. BUT, some points are more convenient than others. For example, if we choose point A, we eliminate Ra from our moment equation
Week 9 Lecture 1 12 And we can easily solve for Rb Now substitute this value back into our equation for vertical equilibrium Now draw reactions as they act.. Does this make sense??

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Week 9 Lecture 1 13 To prove that the point we choose to take moments about does not influence our answer, let's do this again, this time taking moments about point C..
Week 9 Lecture 1 14 Summary Analysing the external forces on an object involves the following steps 1. identify the object 2. Idealise the support conditions for the object (will usually be fixed, pinned or roller supports, but be aware of others..) 3. Sketch the FBD (very important to include all forces applied, + gravitational forces (i.e. weight forces at centroid) and all UNKNOWN reaction forces.) 4. Apply equation of equilibrium to solve for unknown reaction forces (Tip; in applying moment equilibrium equation, take moments about a point which eliminates as many unknowns as possible) Preparation for next week's quiz Work through the examples problems below. Compare and discuss your answers with other students. Some of these problems may be in the quiz. Do your online assignments!

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Week 9 Lecture 1 15
Week 9 Lecture 1 16 Given these examples, solve the FBD problems on the following pages

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Week 9 Lecture 1 17
Week 9 Lecture 1 18

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Week 9 Lecture 1 19 Use the 4 steps outlined above to solve for the external forces on these objects
Week 9 Lecture 1 20

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Week 9 Lecture 2 1 Further equilibrium example
Week 9 Lecture 2 2

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Week 9 Lecture 2 3 Determinacy Add a roller support to the right hand end of the above example and solve for reactions.
Week 9 Lecture 2 4 It is not possible to determine the vertical and moment reactions for this problem. We have two equations and 3 unknowns. The equilibrium equations still apply to this problem and must be satisfied. BUT we do not have enough information to solve using equilibrium alone. Structures that have more unknown forces than equilibrium equations are known as statically indeterminate . Statically indeterminate structures are very common in practice. It is possible to solve for the extra reactions using extra information we get from the known displacement.

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Week 9 Lecture 2 5 Solving statically indeterminate structures is outside the scope of this course. However, you are expected to be able to classify a
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