St_Mod7_F10

St_Mod7_F10 - Module 7: Equivalence &...

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Unformatted text preview: Module 7: Equivalence & Distributed Loads September 13, 2010 Module Content: 1. Equivalence calculaLons allow us to simplify a loading scenario on a structure. 2. Equivalence condiLons are ensured only if we saLsfy both force equivalence AND moment equivalence. Module Reading, Problems, and Demo: Reading: Chapter 4 Problems: Fund. Prob. 4.26, Fund. Prob. 4.30 (equivalent systems) Demo: none Homework PlaGorm: hHp://www.masteringengineering.com Course Blog: hHp://pages.shanL.virginia.edu/staLcs2010 MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 1 Theory: Couple Moments • couple moments are created when two equal and opposite forces exist offset from each other: • from an equilibrium standpoint, the result is a pure moment (the forces cancel out because they are equal and opposite) • couple moments are free vectors, which means that the moment they create is the same regardless of the point we choose around which to take the moment MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 2 Theory: Couple Moments • couple moments are created when two equal and opposite forces exist offset from each other: • from an equilibrium standpoint, the result is a pure moment (the forces cancel out because they are equal and opposite) • couple moments are free vectors, which means that the moment they create is the same regardless of the point we choose around which to take the moment MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 2 Theory: Couple Moments • couple moments are created when two equal and opposite forces exist offset from each other: • from an equilibrium standpoint, the result is a pure moment (the forces cancel out because they are equal and opposite) • couple moments are free vectors, which means that the moment they create is the same regardless of the point we choose around which to take the moment MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 2 Theory: Couple Moments • couple moments are created when two equal and opposite forces exist offset from each other: M = Fd • from an equilibrium standpoint, the result is a pure moment (the forces cancel out because they are equal and opposite) • couple moments are free vectors, which means that the moment they create is the same regardless of the point we choose around which to take the moment MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 2 Theory: Couple Moments • couple moments are created when two equal and opposite forces exist offset from each other: M = Fd (d is the distance between the forces) • from an equilibrium standpoint, the result is a pure moment (the forces cancel out because they are equal and opposite) • couple moments are free vectors, which means that the moment they create is the same regardless of the point we choose around which to take the moment MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 2 Deriva=on: Huh? MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 3 Concept: Equivalence • we can define this: if two loading scenarios produce idenLcal effects on the structure, then they are equivalent • “idenLcal effects” simply means that from the standpoint of equilibrium calculaLons, the effects are the same MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 4 Concept: Equivalence • we can define this: if two loading scenarios produce idenLcal effects on the structure, then they are equivalent • “idenLcal effects” simply means that from the standpoint of equilibrium calculaLons, the effects are the same MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 4 Concept: Equivalence • we can define this: if two loading scenarios produce idenLcal effects on the structure, then they are equivalent • “idenLcal effects” simply means that from the standpoint of equilibrium calculaLons, the effects are the same MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 4 Theory: Equivalence Calcula=ons • remember that we wish to calculate an equivalent set of loads whose effect in the equilibrium calculaLon (i.e., it has the same “external effects” on the body) • original two types: • • • force equivalence moment equivalence so we need to make sure that the original and the equivalent systems appear the same in the equilibrium equaLons equivalent loading at O MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 5 Theory: Equivalence Calcula=ons • remember that we wish to calculate an equivalent set of loads whose effect in the equilibrium calculaLon (i.e., it has the same “external effects” on the body) • original two types: • • • force equivalence moment equivalence so we need to make sure that the original and the equivalent systems appear the same in the equilibrium equaLons equivalent loading at O MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 5 Theory: Equivalence Calcula=ons • remember that we wish to calculate an equivalent set of loads whose effect in the equilibrium calculaLon (i.e., it has the same “external effects” on the body) • original two types: • • • force equivalence moment equivalence so we need to make sure that the original and the equivalent systems appear the same in the equilibrium equaLons equivalent loading at O MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 5 Concept: Distributed Load • distributed loads act over a line or area, and oXen represent mechanics of contact between two objects • we have tools available to analyze distributed loads, and oXen we like to find a point force equivalent to a given distribute load • in this case, MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 6 Theory: Generalized Distributed Load • how do we use our general rules about equivalence to simplify this distributed load? MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 7 Theory: Generalized Distributed Load • how do we use our general rules about equivalence to simplify this distributed load? MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 7 Theory: Generalized Distributed Load • how do we use our general rules about equivalence to simplify this distributed load? MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 7 Theory: Magnitude of the Resultant • this requires FORCE equivalence MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 8 Theory: Loca=on of the Resultant • this required MOMENT equivalence MAE 2300 Sta=cs © E. J. Berger, 2010 7 ­ 9 ...
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