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Forces and Moments MET 2214

Forces and Moments MET 2214. Moments and Forces. Part 8. Types of Forces (Loads). Point loads - concentrated forces exerted at point or location. Distributed loads - a force applied along a length or over an area. The distribution can be uniform or non-uniform. Equivalent system.

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Forces and Moments MET 2214

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  1. Forces and Moments MET 2214 Statics (MET 2214) Prof. S. Nasseri

  2. Moments and Forces Part 8 Statics (MET 2214) Prof. S. Nasseri

  3. Types of Forces (Loads) Point loads - concentrated forces exerted at point or location. Distributed loads - a force applied along a length or over an area. The distribution can be uniform or non-uniform. Statics (MET 2214) Prof. S. Nasseri

  4. Equivalent system Distributed loading: Wind, fluids, and the weight of a material supported over a body’s surface are examples of distributed loadings. Pressure p (force/unit area) is the intensity of these loadings. Statics (MET 2214) Prof. S. Nasseri

  5. Application A distributed load on the beam exists due to the weight of the lumber. Is it possible to reduce this force system to a single force that will have the same external effect? If yes, how? Statics (MET 2214) Prof. S. Nasseri

  6. Application The sandbags on the beam create a distributed load. How can we determine a single equivalent resultant force and its location? Statics (MET 2214) Prof. S. Nasseri

  7. Equivalent system The loading function is written as p= p(x) inPa or N/m2. Because it is a function of and it is uniform along the y-axis. If we multiply p = p(x) by width a, we get w= p(x). a which is called the load intensity. [with the dimension of (N/m2)(m)=N/m] Sow= w(x) N/m. w=load per unit length Statics (MET 2214) Prof. S. Nasseri

  8. Equivalent system The system of forces of intensity w=w(x) can be simplified into a single resultant force FR and its location x can be specified. Magnitude of the resultant force: Statics (MET 2214) Prof. S. Nasseri

  9. Equivalent system So if we consider the 3D pressure loading, the magnitude of FR is defined by calculating the volume under the distributed loading curve p = p(x) . The location of resultant force is determined by finding the centroid of this volume. Statics (MET 2214) Prof. S. Nasseri

  10. Concept test 1. The resultant force (FR) due to a distributed load is equivalent to the _____ under the distributed loading curve, w = w(x). A) centroid B) arc length C) area D) volume 2. The line of action of the distributed load’s equivalent force passes through the ______ of the distributed load. A) centroid B) mid-point C) left edge D) right edge Statics (MET 2214) Prof. S. Nasseri

  11. F R A B A B d 3 m 3 m 2. If F1 = 1 N, x1 = 1 m, F2 = 2 N and x2 = 2 m, what is the location of FR, i.e., the distance x. A) 1 m B) 1.33 m C) 1.5 m D) 1.67 m E) 2 m F x F x 1 F 2 R 2 x 1 Concept test 1. What is the location of FR, i.e., the distance d? A) 2 m B) 3 m C) 4 m D) 5 m E) 6 m Statics (MET 2214) Prof. S. Nasseri

  12. Concept test F 100 N/m R 12 m x 2. x = __________. A) 3 m B) 4 m C) 6 m D) 8 m 1. FR = ____________ A) 12 N B) 100 N C) 600 N D) 1200 N Statics (MET 2214) Prof. S. Nasseri

  13. Example 1 Replace the loading by an equivalent resultant force and specify its location on the beam, measured from point B. Statics (MET 2214) Prof. S. Nasseri

  14. Example 1 Statics (MET 2214) Prof. S. Nasseri

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