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

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

3. Statics (MET 2214) Prof. S. Nasseri 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.

4. Statics (MET 2214) Prof. S. Nasseri 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.

5. Statics (MET 2214) Prof. S. Nasseri 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?

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

7. Statics (MET 2214) Prof. S. Nasseri Equivalent system The loading function is written as p= p(x) in Pa or N/m 2. 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/m 2 )(m)=N/m] So w= w(x) N/m. w=load per unit length

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

9. Statics (MET 2214) Prof. S. Nasseri Equivalent system So if we consider the 3D pressure loading, the magnitude of F R 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.

10. Statics (MET 2214) Prof. S. Nasseri Concept test 1. The resultant force (F R ) 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

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

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

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

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