Forces and Moments MET 2214 Statics MET 2214

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

Moments and Forces Part 8 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. 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. 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? 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? 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 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 FR and its location x can be specified. Magnitude of the resultant force: Statics (MET 2214) Prof. S. Nasseri

Equivalent system So if we consider the 3 D 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

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 C) area B) arc length 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

Concept test 1. What is the location of FR, i. e. , the distance d? A) 2 m B) 3 m D) 5 m E) 6 m C) 4 m FR A BA 3 m 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 FR, i. e. , the distance x. A) 1 m B) 1. 33 m C) 1. 5 m F 1 x 2 D) 1. 67 m E) 2 m x 1 Statics (MET 2214) Prof. S. Nasseri F 2 B d x FR

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

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