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Learning Goal To use the vector cross product to calculate the moment produced by a force or forces about a specified point on a member. The moment of a force F about the moment axis pvectoring through O and perpendicular to the plane containing O and F can be expressed using the vector cross product. Part A- Moment due to a force specified by magnitude and endpoints Learning Goal To use the vector cross product to calculate the moment produced by a force or forces about a specified point on a member As shown a member is foxed at the origin point O and has an applied force F the tension in the rope applied at the get end point B. Figure 1) The force has magnitude F 180 N and is Moment of a Force-Vector Formulation Learning Goal To use the vector cross product to calculate the moment produced by a force or forces. about a specified point on a membe The moment of a force F about the moment axis pvectoring through O and perpendicular to the plane containing O and F can be expressed using the vector cross product Mo -rx F.

where is the position vector measured from the moment center to any point along the line of action of the force vector .The directional sense of the moment is found by first aligning the position and the force vectors tail to tail then curling the four fingers of the right hand from to with the thumb pointing in the direction of the moment vector. Cross Products and Moments of Force Ref Hibbeler 4.2-4.3 Bedford & Fowler Statics 2.6 4.3 In geometric terms the cross product of two vectors A and B produces a new vector C with a direction perpendicular to the plane formed by A and B (according to right-hand rule) and a magnitude equal to the area of the parallelogram formed using A and B as adjacent sides. MOMENT OF A FORCE VECTOR FORMULATION (Section 4.3) Moments in 3-D can be calculated using scalar (2-D) approach but it can be difficult and time consuming. Thus it is often easier to use a mathematical approach called the vector cross product. Using the vector cross product M O r F .

Moment of this force about the z axis of the value. Plan 1) We need to use M z u (r F). 2) Note that u 1 k. 3) Choose point on z axis and on line of action. These can only be A and B here. The vector r is the position vector from A to B. 4) Force F is already given in Cartesian vector form. A B Chapter 2 Review of Forces and Moments 2.1 Forces In this chapter we review the basic concepts of forces and force laws. Most of this material is identical to material covered in EN030 and is provided here as a review. There are a few additional sections for example forces exerted by a damper or dashpot an inerter and interatomic forces are discussed in Section 2.1.7. 2.1.1 Definition MOMENT OF A FORCE VECTOR FORMULATION (Section 4.3) Moments in 3-D can be calculated using scalar (2-D) approach but it can be difficult and time consuming. Thus it is often easier to use a mathematical approach called the vector cross product. Using the vector cross product M O r F . Unformatted text preview MOMENT OF A FORCE SCALAR AND VECTOR FORMULATION LEARNING OBJECTIVES Be able to understand and define moment Be able to determine the moment of a force in 2-D and 3-D cases PRE-REQUISITE KNOWLEDGE Units of measurements Trigonometry concepts Vector concepts Rectangular components concepts MOMENT OF A FORCE A moment of a force around a point or an axis is a measure of