Moment About an Axis

4 Key excerpts on "Moment About an Axis"

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  eBook - ePub

  Principles of Structure

  • Ken Wyatt, Richard Hough(Authors)
  • 2013(Publication Date)
  • CRC Press

    (Publisher)

  In most instances both tendencies are present, and we need a concept to measure the turning effect or rotating effect of a force about a point. The torque or moment of a force about a point is the product of the force and the perpendicular distance from the point to the force (Figure 1.6). The perpendicular distance is called the ‘lever arm’ of the force. Being the product of force and length, moments have the units of Newton-metres, Nm, or kNm, etc. It is most important to note that we may measure the moment of a force about any point we choose ; the point does not have to be the centre of gravity, the fulcrum, the point of support or any such particular point. The moment of a force about a point is simply a measure of the turning effect produced by that force about that point. We shall adopt a convention that clockwise moments are positive, and anti-clockwise moments are negative. WORKSHEET 1.1 1.1  A force of 10 kN is applied at an angle of 30° to the horizontal (Figure 1). (a) Calculate the component of this force in each of the directions AB, CD and EF. (b)  Confirm for yourself, by rapid sketches drawn approximately to scale, that the values you have computed seem reasonable. 1.2 Figure 2 shows three concurrent forces acting on a body. (a)  Are these forces in equilibrium? (b)  If not, what additional force would need to be applied to the body in order to produce equilibrium? FIGURE 1 FIGURE 2 1.3 Figure 3 shows an awning erected at the front of a suburban shop. If we assume that the weight of the awning is concentrated at its mid-point: (a)  What is the moment of this weight about the hinged support at A? (b)  The force in the steel bar BC will also produce a moment about A

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  eBook - ePub

  Basic Engineering Mechanics Explained, Volume 1

  Principles and Static Forces

  • Gregory Pastoll, Gregory Pastoll(Authors)
  • 2019(Publication Date)
  • Gregory Pastoll

    (Publisher)

  Chapter 5 Force moments, torque, equilibrium of rigid bodies and free-body diagrams

  • Definition of a force moment and a torque

  • Equilibrium conditions for a solid object

  • Free-body diagrams

  • Constraints on the equilibrium of solid objects

  • Equilibrium of beams under load

  The moment of a force

  The expression ‘moment of a force’ is used in mechanics to mean ‘the rotating effect produced by a force’. The moment of a force about a given point is the product of the magnitude of the force and the shortest distance between the given point and the line of action of the force.

  When stating the value of a force moment, it is essential to specify about which point a moment is being measured, and whether the moment is clockwise or anticlockwise.

  In this diagram, the moment of the 600 N force about point A is (600 N x 2 m), namely 1200 Nm clockwise. This is denoted as MA = 1200 Nm ⤵ .

  The moment of this same force about point B is (600 N x 3 m), namely 1800 Nm anticlockwise, denoted as MB = 1800 Nm ⤴ .

  It is easy to relate to force moments when we think of tightening a nut with a spanner. We know from experience that the greater the force F we exert, and the greater is dimension d, the greater will be the turning effect we can exert on the nut. The moment of the force we can apply is F x d.

  In each of the diagrams at right, the moment of the force F about point O is given by:

  Mo = F x d, clockwise.

  The moment of an oblique force

  Sometimes a force is directed at an angle to the line joining its point of application to the point about which moments are being determined. In such cases, the moment about that point may determined by either of two methods, as follows:

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  eBook - ePub

  Introduction to Structures

  • Paul McMullin, Jonathan Price, Paul McMullin, Jonathan Price, Paul W. McMullin, Jonathan S. Price(Authors)
  • 2016(Publication Date)
  • Routledge

    (Publisher)

  Figure 6.2 in how the forces balance one another.

  6.3 Definitions

  Figure 6.3 Wrench

  • Magnitude : Direction and sense of a force vector (see Chapter 5 ).
  • Moment arm or lever arm: The distance measured from the applied force in a perpendicular direction to a reference or pivot point. In Figure 6.3 , the most logical reference point is the bolt centerline. Different reference points could be chosen but they would not help us quantify how much moment (or in the case of a bolt, how much torque) is being applied.
  • Axis of rotation : If a load or force tends to cause rotation of a two-dimensional object in the x –y plane, then the axis of rotation is about the z axis (perpendicular to the x –y plane). Most problems in this text are two-dimensional and will be in the x –y plane. For example, the wheel in Figure 6.4 has an axle in the z -axis so the wheel is in the x –y plane.
    Figure 6.4 Wheel and axis
  • Force couple : A force couple is similar to a moment but there are no net y or x direction forces. A couple applies only a pure moment on an object. Taken about a central point, the two forces exert either a clockwise or counterclockwise moment (Figure 6.5 ).
  • Positive moment : A moment is positive if the effect is counterclockwise with respect to the object. Known as the right-hand rule , the thumb represents the axis of rotation and the curled fingers pointing in a counterclockwise direction represent the moment. Figure 6.3 through Figure 6.5 indicate positive moments.
    Figure 6.5 Couple exerting only positive moment
  • Orthogonal moments: In the Cartesian coordinate system moments acting about the x , y , or z axes are independent of one another (see Figure 6.6

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  eBook - ePub

  The Practice of Engineering Dynamics

  • Ronald J. Anderson(Author)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  We will use the reference point defined in Section 2.6 and, particularly, in Figure 2.3. If a force acts on a point in the body, then the moment or torque produced by that force around point is defined to be, (2.30) where is the moment about, is the applied force, and is the position vector from to the point of application of the applied force 6. Consider the total moment about point resulting from the two forces applied on the particle. Remember that the forces are an externally applied force,, and an internal constraint force,. The moment about due to these forces is therefore, (2.31) Using Equation 2.19 with Equation 2.31, the following equality can be written. (2.32) As was done for the force balance, we consider the case where Equation 2.32 has been written for every particle in the body and the resulting equations have all been added together to give, (2.33) Two of the terms in Equation 2.33 can be dealt with immediately. These are, : this is the total moment about the reference point caused by internal forces. Since these forces occur in equal and opposite pairs, the moment caused by any given force is canceled out by its counterpart and,. : this is the total moment about the reference point caused by externally applied forces. Let this be denoted by. Equation 2.33 can then be rewritten as, (2.34) The third term (i.e.) is more difficult to deal with. We start by defining the angular momentum of the rigid body about point. In the same way that we defined moments caused by forces as a vector cross product, we define the angular momentum about point due to the particle (i.e.) to be the moment of the linear momentum of about

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