31 Moments in 3D Wednesday ,September 19, 2012 Determine the moment of force F about point O. Bending moment M x at a distance x from free end = W x x = Wx. The moment arm is the shortest distance from the line of force to the axis. For example, the moment of force, often called torque, is the product of a force on an object and the distance from the reference point to the object. Case II Bending moment due to a uniformly distributed load ProblemF412 32 Moments in 3D Wednesday ,September 19, 2012 If F 1 = {100i – 120j +75k} lb and F 2 = {-200i – 250j +100k} lb, determine the resultant moment produced by these forces about A moment arm (MA) determines the degree of effectiveness or influence of a force to produce or prevent the rotation of an object around an axis. Express the result as a Cartesian vector. Calculate the magnitude of the moment applied by the 5 newton force about the point A. To solve : The total moment about any fixed point of the body is zero. This is equation of a straight line and the plotted bending moment diagram in the above figure shows that the variation of bending moment along the span of a cantilever is a straight line. The magnitude of the moment that force F exerts about point A on this lever will be equal to the magnitude of the force times distance d. When using scalar quantities, the magnitude of the moment will be equal to the perpendicular distance between the line of action of the force and the point we are taking the moment about. Therefore, the moment of inertia of a uniform rod about a perpendicular bisector (I) = ML 2 /12. Extending for the perpendicular, For a see saw in equilibrium, the total moment about the pivot is zero. 44 Influence Line … The moment, M, about some arbitrary point O can be calculated. Given that the see saw is balanced, calculate force P. Static Rigid Bodies . Moments are usually defined with respect to a fixed reference point; they deal with physical quantities located at some distance relative to that reference point. Influence line is a diagram that shows the variation for a particular force/moment at specific location in a structure as a unit load moves across the entire structure. d F A F B O r A r B A A B A A A B B r F r F M r F r F = × + ×− = × + × If point O is placed on the line of action of one of the forces, say F B, then that force causes no rotation (or tendency toward rotation) and the calculation of the moment is simplified. The line perpendicular to the plane of the ring through its centre – Consider the radius of the ring as R and its mass as M. All the elements are at the same distance from the axis of rotation, R. To draw a qualitative influence line for moment at C. Introduce hinge at C and that will only permit rotation at C. Now apply moment in the positive direction that will cause a unit rotation in the direction of M C. Examples. The influence of a certain force (or moment) in a structure is given by (i.e.it is equal to) the 41. Example on ILD for Bending Moment. A line that is midway between the upper surface and lower surface is called the camber line. Moment of Inertia of a Circular Ring about its Axis . Geometrically it is the perpendicular distance from the line of force to the axis, 41 Influence Line for the Reaction at Point A 42. Example How is the moment about the leading edge of the wing related to the moment about point A? F A O F B r M =r×FA The ... example the lift coefficient, 2-D is as compared to used for the 3-D lift coefficient. 42 Influence Line for the Reaction at Point A 43. 40 Example 4 draw an influence line for the reaction, shear, and moment for both points A and B using the tabular method. 43 Influence Line for the BM at Point A 44. 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