Force and Moment Vectors Steven A. Jones 9/20/2018

Basics Force is rate of change of momentum If you push on a wall, it exerts an equal force on you Force is in Kg m/s2 or Newtons Can also be g cm/s2 or dynes A Newton is a little less than ¼ lbs, or a little less than the weight of ½ cup of water. A dyne is 5 orders of magnitude smaller. 9/20/2018

Forces Forces add as vector quantities Can draw a free body diagram All forces must balance one another Some forces may be discrete, some distributed. With distributed forces, often concerned with the resultant force. 9/20/2018

Forces Normal forces act normal to a surface (e.g. pressure). Tangential forces act tangentially to the surface (e.g. frictional forces). Tensile & compressive forces may have different consequences: Concrete – works well in compression, not so well in tension. A bicycle spoke works poorly in compression. 9/20/2018

Forces Coplanar Forces – in the same plane Collinear Forces – along the same line Concurrent Forces – lines of action pass through the same point. Parallel Forces – act in the same direction 9/20/2018

Gravity Gravity – the least well-understood force On Earth: g = 9.81 m/s2 g = 981. cm/s2 g = 32.2 ft/s2 9/20/2018

Distributed Forces A distributed load in a free body can be replaced with it a point load at the center of mass. p P 9/20/2018

Friction F=cN Coefficient differs for sliding and static friction. Coefficient must also depend on velocity of motion (otherwise it would require just as much force to slide a refrigerator at 100 ft/s as at 1 ft/s). Friction burns up energy. We consider it a nuisance, but just try ice skating without it. 9/20/2018

Moment F1 F2 r F1 and F2 apply the same moment around p r’ p Can translate F1 anywhere along its line of action. r’ p 9/20/2018

Moment Direction of moment is perpendicular to the plane. Right-hand rule gives sign of direction. Resultant momentum is sum of momenta A couple is caused by 2 forces of same magnitude and opposite direcdtion. Magnitude of moment of a couple is F times distance. (True of any point affected by the couple). 9/20/2018

Mechanically Equivalent Systems 9/20/2018

Statics Concepts Sum of forces must be zero (translational equilibruim) Sum of moments must be zero (rotational equilibrium) The above gives 6 equations in space. 9/20/2018

Types of problems solved in Statics Truss problems Beam problems Machine problems Rope/Pully problems Friction Problems (ramp problems) 9/20/2018

Types of Problems Solved in Mechamics of Materials Torsion problems Elastic beam problems (force along the beam length) Finding V and M in a beam Location of maximum stress for a beam Beam deflection problems 9/20/2018

To Review Center of Mass I for a beam J for a shaft Q for a beam 9/20/2018

Shaft J is the polar moment of inertia G is the shear modulus Principle stresses are at 45 degrees 9/20/2018

Beams: Flexural Stress 9/20/2018

Beams: Shear Stress 9/20/2018