Budynas-Nisbett:Shigley's I.Basics 1.Introduction to T©The McGraw--Hill Mechanical Engineering Mechanical Engineering Companies,2008 Design,Eighth Edition Design Introduction to Mechanical Engineering Design 21 given in terms of standard deviations of the dimension distribution,the standard devia- tion of the gap would be=.However,this assumes a normal distribution for the individual dimensions,a rare occurrence.To find the distribution of w and/or the probability of observing values of w within certain limits requires a computer simulation in most cases.Monte Carlo computer simulations are used to determine the distribution of w by the following approach: 1 Generate an instance for each dimension in the problem by selecting the value of each dimension based on its probability distribution. 2 Calculate w using the values of the dimensions obtained in step 1. 3 Repeat steps 1 and 2 N times to generate the distribution of w.As the number of trials increases,the reliability of the distribution increases. 1-14 Units In the symbolic units equation for Newton's second law,F=ma. F=MLT-2- (1-4 F stands for force,M for mass,L for length,and T for time.Units chosen for any three of these quantities are called base units.The first three having been chosen,the fourth unit is called a derived unit.When force,length,and time are chosen as base units,the mass is the derived unit and the system that results is called a gravitational system of units.When mass,length,and time are chosen as base units,force is the derived unit and the system that results is called an absolute system of units. In some English-speaking countries,the U.S.customary foot-pound-second system (fps)and the inch-pound-second system (ips)are the two standard gravitational systems most used by engineers.In the fps system the unit of mass is M(pound-forceX(second) _lbf.s2/ft slug (1-5) foot Thus,length,time,and force are the three base units in the fps gravitational system. The unit of force in the fps system is the pound,more properly the pound-force.We shall often abbreviate this unit as lbf;the abbreviation lb is permissible however,since we shall be dealing only with the U.S.customary gravitational system.In some branches of engineering it is useful to represent 1000 Ibf as a kilopound and to abbreviate it as kip.Note:In Eq.(1-5)the derived unit of mass in the fps gravitational system is the Ibf.s2/ft and is called a slug:there is no abbreviation for slug. The unit of mass in the ips gravitational system is M2(pound-force)(second) =lbf.s/in (1-6) L inch The mass unit Ibf.s2/in has no official name. The International System of Units(SI)is an absolute system.The base units are the meter,the kilogram (for mass),and the second.The unit of force is derived by using Newton's second law and is called the newton.The units constituting the newton (N)are F=ML=(kilogram)(meter) T2= =kg.m/s2 =N (1-7 (second)2 The weight of an object is the force exerted upon it by gravity.Designating the weight as W and the acceleration due to gravity as g,we have W=mg (1-8)Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition I. Basics 1. Introduction to Mechanical Engineering Design © The McGraw−Hill 27 Companies, 2008 Introduction to Mechanical Engineering Design 21 given in terms of standard deviations of the dimension distribution, the standard devia￾tion of the gap w¯ would be tw =  all t 2 . However, this assumes a normal distribution for the individual dimensions, a rare occurrence. To find the distribution of w and/or the probability of observing values of w within certain limits requires a computer simulation in most cases. Monte Carlo computer simulations are used to determine the distribution of w by the following approach: 1 Generate an instance for each dimension in the problem by selecting the value of each dimension based on its probability distribution. 2 Calculate w using the values of the dimensions obtained in step 1. 3 Repeat steps 1 and 2 N times to generate the distribution of w. As the number of trials increases, the reliability of the distribution increases. 1–14 Units In the symbolic units equation for Newton’s second law, F ma, F = MLT −2 - (1–4) F stands for force, M for mass, L for length, and T for time. Units chosen for any three of these quantities are called base units. The first three having been chosen, the fourth unit is called a derived unit. When force, length, and time are chosen as base units, the mass is the derived unit and the system that results is called a gravitational system of units. When mass, length, and time are chosen as base units, force is the derived unit and the system that results is called an absolute system of units. In some English-speaking countries, the U.S. customary foot-pound-second system (fps) and the inch-pound-second system (ips) are the two standard gravitational systems most used by engineers. In the fps system the unit of mass is M = FT 2 L = (pound-force)(second)2 foot = lbf · s 2 /ft = slug (1–5) Thus, length, time, and force are the three base units in the fps gravitational system. The unit of force in the fps system is the pound, more properly the pound-force. We shall often abbreviate this unit as lbf; the abbreviation lb is permissible however, since we shall be dealing only with the U.S. customary gravitational system. In some branches of engineering it is useful to represent 1000 lbf as a kilopound and to abbreviate it as kip. Note: In Eq. (1–5) the derived unit of mass in the fps gravitational system is the lbf · s2/ft and is called a slug; there is no abbreviation for slug. The unit of mass in the ips gravitational system is M = FT 2 L = (pound-force)(second)2 inch = lbf · s 2 /in (1–6) The mass unit lbf · s2/in has no official name. The International System of Units (SI) is an absolute system. The base units are the meter, the kilogram (for mass), and the second. The unit of force is derived by using Newton’s second law and is called the newton. The units constituting the newton (N) are F = ML T 2 = (kilogram)(meter) (second)2 = kg · m/s 2 = N (1–7) The weight of an object is the force exerted upon it by gravity. Designating the weight as W and the acceleration due to gravity as g, we have W = mg (1–8)