NATIONAL COUNCIL OF EXAMINERS FOR ENGINEERING AND SURVEYING ® FUNDAMENTALS OF ENGINEERING SUPPLIED-REFERENCE HANDBOOK Fourth Edition National Council of Examiners for Engineering and Surveying ® P.O. Box 1686 Clemson, SC 29633-1686 800-250-3196 www.ncees.org Rev. 0 FUNDAMENTALS OF ENGINEERING SUPPLIED-REFERENCE HANDBOOK Fourth Edition  2000 by the National Council of Examiners for Engineering and Surveying ® . All rights reserved. First edition 1996 Fourth edition 2000 . iii FOREWORD During its August 1991 Annual Business Meeting, the National Council of Examiners for Engineering and Surveying (NCEES) voted to make the Fundamentals of Engineering (FE) examination an NCEES supplied-reference examination. Then during its August 1994 Annual Business Meeting, the NCEES voted to make the FE examination a discipline-specific examination. As a result of the 1994 vote, the FE examination was developed to test the lower-division subjects of a typical bachelor engineering degree program during the morning portion of the examination, and to test the upper-division subjects of a typical bachelor engineering degree program during the afternoon. The lower-division subjects refer to the first 90 semester credit hours (five semesters at 18 credit hours per semester) of engineering coursework. The upper-division subjects refer to the remainder of the engineering coursework. Since engineers rely heavily on reference materials, the FE Supplied-Reference Handbook will be made available prior to the examination. The examinee may use this handbook while preparing for the examination. The handbook contains only reference formulas and tables; no example questions are included. Many commercially available books contain worked examples and sample questions. An examinee can also perform a self-test using one of the NCEES FE Sample Questions and Solutions books (a partial examination), which may be purchased by calling (800) 250-3196. The examinee is not allowed to bring reference material into the examination room. Another copy of the FE Supplied-Reference Handbook will be made available to each examinee in the room. When the examinee departs the examination room, the FE Supplied- Reference Handbook supplied in the room shall be returned to the examination proctors. The FE Supplied-Reference Handbook has been prepared to support the FE examination process. The FE Supplied-Reference Handbook is not designed to assist in all parts of the FE examination. For example, some of the basic theories, conversions, formulas, and definitions that examinees are expected to know have not been included. The FE Supplied-Reference Handbook may not include some special material required for the solution of a particular question. In such a situation, the required special information will be included in the question statement. DISCLAIMER: The NCEES in no event shall be liable for not providing reference material to support all the questions in the FE examination. In the interest of constant improvement, the NCEES reserves the right to revise and update the FE Supplied-Reference Handbook as it deems appropriate without informing interested parties. Each NCEES FE examination will be administered using the latest version of the FE Supplied-Reference Handbook. So that this handbook can be reused, PLEASE, at the examination site, DO NOT WRITE IN THIS HANDBOOK. v TABLE OF CONTENTS UNITS 1 CONVERSION FACTORS 2 MATHEMATICS 3 STATICS 22 DYNAMICS 24 MECHANICS OF MATERIALS 33 FLUID MECHANICS 38 THERMODYNAMICS 47 HEAT TRANSFER 58 TRANSPORT PHENOMENA 63 CHEMISTRY 64 MATERIALS SCIENCE/STRUCTURE OF MATTER 68 ELECTRIC CIRCUITS 72 COMPUTERS, MEASUREMENT, AND CONTROLS 76 ENGINEERING ECONOMICS 79 ETHICS 86 CHEMICAL ENGINEERING 88 CIVIL ENGINEERING 92 ELECTRICAL AND COMPUTER ENGINEERING 108 INDUSTRIAL ENGINEERING 115 MECHANICAL ENGINEERING 125 INDEX 136 [...]... kth row The cofactor of this element is the value of the minor of the element (if h + k is even), and it is the negative of the value of the minor of the element (if h + k is odd) If n is greater than 1, the value of a determinant of order n is the sum of the n products formed by multiplying each element of some specified row (or column) by its cofactor This sum is called the expansion of the determinant... product of the radius vector distance r and the force F from a point to the line of action of the force Mx = yFz zFy, MOMENT OF INERTIA The moment of inertia, or the second moment of My = zFx xFz, and M = r ì F; area, is defined as Mz = xFy yFx Iy = ũ x2 dA Ix = ũ y2 dA SYSTEMS OF FORCES F = Fn The polar moment of inertia J of an area about a point is equal to the sum of the moments of inertia of the... X i2 The median is defined as the value of the middle item when the data are rank-ordered and the number of items is odd The median is the average of the middle two items when the rankordered data consists of an even number of items F(x) = the area under the curve from to x, R(x) = the area under the curve from x to , and W(x) = the area under the curve between x and x The mode of a set of data is... conditions: Radius of Gyration The radius of gyration rp, rx, ry is the distance from a reference axis at which all of the area can be considered to be concentrated to produce the moment of inertia 1 The members of the truss lie in the same plane 2 The members are connected at their ends by frictionless pins 3 All of the external loads lie in the plane of the truss and are applied at the joints only... the values of the observations to be averaged, and A table at the end of this section gives the values of tn for values of and n Note that in view of the symmetry of the tdistribution, wi = the weight applied to the Xi value t1,n = t,n The function for follows: the weighted arithmetic mean, The variance of the observations is the arithmetic mean of the squared deviations from the population mean In... can be developed is practically independent of the velocity, although experiments show that the force F necessary to start sliding is greater than that necessary to maintain sliding Fs = k x, where x = the change in length of the spring from the undeformed length of the spring The potential energy stored in the spring when compressed or extended by an amount x is U = k x2/ 2 The change of potential energy... Ix = ũ (x2 + y2) dA Fn = 0 = rp2A, where Mn = 0 rp = the radius of gyration (see page 23) 22 STATICS (continued) Moment of Inertia Transfer Theorem The moment of inertia of an area about any axis is defined as the moment of inertia of the area about a parallel centroidal axis plus a term equal to the area multiplied by the square of the perpendicular distance d from the centroidal axis to the axis... s = 2r [tan (/2)] Paraboloid of Revolution A = (nsr)/2 Prismoid V= d 2 h 8 Gieck, K & R Gieck, Engineering Formulas, 6th Ed. , Copyright 8 1967 by Gieck Publishing Diagrams reprinted by permission of Kurt Gieck V = (h/6)( A1 + A2 + 4A) 17 MATHEMATICS (continued) f(x) A Aex A1 sin x + A2 cos x CENTROIDS AND MOMENTS OF INERTIA The location of the centroid of an area, bounded by the axes and the function... (t )dt x Laws of Probability Property 1 General Character of Probability which implies that F(a) is the probability that x a The probability P(E) of an event E is a real number in the range of 0 to 1 The probability of an impossible event is 0 and that of an event certain to occur is 1 The expected value g(x) of any function is defined as E{g (x )} = ũ g (t ) f (t )dt x Property 2 Law of Total Probability... perpendicular to the plane containing A and B The product is determinant of A DETERMINANTS A determinant of order n consists of n2 numbers, called the elements of the determinant, arranged in n rows and n columns and enclosed by two vertical lines In any determinant, the minor of a given element is the determinant that remains after all of the elements are struck out that lie in the same row and in the same . copy of the FE Supplied- Reference Handbook will be made available to each examinee in the room. When the examinee departs the examination room, the FE Supplied- Reference Handbook supplied in. be returned to the examination proctors. The FE Supplied- Reference Handbook has been prepared to support the FE examination process. The FE Supplied- Reference Handbook is not designed to assist. informing interested parties. Each NCEES FE examination will be administered using the latest version of the FE Supplied- Reference Handbook. So that this handbook can be reused, PLEASE, at