NA TURE 



2 5 



THURSDAY, NOVEMBER 9, 1905. 



STRENGTH OF MATERIALS. 

 Mechanics of Materials. By Mansfield Merriman. 

 Tenth edition, re-written and enlarged. Pp. xi + 

 507. (New York : Wiley and Sons; London : Chap- 

 man and Hall, Ltd., 1905.) Price 21s. net. 

 THE great development of engineering schools in 

 the United States has led to the production of 

 a considerable number of technical text-books 

 primarily intended for students. It may at once be 

 slated that, taken as a whole, these books are in- 

 creasingly scholarly and sound; but they are largely 

 compiled from similar European text-books, and often 

 disclose a want of any serious independent investi- 

 gation of the subject dealt with. 



The present book is in some respects an excellent 

 treatise, and as it has reached a tenth edition it must 

 have been found useful. It deals with the elastic 

 and, to a limited extent, with the plastic properties 

 of materials of construction and the application of the 

 laws of strength of materials to the simpler machine 

 parts and structures. The treatment is essentially 

 theoretical, and the book must be judged by the way 

 in which it presents theory to students. The first 

 point which strikes a reader is the great looseness of 

 terminology. In the first two or three pages tension, 

 tensile force, pull and axial force are all used as 

 equivalent, which may not be wrong, but is confusing. 

 Also a compression is a shortening, a sliding (in shear) 

 is a detrusion, and the word strain does not appear 

 in the volume, which is unusual. Young's modulus 

 i- termed throughout the modulus of elasticity; the 

 condition that lateral contraction is unhindered is not 

 explained. The coefficient of rigidity is referred to 

 (p. 38) as the " modulus of elasticity for shear," but 

 the relation of E and G is not discussed until p. 465. 

 The volumetric modulus is described on p. 467, but 

 these are the only elastic coefficients mentioned. 



I he author has an aggravating way of describing 

 a thing at first very crudely and inaccurately, but 

 without any reservations, giving a revised statement 

 much later on and a further revision later still, and 

 this in the case of quite simple matters. Take, for 

 instance, the treatment of shear. On p. 38 the author 

 takes as the typical example of shear a force P acting 

 at the end of a T-shaped short beam. This is, of 

 course, a case of shear and bending, and the rect- 

 angular elevation of the beam would not become a 

 rhombus as the author states. The shear on hori- 

 zontal planes is not referred to, and the unit stress is 

 given as P/a without any caution that it is not 

 uniformly distributed; and it is from this complex 

 case that he deduces, as if it were a simple shear, thi 

 coefficient of rigidity. All this is inaccurate and con- 

 fusing to students. It is not until p. 204 that it is 

 explained that shear on one pair of planes is accom- 

 panied by an equal shear on a pair of planes at right 

 angles, and cm p. 465 the author goes back l<i re- 

 presenting shear as a single couple on a pair of 

 parallel planes. In both Figs. 15 and 1S1 the de- 

 NO. 1880, VOL. 73] 



formation is so drawn that a student would infer a 

 change of volume in shear, and nowhere, so far as 

 can be found, is the constancy of volume in shear 

 referred to. On p. 14 the end of a beam strained by 

 a couple is used as an illustration of shear. The 

 unit shearing stress is given as P/a, which is only 

 the mean stress, and it is added that the bar will 

 shear off when P/a is " equal to the ultimate shear- 

 ing strength of the material," which is not the case. 

 Can a more misleading statement for a student be 

 imagined than (p. 14) " tensile and compressive 

 stresses usually act parallel to the axis of a bar, but 

 shearing stresses at right angles to it "? or this state- 

 ment, p. 363, " it is best to consider shear as a sign- 

 less quantity"? All these matters are elementary, 

 and they are not so much wrong as slovenly and 

 confusing — and similar faults occur constantly. 



When the elastic limit is exceeded, the strains in- 

 crease faster than the stresses. " Therefore the elastic 

 properties of a bar are injured when it is stressed 

 bevond the elastic limit." It would not be exact, but 

 it would be more accurate, to say that the elastic 

 properties are improved by straining beyond the 

 elastic limit. " Accordingly it is a fundamental rule 

 that the unit stresses should not exceed the elastic 

 limit." The large deformation in ordinary materials 

 beyond the elastic limit is the primary reason for 

 limiting stresses to the elastic strength. It would be 

 undesirable for a bridge to deflect several feet. The 

 elastic limit is always assumed by the author to be a 

 definitely fixed stress, and its variation under variation 

 of loading is never referred to. 



" The stresses are usually computed for dead and 

 live loads separately regarding each as a static load. 

 The live load, however, really produces greater 

 stresses than the computed ones." 



The live load undoubtedly may cause rupture when 

 an equal dead load would not, but the author's state- 

 ment is extremely doubtful, and the question is one 

 of the most fundamental in applying the rules of 

 strength of materials, and should on no account be 

 slurred over in a text-book. The account of Wohler's 

 fatigue experiments (p. 352) is very brief and im- 

 perfect. American bridge builders have never fully 

 accepted Wohler's results, and have been disposed to 

 explain the smaller working stress in members sub- 

 ject to great variation of stress as justified by the 

 effect of impact. Practically it does not matter much 

 whether the reduction of the working stress is termed 

 an " allowance for impact " or " an allowance for 

 fatigue," but it is a fundamental point, and the 

 author's treatment of it on p. 358 will not much help 

 a student. The author's theory that a live load pro- 

 duces more stress "because it is applied quickly," 

 and the statement that the dynamic stress T can be 

 expressed in terms of the static stress S by the rela- 

 tion T=<j>{t)S. where <l>(t) is a function of the time 

 of application, will require much more investigation 

 before it is accepted. The effect of variation of stress 

 in inducing fatigue, the effect of impact or of loads 

 which have kinetic energy before deformation begins, 

 and of loads which are unbalanced so that they 

 acquire kinetic energy during deformation, require 



