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------- -^^^ ^ REESE LIBRARY OFTHK OF CALIFORNIA. UNIVERSITY -; Glass APPLIED MECHANICS. BY GAETANO LANZA, S.B., C. &M.E., ii PROFESSOR OF THEORETICALAND APPLIED MECHANICS, MASSACHUSETTS INSTITUTE OF TECHNOLOGY. NINTH EDITION, REVISED. FIRST THOUSAND. UNIVERSITY OF NEW YORK: JOHN WILEY & SONS. LONDON : CHAPMAN & HALL, LIMITED. 1905. REESE c COPYRIGHT, 1885, 1900, 1905, BY GAETANO LANZA. RObBKT DRUMMOND, 1RIN1BK, NBW YORK. PREFACE. THIS book is the result of the experience of the writer in teaching the subject of Applied Mechanics for the last twelve years at the Massachusetts Institute of Technology. The immediate object of publishing it is, to enable him to dispense with giving to the students a large amount of notes. As, however, it is believed that it may be found useful by others, the following remarks in regard to its general plan are submitted. The work is essentially a treatise on strength and stabil- ity ; but, inasmuch as it contains some other matter, it was " thought best to call it Applied Mechanics," notwithstanding the fact that a number of subjects usually included in trea- tises on applied mechanics are omitted. It is primarily a text-book; and hence the writerhas endeavored to present the different subjects in such a way as seemed to him best for the progress of the class, even though it be at some sacrifice of a logical order of topics. While no attempt has been made at originality, it is believed that some features of the work are quite different from all pre- 147GG3 iv PREFACE. vious efforts and a few of these cases will be referred to, ; with the reasons for so treating them. In the discussion upon the definition of "force," the object is, to make plain to the student the modern objections to the usual ways of treating the subject, so that he may have a clear conception of the modern aspect of the question, rather than to support the author's definition, as he is fully aware that this, as well as all others that have been given, is open to objection. In connection with the treatment of statical couples, it was thought best to present to the student the actual effect of the action of forces on a rigid body, and not to delay this subject until dynamics of rigid bodies is treated, as is usually done. In the common theory of beams, the author has tried to A make plain the assumptions on which it is based. little more prominence than usual has also been given to the longi- tudinal shearing of beams. In that part of the book that relates to the experimental results on strength and elasticity, the writer has endeavored to give the most reliable results, and to emphasize the fact, that, to obtain constants suitable for use in practice, we must deduce them from tests on full-size pieces. This prin- ciple of being careful not to apply experimental results to cases very different from those experimented upon, has long been recognized in physics, and therefore needs no justifica- tion. The government reports of tests made at the Watertown Arsenal have been extensively quoted from, as it is believed