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STRESSES IN AIRCRAFT AND SHELL STRUCTURES Nuatta) BicceleWieLUinem ereceeo)iDNemes eeeOMe cn ro McGRAW-HILL PUBLICATIONS IN AERONAUTICAL SCIENCE Jerome C. Hunsaxer, Consulting Editor STRESSES IN AIRCRAFT AND SHELL STRUCTURES McGRAW-HILL PUBLICATIONS IN AERONAUTICAL SCIENCE Jerome C. Hunsaxer, Consulting Editor Draren, McKay, ano Lees:Instrument Engineering Vol. 1 Pundamentale Vol. 2 Mathematics Vol. 3 Applications Part 1 Measurement Systems Part 2 Control Systems Ktcuemann anv Weer: Aerodynamics of Propulsion Kuuw:Stresses in Aircraft and Shell Structures Suatno:Principles of Helicopter Engineering Suaw anv Macks: Analysis and Lubrication of Bearings Srreerer:Fluid Dynamics VON Mises: Theory of Flight STRESSES IN AIRCRAFT AND SHELL STRUCTURES PAUL KUHN,B.S. (Ac.E.) Assistant Chief, Structures Research Division National Advisory Committce for Aeronautics McGRAW-HILL BOOK COMPANY, INC. New York Toronto London 1956 STRESSES IN AIRCRAFT AND SHELL STRUCTURES Copyright © 1956 by the McGraw-Hill Book Company,Inc. Printed in the United States of America, All rights reserved. This book, or parts thereof, may not be reproduced in any form without permission of the publishers. Library of Congress Catalog Card Number 55-1174 THE MAPLE PRESS COMPANY, YORK,PA. This book is dedicated to myteachers in the arts and sciences of structures Proressor S. TimosienKo and Proressor J. A. Van Den Broex PREFACE Aircraft engineering is generally acknowledged to have given a great impetus to research in structures. Much of this researchwork, however, ia available only in the form of original papers, a form which renders the results rather ineffective. This book represents an attemptto correlate and unify a certain amountof work and to makeit more effective by making it readily accessible. The aim of the work may be described most concisely as: One step beyond Mc/I and T/2Ain thesimplest mannerpossible. The elementary theories continue to be the foundationof stress analysis, but correc- tions are often required even for simple box beams, and major additions to the theory are necessary to deal, far instance, with stresses around cutouts. General progress in design refinement, the use of less ductile materials, and the emergence of fatigue as a design criterion are con- tributing to an ever-increasing need for more accurate stress calculations. The scopeis confined to thecalculationof the (“applied”) stresses that result from a givenload; the calculation of the (‘‘allowable”) stresses that cause failure is not discussed, with one major exception (diagonal ten- sion). Thetwo fields have grown to such anextentthatit is no longer feasible to combine them. Moreover, as methods become more refined, the twofields tend to separate more clearly than they did formerly. (It would be highly desirable to recognize this separation byrestricting the term “‘stress analysis” to thefirst field and by using the term “strength analysis” to denote the typeof calculation more frequently referred to as stress analysis. This explicit distinction between stress analysis and strength analysis should help to avoid such errors as using moments of inertia computed for ultimate-load conditions in the calculation of dynamic modes.) Simplicity of method is highly desirable because the valueof any caleu- lation decreases sharply if it is not completed before the designis frozen. In the quest for maximum simplicity, the device of working with simpli- fied conceptual “models,” or phantoms, of the structure has in some cases been carried to unconventional lengths in this book. Empirical relations have been employed freely. Finally, the stresses are divided, when feasible, into an elementary system and a correction, or perturba- tion, system. The elementary stresses can be dealt with efficiently by vii