An Investigation of the Deflection Curve for a Pile Due to a Horizontal Load Citation Cobb, Charles Lewis (1941) An Investigation of the Deflection Curve for a Pile Due to a Horizontal Load. Dissertation (Ph.D.), California Institute of Technology. https://resolver.caltech.edu/CaltechTHESIS:02122025-180025793 Abstract No abstract. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Civil Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Civil Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Martel, Romeo Raoul Thesis Committee: Unknown, Unknown Defense Date: 1 June 1941 Record Number: CaltechTHESIS:02122025-180025793 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:02122025-180025793 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16998 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 13 Feb 2025 19:48 Last Modified: 13 Feb 2025 19:48 Thesis Files PDF - Final Version See Usage Policy. 21MB Repository Staff Only: item control page

AN TITTTESTIGATION OF THE ·DEFLECTION CURVE FOR A PILE DUE TO A HORIZONTAL LOAD By Charles Lewis Cobb. B. s. inc. E. University of Notre Da:me, 1940 , ' . • ~. ( { ' J- -~- ~ :;. ' _, ' -:;,. Signed TABLE OF CONTENTS Presentation · .. ... Page 1. Aclrnowledgment 2 Procedure ·3 Conclusions Appen4ix . . . -• . . .. •• • 24 26 - 1 - PRESENTATION I, Charles L. Cobb submit this ·thesis to the faculty of the Califomia Institute of' Technology. Department of Civil Engineering, in .partial, ful:t'ill.tnent of the requirements for a Degree of Master of . ' . . . Sci~o,e in Civil Engineering. - G- ACKNOOLEDG1·_ENT I wish to extend my thanks to Professor R. R. Martel for the help and suggestions he has given me in the, preparation of this Thesis. PROCEDURE . I have chosen to investigate the deflection curve for a horizontally loa.d ed sheet pile, and to draw from this investigation information that may . lead to a better understanding; of the behavior of sheet piling due to horizontal loading. I proceed from the basis that as the pile is first loaded, it is infinitely stiff and simply deflects in a straight line. The forces acting upon this infinitely stiff beam or pile are in equilibrium and hence eiJ..y additional forces that might be applied to it due to the release of this infinitely stiff pile must also be in equilib- . ' rium. These forces may be fountl from the differences in the ~eflections between the assumed and computed pile. The first assumption that must be made is in what manner does the soil pressure vary with depth? For the sake of shnplicity I hav~ chosen that it varies as a straight line. This assumption is in close accordance with the manner in which sandy soil will act, but varies from tlw,t of clay considerably. In the first calculations 1 will prove that the infinitely stiff pile, when loaded horizontally e.t the top, vrill rotate about a point three-quarters the length from the top. From this deflected position I will find the defiection curves for the first approximation, provided the pile was released from its infinitely stiff condition and allowed to bend. This added deflection will cause a new set of forces to be set up and thus these forces will ca.use an added deflection. 'I'his process will be continued until the a.mount of added deflection will become negligible. The force applied to a pile is proportional to the soil The soil pressure "e 1• is pressure "e" and to the deflection "u". proportional to the depth, varying a.s a. straight line; thus making the force applied to the pile proportional to the depth and the · deflection: Equ. 1. f = e u y y being the depth If the total fore es acting on the pile a.re in equilibrium, then the si.munation of these forces must be equal to zero. Equ. 2. H • H = 1~ u Y dy,. 0 o 0 The pile being a free ended beam, the s1.l!IllMtion of the moments about the e.n d must also be equal to zero. Equ. 3. M • euY 1~ 0 M• 0 2. dy•O The equations 2 and 3 make it possible then to find the forces applied and the amount of deflection. If these two unknowns are found for each subsequent deflection, and these dampen to a zero value, the total deflection and forces may be found. For my first deflection I will calculate both .analytically :and grapllically, and the subsequent deflections I will do only graphically. The graphioai ll'lethod may introdµce a small human error, but I will put this as small as possibl-e. •I ,"till now proceed to determine the point of zero deflection for the infinitely stiff pile. Aft.e r this I. will detennine the fir~t deflection Qll.8.lytioa.lly, and finally give the reEI'4lts of the subsequent. defleoti-ons from the graphical ~thod · in tables 2 and 3. CONCLUSIONS Finding the deflection curve for a pile due to a horizontal load has proven to be most interesting. The final curve for the deflection. .o f the pile as seen in figure 3 is very much different from • that of the straight line as was assumed in the beginning. The results obtained in this investigation, both from the analytical and graphical method, are in very close agreement, and the . . -. • best place to com.pare the results is in tl':i.E) caJ.culation for the By the analytical method from equation 7, original deformation "Q.". 18 P . 18.5 P Q • - - - , where by the graphical method Q = , giving an e 1 e 1 · · error of about three per cent, which for all practical purposes is negligible. li' the results of table 2 a.re studied, oile can see that the amm.mt of added deflection obtained by each trial is.less. This Js an indication that the curve is gradually becoming fixed, but a.t a very slow rate. It is notioed in equation 7 that the original deformation "Q" is in proportion to the soil pre8sure tten, but the results of the •. '3 .· added deflection a.re in terms of . • l . EI which a.re not found in equa.- tion 7, -so for the sake of simplicity I have ta.ken the soil pressure 1080 EI ·J. + By a~~-ng this value of "en, the value of . p 13 Q • - - - and makes it possible to add the 60 EI original deformation of the infinitely stiff pile to tlle added • deflectidns found by the investigation, so that a final curve - 25 - can be obtained. The final results may be found in table 3, and the deflection curve from the results is shown in figure 3. The shape of the fina.l deflection curve of figure 3, is quite different from the deflection curve of the infinitely stiff pile. Upon examination of this curve we find that we have two points of ze:so bend, and the lower end of the pile is deflecting in the same direction as the top. I was able to carry the investigation through only eight trials, a.nd the final deflection curve would only be obtained after a.n infinite number of thei$e trials. If this had been done the curve in the lower portion would .have looked like .a damped sine curve instead of being as it is shown in figure 3. The points of zero defle~tions in the general case an almost infinite in number, bees.use of the curve being a damped sine curve, which will cross the zero line several times, but I believe for practical purposes this curve shows the general shape. The diirtanoe the first point of zero bend moves up from the three-quarter point of the infinitely 1;1tiff pile, is in relation to the moment of inertia of the pile, and mmit be considered in design. In general it can be said that the defiection curve i'or a pile due to a horizontal applied load is: 18 p r I~ 1 - 4 y --1 + K p 1,_ e 1 L 3 1 _.) 60 E I y ~ K being a variable with the depth, and may be found by determining y . the added deflection. - 26 - APPENDIX .