A Treatise On The Principles And Practice Of Dock Engineering

I/O DOCK ENGINEERING. cos (y - /3) tan p sin2 y sin (y - ß) (1 - tan p\ = 0 tan y) Multiply by tan2 y cos (y - ß)’ tan p cos2 y - tan2 y tan (y - ß) + tan p tan y tan (y - ß)= 0. Substitute , - 1 j tan y - tan /3 „ ., ™ 1 + tan2 y for — 5—, and . -* --—for tan (y - ß\ ' cos2 y 1 + tan y tan ß Tben, i q 2 tan p + tan /? tan p tan3 y — tan2 y = = -- —f™ • (31) 1 1 - tan p tanß 1 — tan p tanp a cubic equation which determines the direction of the résultant and its maximum value. The case of a retaining wall with a horizontal ground surface has alone been dealt with, the investigation of the general case being far too lengthy and involved for insertion. It may be stated, however, that the general formula is deduced as p= «^ cos (y - ß)A 2 ’ cos /3 \ tan p\ sin y cos {ß — a) tan y/ ’ sin (y — œ) cos ß’ ■ (32) and the direction of the résultant is to be derived from the following :— tan® y — 2 tan p + tan ß 1 — tan p tan ß + tan ß tan a (tan p + tan ß) tan a 1 — tan p tan ß + tan ß tan a tan2 y tan y tan p - tan a (1 - tan p tan ß) 1 — tan p tan ß +tan ß tan a (33) So much for the purely theoretical aspect of the question which, how- ever, is by no raeans exhausted. Should the student be desirous of still further investigation, he will find, at the end of the chapter, reference to a few of the sources from which he may obtain additional information. Weight of Earthwork.—The weight, w, per unit volume of the earth- work behind a retaining wall can only be estimated from experimental results, a number of which are embodied in the following table. Much, however, depends on the degree of humidity of the earth in question, as well as on its actual chemical composition, which, within the limits of the same generic name, may vary considerably. Then it must also be borne in mind that unless the backing consist entirely of carefully selected filling, it is a practical impossibility to accurately gauge for the full extent of the wall the depths of the different strata to be met with. In the majority of cases an estimate has to be founded upon the information derived from a few isolated borings, which may entirely fail to take account of pot-holes or adventitious beds of treacherous material.