CHAPTER VI-CALCULATION OF ARCH DATA INTRODUCTION 120. Preliminary Statement. This chapter discusses the application of computation forms in analyzing a uniform-thickness circular arch, a variable-thickness arch with a circular upstream face, and a circular arch with fillets at the downstream face. Calculations for other types of arches given in chapter V are not discussed herein. However, the forms illustrated can be used for other arch types by making a few changes and additions in tabular arrangements. Types of loads considered are symmetrical and nonsymmetrical unit radial, tangential, and twist loads on symmetrical or nonsymmetrical arches, and a temperature change load of +1° F. 121. Quantities Required for Analysis.-Dimensions and physical properties, together with symbols, required in analyses of arch elements are given below. T = radial thickness of arch. For variable thickness arches, T is required at the quarter points. For fillet arches, T is required at the quarter points of the fillet section. = PL, OR angles from reference plane or maximum cantilever section to left and right arch abutments, respectively. These are used as angles in analyzing nonsymmetrical arches. The value of A for analyzing symmetrical arches is the average of 1 and R. Values of þ, or 1 and R, must be in whole degrees to utilize the tables in chapter IX. = 4L, 4R angles between canyon walls and the vertical direction at the left and right arch abutments, respectively. They are measured in a vertical tangential plane. Unless 1 and R differ greatly, their average value can be used. This simplifies the computations and involves very little error. a, b short and long dimensions, respectively, of the equivalent rectangle of the developed foundation surface. The above quantities are tabulated on a separate sheet for convenient use or reference. With values of ER, TA, L, R, α, and b, arch abutment constants a, ẞ, y, and 2 can be determined on the computation form given in figure 14, chapter III. 122. COMPUTATION FORMS General.-General computation forms consist of four sheets as shown in figures 40 to 43, inclusive. These are adaptable to the solution of any circular arch carrying symmetrical or nonsymmetrical unit loads. The forms are directly applicable to a nonsymmetrical circular arch with a nonsymmetrical loading. With a symmetrical arch or a symmetrical load, certain quantities for the left and right sides of the arch are eliminated or duplicated, obviating the use of certain portions of the forms and simplifying the computations. Analyses of variable thickness and fillet arches require supplementary computation forms for evaluating arch and load constants, as given later. A comparison of the forms with the arch formulas in chapter V shows the purpose of the forms and the significance of the various quantities. The notation in the preceding chapter applies to the computation forms except that is the angle from the crown to the abutment and is the angle from the crown to the point where the deflection is desired. The following additional terms are also used on the forms: Φι Ф2 = = angle from crown to quarter-point. angle from crown to half-point. $3 angle from crown to three-quarter point. 123. Arch and Abutment Data.-The first sheet of the four general forms, figure 40, deals with arch constants, abutment constants, and functions needed in arch analysis. The procedure and sequence of computations for this sheet are as follows: 1. With values of r, T, Rʊ, and Ec compute the various factors involving these constants. The magnitude of the unit load, P, is |