FIGURE 53-TYPICAL ARCH DEFLECTION CURVES FOR 0,024 יזיזיזיזיז CONCENTRATED LOAD CONCENTRATED LOAD יזיזיזיזיז • CONCENTRATED LOAD 139. Nonsymmetrical Unit Loads.-Figures 51, 52, and 53 show typical deflection curves for nonsymmetrical unit loads on a symmetrical arch. These curves are for a variable thickness arch with dimensions similar to those for the arch represented in figures 48 to 50. The curves for unit triangular and concentrated loads are for loads on the left part of the arch only. If the curves are reversed, so that the left abutment becomes the right abutment and vice versa, and if the changes of sign indicated on table 8, section 130, are applied, the curves will be those for unit triangular and concentrated loads on the right side of the arch. The deflections for uniform loads remain the same. 140. Arch Forces and Deflections.-Moments, thrusts, and shears caused by unit loads, at the crown and abutment points are tabulated for use in calculating stresses. Values at other arch points are included if stresses are desired at such points. Tabulations of arch point deflections are also made for all unit loads. These are used in deflection adjustments as described in chapter VII. CHAPTER VII-LOADS AND ADJUSTMENTS INTRODUCTION 141. General Statement.-Trial load adjustments consist of divid ing external loads between the arch and cantilever systems and applying internal self-balancing tangential and twist loads to the two systems, until geometrical continuity is established throughout the structure. To accomplish this, required loads are estimated and gradually determined by trial until deflections and rotations of arches and cantilevers agree at conjugate points. Radial, tangential, and angular movements due to forces acting on the dam are considered respectively in radial, tangential, and twist adjustments. 142. Arches and Cantilevers. In beginning a trial load analysis the number and location of sample arches and cantilevers to be used must be determined. If the dam is reasonably symmetrical about the maximum cantilever section, only half the structure is considered in the analysis. In this case about five to seven arches and four to seven cantilevers are used. If the parts of the dam on the left and right sides of the maximum section are considerably different, a nonsymmetrical analysis, in which the entire dam is considered, is required. More cantilevers, usually nine to eleven, are used for this type of analysis. One cantilever is located at the maximum section and the others on the arch abutments, as indicated in chapter II. With this selection of elements, it may not always be feasible to bring arch and cantilever deflections into reasonable agreement in some parts of the dam. In such cases additional elements may be necessary. A sharp break in abutment slope often requires additional cantilevers. After sample arches and cantilevers are selected, properties and dimensions needed in analyzing elements are determined. 143. Constants and Structural Data.-Constants and structural data required for a trial load analysis are given in the following list: 1. Dimensions of arches and cantilevers. Modulus of elasticity of concrete in tension and compression. 3. Modulus of elasticity of concrete in shear. 4. Poisson's ratio of concrete. 5. Modulus of elasticity of abutment rock in tension and com 13. Acceleration, direction, and period of vibration of assumed earthquake shock. 14. Temperature changes at elevations of arches. 16. 17. FORCES ACTING ON A DAM 144. General.-Forces acting on a dam include weight, temperature changes, and some combination of external loads produced by reservoir water, tailwater, uplift pressure, silt, ice, and earthquake shocks. 145. Concrete Weight.-Evaluations of weights, moments, and deflections due to concrete loads are described in chapter IV. If the dam is built in vertical sections and construction joints grouted after completion, effects of concrete weight are taken by the cantilevers alone. In this case concrete weight does not affect trial load adjustments and need not be considered until stresses are computed. If grouting is started before completion, deflections due to weights of concrete added subsequently must be included in the analysis. Likewise, when cracking of the cantilevers is assumed to take place, concrete weight becomes a factor in computing deflections of vertical elements. This subject is treated in chapter IV. 146. Temperature.-Seasonal variations of water and air temperatures at the faces of the dam cause changes in concrete temperature. These changes cause stresses and movements in the arches. Increases in concrete |