ARCH DAM ANALYSIS 163
implicit in elastic ring theory is similarly untenable because of restraint at
the abutment, and also the fact that arch span will marginally increase
owing to elastic deformation of the abutment. Arch deflection will, in turn,
reducehnear the crown and progressively increase has the abutments
are approached.
In theory, arch thickness should therefore diminish towards the
crown and increase close to the abutments. In practice it is usual to main-
tain a uniform thickness at any elevation for a single-curvature dam, and
the maximum tangential stresses will therefore be those generated at
either abutment.
Assuming that no abutment yielding occurs, an approximation of the
maximum stress at the abutment can be made by application of a correc-
tion factor, KR. In terms of thin ring theory, therefore, at the abutment
hKR (^) wz 1 Ru/Tr. (3.47)
FactorKRis a function of 2and of ratio Ru/Tr, and curves for KRare pre-
sented in Fig. 3.16. It will be noted that KR→1.0 for high values of 2, i.e.
the solution tends to that of pure thin ring theory.
3.4.4 Advanced arch analysis
Certain of the deficiencies of elastic ring analysis have been alluded to. Early
recognition of the importance of arch–cantilever and arch–abutment interac-
tions led to the development of trial load analysis, TLA. The principles
Fig. 3.16 Arch dam abutment stress correction factor KR