We investigate isospin-symmetry breaking effects in the sd-shell region with large-scale shell-model calculations, aiming to understand the recent anomalies observed in superallowed Fermi β -decay. We begin with calculations of Coulomb displacement energies (CDE's) and triplet displacement energies (TDE's) by adding the T = 1, J = 0 isospin nonconserving (INC) interaction into the usual isospin-invariant Hamiltonian. It is found that CDE's and TDE's can be systematically described with high accuracy. A total number of 122 one-and two-proton separation energies are predicted accordingly, and locations of the proton drip-line and candidates for proton-emitters are thereby suggested. However, attempt to explain the anomalies in the superallowed Fermi β -decay fails because these well-fitted T = 1, J = 0 INC interactions are found no effects on the nuclear matrix elements. It is demonstrated that the observed large isospin-breaking correction in the 32 Cl β -decay, the large isospin-mixing in the 31 Cl β -decay, and the small isospin-mixing in the 23 Al β -decay can be consistently understood by introducing additional T = 1, J = 2 INC interactions related to the s 1/2 orbit.The degeneracies of energy levels in nuclei with interchanging number of protons and neutrons indicate the existence of isospin symmetry [1,2]. The concept of this approximate symmetry is successful in describing various observables, there are conditions where it does not hold. Isospin symmetry is broken in QCD due to the mass difference between the up and down quarks and their electromagnetic interaction [3]. In nuclei, the Coulomb interaction and the charge-dependent nucleonnucleon interaction break this symmetry, giving rise to observable effects. Especially for nuclei near the N = Z line, both the ground states and excited spectra are affected by isospin-symmetry breaking (ISB). Therefore, investigation of protonrich nuclei far from the line of stability provides important testing ground for ISB effects. It has been known that ISB in nuclear many-body systems in terms of the isospin nonconserving (INC) interactions [4] leads to non-zero Coulomb displacement energy (CDE) [5,6] and triplet displacement energy (TDE) (see definitions in Eq. (1) below). While the microscopic origin of possible INC sources is yet to be understood, study of these quantities must involve the knowledge of the many-body effects in nuclear structure [7]. This suggests that the detailed shell-model calculations with an inclusion of INC forces are es-