In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the …rst time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The conditi...

One of the methods for retrofitting reinforced concrete moment frames is the use of steel braces. In this research, the seismic performance of a double-skinned concrete framing system reinforced with two concentric (CBF) and eccentric (EBF) steel bracing, was investigated under seven near-fault earthquake records of varying intensity. For this purpose, two ten-story concrete frames with five sp...

by minimizing the total potential energy function and deploying the virtual work principle, a higher-order stiffness matrix is achieved. this new tangent stiffness matrix is used to solve the frame with geometric nonlinear behavior. since authors’ formulation takes into account the higher-order terms of the strain vector, the convergence speed of the solution process will increase. in fact, bot...