Confined concrete with variable crack angle – Part II: shear friction model

Abstract

This study investigates shear transfer across a definite plane, which must be considered in the formation of the crack opening path as discussed in the companion paper, Part I. Experimental investigation of the shear friction coefficient for a wide density range of 1200-2259 kg/m 3 for normal and lightweight concrete is presented for determination of parameters for the analytical model discussed in Part I, which explains the behaviour of confined concrete. The specimen variables include concrete strength, unit weight, volume percentage of air in the matrix (A/M), and volume percentage of matrix in the concrete (M/T). Test results show that the friction coefficient is dependent on concrete strength. However, shear strength is weakly dependent on the volume percentage of matrix in the concrete and strongly dependent on the volume of air in the matrix.

Finite Element Analysis Using the Crack Strain Separation Model for Reinforced Concrete Membrane

“…As a result, a regular friction coefficient is achieved rather than one which differs from the crack opening path slope. Dilatancy and friction effects are separated, thus making the friction coefficient nearly constant [11][12][13][14][15]. The friction coefficient definition leads to values that vary to a small extent in terms of slip.…”

Finite Element Analysis using Crack Strain Separation Model for Reinforced Concrete Membrane

“…As such, a regular friction coefficient is achieved instead of the one which differs from the crack opening path slope. Dilatancy and friction effects are separated thus making the friction coefficient to be nearly constant [10][11][12][13][14]. The friction coefficient definition leads to values that vary to a small extent in terms of slip.…”

Analytical Model of Two-Directional Cracking Shear-Friction Membrane for Finite Element Analysis of Reinforced Concrete

“…In addition, Equation 14through Equation 16need to be modified to account for the changes to Equation (13). The DOFs and the two load vectors (Ã and B) will be partitioned again into free, prescribed and restrained portions as follows:…”

“…The friction developed on the surface of the crack can then be defined by the normal and shear forces acting on the crack surface, as shown in Figure 1 , in which the friction coefficient ( μ ) is equal to τ/σ . However, further evaluation of previous testing showed that the coefficient of friction relative to the crack surface varied considerably with the amount of slip, an approximate value of between 0.6 and 0.7, which showed that it was more suitable to define the coefficient of friction in terms of the crack-opening path [ 11 , 12 , 13 , 14 ].…”

“…shape vector applied to the element's DOFs. By applying Equation(13) to the global stiffness matrix, and performing the matrix multiplication, the following equations can be written:…”