A numerical technique based on the theory of plasticity is developed to predict an optimum failure surface generatrix and concrete breakout capacity of single anchors away from edges under tensile loads. Concrete is regarded as a rigid, perfectly plastic material obeying a modified coulomb failure criteria with effective compressive and tensile strengths. The failure mode is idealized as an assemblage of two rigid blocks separated by failure surfaces of displacement discontinuity. Minimization of the collapse load predicted by the energy equation produces the optimum shape of the failure surface generatrix. A simplified solution is also developed by approximating the failure surface as two straight lines. The effect of different parameters on the concrete breakout capacity of anchors is reviewed using the developed mechanism analysis, ACI 318-05, and test results of 501 cast-in-place and 442 post-installed anchor specimens. The shape of failure surface and concrete breakout capacity of anchors predicted by the mechanism analysis are significantly affected by the ratio between effective tensile and compressive strengths of concrete. For anchors installed in concrete having a low ratio between effective tensile and compressive strengths, a much larger horizontal extent of failure planes in concrete surface is predicted by the mechanism analysis than recommended by ACI 318-05, similar to test results. Experimental concrete breakout capacity of anchors is closer to the prediction obtained from the mechanism analysis than ACI 318-05. ACI 318-05 provisions for anchors sharply underestimate the breakout capacity of cast-in-place and post-installed anchors having effective embedment depths exceeding 200 and 80 mm (7.87 to 3.15 in.), respectively, installed in concrete of compressive strength larger than 50 MPa (7250 psi).

Nonlinear explicit finite element (FE) simulations are used to study the axial collapse behavior of multi-corner. single- and multi-cell crush tubes under quasi-static and dynamic loading conditions. It is shown that the higher hardening modulus and yield stress increases the crush force and its resulting energy absorption. Moreover, the multi-cell tubes are found to have complicated collapse modes because of the geometrical complexity of the corner region unlike single-cell tubes. it was also shown that the stress wave propagation has a significant effect on the formation of crush modes in the tubes without imperfections whereas this effect can be ignored in tubes with imperfection or trigger mechanism. An analytical formula for the prediction of mean crush force of multi-corner multi-cell tubes is derived based on the super folding element theory. The analytical predictions for the mean crush force are found to be in good agreement with the FE solutions. Results also show a strong correlation between the cross-sectional geometry and the crash behavior with the method of connecting the inner to the outer walls having large influence on the energy absorption.