Flexural response

Typical resistance-deflection curve for flexural response of concrete elements. 

Reinforced concrete is a complex material to model due to the brittle nature of concrete and non-homogenous properties. Although sophisticated methods are available to model crack propagation and other responses, simplified methods are normally used in blast design of facilities. These methods are based on a flexural response and rely on elimination of brittle modes of failure. To achieve a ductile response for concrete, proper proportioning and detailing of the reinforcing is necessary. 

DIF values vary for different stress types in both concrete and steel for several reasons. Flexural response is ductile and DIF values are permitted which reflect actual strain rates. Shear stresses in concrete produce brittle failures and thus require a degree of conservatism to be applied to the selection of a DIF. Additionally, test data for dynamic shear response of concrete materials is not as well established as compressive strength. Strain rates for tension and compression in steel and concrete members are lower than for flexure and thus DIF values are necessarily lower. 

Structural dements resist blast loads by developing an internal resistance based on material stress and section properties. To design or analyze the response of an element it is necessary to determine the relationship between resistance and deflection. In flexural response, stress rises in direct proportion to strain in the member. Because resistance is also a function of material stress, it also rises in proportion to strain. After the stress in the outer fibers reaches the yield limit, (lie relationship between stress and strain, and thus resistance, becomes nonlinear. As the outer fibers of the member continue to yield, stress in the interior of the section also begins to yield and a plastic hinge is formed at the locations of maximum moment in the member. If premature buckling is prevented, deformation continues as llic member absorbs load until rupture strains arc achieved. 

Flexural response of (a) monolithic Si3N4 and (b) Si3N4/BN FM after thermal shock test. Monolithic Si3N4 showed brittle fracture, while fibrous monolith showed graceful fracture due to its unique architecture (adapted from ref. [29]). 

Ahmed, S.F.U., Maalej, M. and Paramasivam, P. (2006). Flexural responses of hybrid steel-polyethylene fibre reinforced cement composites containing high volume fly ash. Journal of Construction and Building Materials, 21 1088-1097. 

Modeling of Nonlinear Flexural Responses in Slender Walls... 

Overall, other than underestimation of compressive strains, the MVLEM proves to be an effective modeling approach for the flexural response prediction of slender RC walls, as the model provides good predictions of the experimentally observed global and local responses, including wall lateral load capacity and lateral stiffness at varying drift levels, yield point, cyclic properties of the load-displacement response, rotations (average over the region of inelastic deformations), position of the neutral axis and tensile strains. 

Allred R E (1981) The effect of temperature and moisture content on the flexural response of Kevlar/epoxy laminates Part II. [ 45,0/90] filament orientation, J Compos Mater 15 117-132. 

Kaewunruen, S., and A. M. Remennikov. Effect of a Lai e Asymmetrical Wheel Burden on Flexural Response and Failure of Railway Concrete Sleepers in Track Systems. Engineering Failure Analysis 15, no. 8 (2008) 1065-1075. 

Shear failure mode, S - initial shear capacity (Yo), i.e., not affected by cyclic degradation, is lower than the plastic shear capacity (Vp), and flexural response is modified by a preemptive shear failure in the elastic response phase of the element. Deformation capacity (i.e., drift, chord rotatirai) is very limited. Subsequent response of the element is characterized by a strictly degrading behavior with significant shear strength reduction and a consequently loss of axial load-carrying capacity see Fig. 2a. 

Flexure-shear failure mode, FS - Vq is higher than Vp, and flexural response is characterized by an inelastic phase. However, if degraded shear strength (VJ), the lower red dotted branch in Fig. 1, is lower than Vp, the inelastic flexural response is modified by a shear failure that occurs at an intermediate shear strength... 

Flexural failure mode, F-Vdis higher than Vp, and flexural response is not affected by... 

The proposed analytical model for predicting the flexural response of existing R/C members strengthened with concrete jacketing under... 

Comparison with Experimental Data The validity of the proposed analytical model for predicting the flexural response of R/C jacketed members was examined by comparing (i) for monotonic loading, the analytical lateral load versus lateral displacement curves along with the envelope experimental curves of the recorded lateral load versus lateral displacement hysteretic loops from various experimental studies (Thermou et al. 2007) (the monotonic moment-curvature response curves were derived according to the analytical model and then converted to force-displacement response curves). In Fig. 10, the experimental lateral load versus drift curves of a representative number of test specimens are compared to the corresponding analytical curves (ii) For cyclic loading, the... 

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