Detailed crack‐based assessment of a 4‐m deep beam test specimen

Abstract

When shear cracking occurs in existing reinforced concrete deep members, engineers are faced with the challenge of determining the safety of the members. This paper presents a crack‐based assessment approach that utilizes the Two‐Parameter Kinematic Theory (2PKT) as a framework for the assessment of lightly reinforced concrete deep beams. The paper presents three assessment approaches with progressively increasing levels of approximation (LoAs). The first level of approximation (LoA I) involves using the 2PKT in a predictive manner for situations where the crack shapes are unknown, LoA II improves upon LoA I by incorporating more detailed modeling of the strain in the transverse reinforcement at the location of the critical cracks, and LoA III includes the details of LoA II but also uses the detailed crack geometry as an input in the assessment. Each of the LoAs is presented and compared with experimental data from a 4‐m deep beam test in the literature. The shear carrying mechanisms determined from the kinematic model are evaluated and compared across LoAs. Finally, the paper utilizes LoA III to study the size effect in shear for deep beams. The results quantify the influence of aggregate interlock on the size effect in shear critical deep beams.

Fatigue behavior of deep concrete beams with critical shear cracks

“…The two DOFs are the average strain along the bottom flexural reinforcement, ε t , avg , and the transverse displacement of the critical loading zone, Δ c . This model has been validated with measured displacement fields and crack data, showing adequate results 13,14 . In fact, it is DOF Δ c that characterizes the behavior of the CLZ and the shear behavior of deep beams in general.…”

“…This model has been validated with measured displacement fields and crack data, showing adequate results. 13,14 In fact, it is DOF Δ c that characterizes the behavior of the CLZ and the shear behavior of deep beams in general. As evident from Figure 9, Δ c is associated with vertical crack displacements, which are in turn associated with slip displacements and aggregate interlock stresses across the critical diagonal crack.…”

“…More precisely, angle α CLZ is the inclination of the line connecting the bottom point of d CLZ to the approximate end of the CLZ along the crack. Trandafir et al 14 have proposed to estimate the length of this line at 3d CLZ ($162 mm), which results in an estimated angle α CLZ of 36 for beam P3. The crack diagram shows that displacement transducers DT-E and DT-F are outside the CLZ, and therefore the calculation of Δ c based on Equation ( 1) is valid.…”

“…An advanced crack‐based assessment approach for shear‐critical deep beams has been recently proposed by Trandafir et al 13,14 for monotonic loading conditions. This approach focuses on the main indicator of damage in deep members: shear cracks which extend from the supports to the loading points of the member.…”

“…Deep members can fail by inclined crushing of the compression region at the zone of loading (socalled critical loading zone, CLZ), by fatigue fracture of the stirrups, or by fatigue fracture of the longitudinal flexural reinforcement. [8][9][10][11][12] An advanced crack-based assessment approach for shear-critical deep beams has been recently proposed by Trandafir et al 13,14 for monotonic loading conditions. This approach focuses on the main indicator of damage in deep members: shear cracks which extend from the supports to the loading points of the member.…”