PSI - Issue 64

Chris Hendy et al. / Procedia Structural Integrity 64 (2024) 206–213 Hendy C/ Structural Integrity Procedia 00 (2019) 000 – 000

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The approach presented in this paper utilises a ULS stress block within the hinge throat at the point of failure after crack formation. This is consistent with the findings of Leonhardt and Reimann (1965) that the uncracked throat section is generally able to resist the stresses until the crack reaches the middle of the throat. The compressive stress diagram in the hinge throat is simplified into a rectangular stress block with constant pressure and a reduced depth equal to x' = 0.8x as shown in Fig. 2.

Fig. 2: ULS stress block in throat

The axial force in the hinge at failure is given by: = , ′ Therefore: ′ = 0.8 = , ⁄ and The curvature = 2, = 2, , 1.25 And finally the ultimate limit state hinge rotation is given by: ∅ = ℎ = 2, , ℎ 1.25 Where: ’ is rectangular stress block compression width of hinge

= 1.25 , ⁄ ≤

(1)

is distance between the most compressed fibre and neutral axis h e is equal 125 mm from CS468 cl.3.15 2,c is the confined concrete strain at failure determined from EN 1992-1-1 which should be safely taken as the unconfined strain 2 as noted below f d,c is the confined concrete stress at failure determined from EN 1992-1-1 which should be safely taken as the unconfined stress f d as noted below ∅ is hinge ultimate rotation capacity at ULS Note: Since this ULS model acknowledges the presence of tensile stresses in the hinge throat, the assumption of confined concrete conditions provided by a hypothetical triaxial compressive stress is difficult to justify. Therefore, this check should be conservatively undertaken considering the unconfined concrete conditions only, unless a triaxial stress state can be justified. The results of Markic and Kaufmann (2023) however suggest that this triaxial constraint is present in practice.