PSI - Issue 44

Maria Teresa De Risi et al. / Procedia Structural Integrity 44 (2023) 966–973 De Risi, Ricci, Verderame / Structural Integrity Procedia 00 (2022) 000–000

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on the panel, and the shear stress (τ j ) is calculated from joint shear, evaluated through equilibrium conditions of the subassemblage. Further details are provided in (Verderame et al., 2022). A comparison between the envelopes of the τ j /√f c – γ j responses is reported in Figure 4. For specimens S, CAM1 and CAM4 an unloading phase is present, highlighting that the softening in the response of the subassemblage was not controlled by the joint panel, and thereby the shear distortion of this element decreased – in the softening phase – with increasing drift demand. On the contrary, a softening phase, with increasing γ j , was observed in specimens whose collapse was controlled by joint failure, i.e., NS, 2NS and CAM3. Note that the τ j demand was limited by flexural strength of the adjacent beam in the case of BJ failure; for this reason, no significant strength increase is observed – both at global (subassemblage) and local (joint panel) level – when CAM1 is compared to NS. The difference in τ j /√f c between CAM4 and NS/S/CAM1 specimens is mostly attributable to the difference in f c . On the contrary, looking at the comparison between the τ j /√f c – γ j responses of specimen 2NS and the corresponding strengthened specimen CAM3, the increase in strength provided by the strengthening is clearly highlighted. Values of τ j /√f c and γ j at the characteristic conditions of joint cracking, beam flexural yielding (if attained) and peak resistance are reported in Table 2. Table 2. Normalized joint shear stress (τ j /√f c ) at joint cracking, beam’s first yielding and peak resistance and corresponding joint shear strain (γ j ) [NA = not available; * : should be interpreted as lower bound values]. Test ID failure mode γ j,cr ( % ) τ j,cr /√f c ( MPa 0.5 ) γ j,y ( % ) τ j,y /√f c ( MPa 0.5 ) γ j,peak ( % ) τ j,peak /√f c ( MPa 0.5 )

NS

BJ

-0.16 -0.31 -0.53 -0.37 -0.55 +0.20

-0.49 +0.50 +0.54 -0.66 -0.86 +0.77

NA/-0.31

NA/-0.53

+0.43/-0.37 +1.20 * /-0.97 * +0.31 * /-0.23 * +0.44/-0.99 +1.27/-1.05 +0.32 * /-0.25 *

+0.53/-0.55 +0.58 * /-0.60 * +0.59 * /-0.60 * +0.99/-1.00 +1.24/-1.20 +0.84 * /-0.84 *

S

B B

+0.39/-0.25 +0.10/-0.18

+0.53/-0.53 +0.53/-0.53

CAM1

2NS

J

NA/NA

NA/NA

CAM3 CAM4

BJ

+0.67/-1.04 +0.11/-0.06

+1.20/-1.20 +0.74/-0.74

B

Note that values of τ j /√f c at peak should be regarded carefully, since in some cases (NS, CAM3) they correspond to a peak condition statically controlled by beam flexural strength (BJ-failure), and in some other cases (S, CAM1, CAM4) they do not even properly correspond to a peak condition, due to the unloading response of the joint panel (B failure). As far as the cracking condition is concerned, note that an increase in (the absolute value of) τ j /√f c is observed with increasing horizontal compression (beneficial effect of prestressed strips) and with decreasing f c . The latter trend is expected if the tensile strength, that should be equated by the principal tensile stress σ nt at cracking, is assumed as depending on √f c only (i.e., if σ nt /√f c at cracking is constant), and recalling that the vertical stress is equal for all tests.

joint shear stress-strain evelope comparison

1.5

1

0.5

0

-0.5

-1

-1.5

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

joint shear strain, j [-]

(a) (b) Fig. 4. Comparison of joint shear stress-strain response envelopes (dashed lines correspond to unloading) at ±0.06 (a) and ±0.02 (b) γ j . Finally, it is possible to analyze the strain in the prestressed steel strips of the strengthened specimens, reported in Figure 5. Theoretically, the maximum strain demand (averaged between the three layers) should be expected when the joint shear demand (and, consequently, the beam shear) is highest (“peak” condition reported in Figure 5), and should be equal to ε 0.2 (corresponding to the assumed strength f 0.2 ) – if an optimum design was carried out.

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