Description

A deep, diagonally-reinforced concrete coupling beam under a full cyclic loading protocol out to 12% chord rotation, reproducing test specimen CB24D, including its strength loss after the diagonal bars and hoops fracture.

Reference

Naish, Fry, Klemencic & Wallace (2013), ACI Structural Journal 110-S86; raw cyclic response digitized via DesignSafe-CI (NEES-2012-1100).

Model

Two elastic beam segments, each at a reduced effective stiffness (30% of the gross-section stiffness, following ASCE 41 §6.7.2 guidance for coupling beams), flanking a concentrated shear hinge at the beam's midspan. The hinge's force–deformation envelope was calibrated directly to the specimen's own measured cyclic response. The assembly is fixed at one end and driven through a multi-level cyclic displacement protocol at the other, matching the specimen's own tested drift levels up to 12%. The hinge envelope falls away past 8% drift, with the lower negative-direction strength as measured, and a cumulative-degradation setting calibrated to the test makes each repeat cycle weaker than the last.

Shear hinge backbone (calibrated to the specimen)

Loading protocol applied

Response comparison

Full loading history, physical test vs. vfopro simulation.

Comparison

Conclusion

The beam now runs the specimen’s complete protocol through 12% chord rotation (4.3 in), past the fracture of the diagonal bars and hoops. Up to 8% drift, 23 of 24 envelope checks are within the 10% criterion, and all of them from 0.25 in upward are within about ±10% of the test (mostly within ±5%). The one band outside is the first, 0.0–0.25 in positive direction, where the simulated beam is about 14% below the test (the test reaches a higher force at very small displacement than the model’s initial stiffness produces). The strength loss is captured: at the 8% peak the first cycle is within 1.3% of the test in both directions, and the weaker second cycle (a 20–27% drop in the test) is within about 1%. At 10% drift the first-cycle peaks are within about 5–7% (+82 vs +78 kip, −66 vs −62 kip), and at 12% the positive peak is within about 7% (+51 vs +47 kip) while the negative peak is small in absolute terms (−17 vs −14 kip). What the model does not reproduce is how much weaker the second cycle is at 10% drift: the test drops by about 40% (+47 and −17 kip) while the model drops by about 23% (+63 and −40 kip), so those two checks fall outside the 10% criterion. The test’s fracture is abrupt, and its force at the displacements between the 8% and 10% peaks is erratic, so the check here compares each cycle’s peak force rather than every displacement band past 3.0 in. Pinching (the pinched shape of the reloading branches) was not enabled, so loop shape and energy dissipation are still to be validated. The envelope beyond 8% drift and the second-cycle loss are calibrated to this specimen; another beam needs its own values.