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Unanchored U-wrapped externally bonded carbon-fiber-reinforced polymer (CFRP) fabrics are widely used to increase the design shear strength of existing reinforced concrete slab-on-beam structures, but current design models do not accurately predict the degree of enhancement. Experimental investigations further indicate that some T-beams retrofit with externally bonded CFRP fabric fail at lower shear loads than nominally identical nonretrofit reference counterparts, suggesting a negative experimental CFRP contribution. This work finds a new application for the upper-bound theorem of plasticity in analyzing the problem of U-wrapped externally bonded CFRP-retrofit beam behavior. The study provides insight into the poor historical prediction of the CFRP contribution, and demonstrates the limitations of a widely used experimental approach to determining this contribution. The analysis suggests a new way of thinking about the behavior of slab-on-beam structures retrofit with unanchored U-wrapped externally bonded CFRP. The upper-bound plastic analysis provides better predictions of retrofit shear capacity than some widely used design models, indicating that this approach can lead to better design of retrofit interventions in future. This work proposes a new design limit on enhancement that can reduce the likelihood of unsafe design in practice.