Calculation for stiffness and crack of beams partially prestressed with unbonded CFRP tendons

In order to deduce unified expressed formulas of stiffness and crack width of concrete beams partially prestressed with unbonded CFRP tendons, the equivalent reduced coefficient of unbonded CFRP tendons is defined as the ratio of the stress increment of unbonded CFRP tendons to that of bonded steel bars. If the ratio of longitudinal tension reinforcement in the stiffness formula in current code is replaced by the ratio of the sum of the equivalent reduced area of unbonded CFRP tendons and the area of steel bars to effective cross-sectional area, and the area of total longitudinal tension reinforcement in the crack width formula in current code is replaced by the sum of the equivalent reduced area of unbonded CFRP tendons and the area of steel bars, the stiffness formula and crack width formula in accordance with current code can be developed. The calculated results by using these two formulas are in good agreement with test results.