19864541-Reinforced-Concrete-Design-Lecture-08-Doubly-Reinforced-Beams

19864541-Reinforced-Concrete-Design-Lecture-08-Doubly-Reinforced-Beams

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Unformatted text preview: Doubly reinforced beams CE 4108 – Concrete Structures Design Doubly reinforced beams • Beams with both tensile and compressive steel. • Compressive steel is sometimes required for small beam sections. • ACI 7.11.1: Compression steel must be enclosed by ties ties or stirrups. • ACI 7.10.5.1: Ties must be at least #3 for longitudinal bars #10 or smaller and at least #4 for larger longitudinal bars. • ACI 7.10.5.2: Ties may not be spaced farther than 16 bar diameters, 48 tie diameter or at least the dimension of the beam cross section. As = As1 + As 2 As 2 f y = A's f 's f‘s = compression steel stress a φM n = φ As1 f y d − + As 2 f y (d − d ' ) 2 Assuming compression steel yields: As f y = 0.85 f 'c β1cb + A's f y ( As − A's ) f y 0.85 f 'c β1b c= c − d' ε 's = 0.003 c Check if this is more than εy, as assumed. • If compression steel doesn’t yield: c − d' As f y = 0.85 f 'c β1cb + A's (0.003)(29,000) c Solve for c. ...
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19864541-Reinforced-Concrete-Design-Lecture-08-Doubly-Reinforced-Beams

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