6.9. The short beam shown in Fig, P6.9 cantilevers from a supporting column at the left. The beam must carry a calculated dead load of 2.0 kips/ft including its own weight and a service live load of 2.6 kips/ft. Tensile flexural reinforcement consists of two No. 10 (No. 32) bars at a 21 in. effective depth.Transverse No. 3 (No. 10) U stirrups with 1.5 in. cover are provided at the following spacings from the face of the column: 4 in., 3 at 8 in. 5 at 10.5 in.Within the beam-column joint. No. 4 (No. 13) closed ties are provided at an 8 in. spacing, with the first tie located 2 in. below the center line of the hooked bar. (a) If the flexural and shear steel use f. = 60.000 psi and if the beam uses lightweight concrete having f'c=4000 psi, check to see if proper development length can be provided for the No. 10 (No. 32) bars. Use the simplified development length equations, Eq. (6.6a) or (6.6b), as appropriate. (b) Recalculate the required development length for the beam bars using the basic Eq. (6.5). Comment on your results. (c) If the column material strengths are f, 60,000 psi and f = 5000 psi(normal weight concrete), check to see if adequate embedment can be provided within the column for the No. 10 (No. 32) bars. If hooks are required, specify detailed dimensions.

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