ARCH 264/564 Structural Elements

Assignment #3

Issued April 1, 2008.
Due: April 8, 2008

For problems 1-3, use f'_c = 5 ksi and f_y = 60 ksi. Assume a continuous reinforced concrete floor system consisting of T-beams with a clear span of 30-feet, and 1-way slabs spanning between the T-beams. The T-beams are spaced at 15-feet on center. The slab thickness, h = 8", and the portion of the T-beam below the slab has a height of 16" and a "web" width of 12". The slab cover, measured to the centerline of steel, is 1 inch; while the beam cover is 2-1/2". Use a live load = 100 psf, and a dead load consisting of slab and beam weight only (with concrete @ 150 pcf). See the typical plan and cross-section below.
section through T-beam

1. Slab design. Using "moment values" from Table A-8.7, and No. 3 bars, find the reinforcing bar spacing for both negative and positive moment. Use the "clear span" in computing moment values. Check if the spacing is within allowable limits. Also check that slab thickness is acceptable for deflection control (Table A-8.2). Do not interpolate in Table A-8.9; just use closest value for an approximate solution.

2. T-beam design. Using "moment values" from Table A-8.7, select bars for both negative and positive moment. Use the "clear span" in computing moment values. Do not interpolate in Table A-8.9; just use closest value for an approximate solution. Check that steel ratio is within acceptable limits. Check bar fit (Table A-4.11). Check that T-beam thickness is acceptable for deflection control (Table A-8.2).

3. Sketch. Sketch the T-beam section for negative and positive moment. Include reinforcing bars and important dimensions.

4. Rectangular beam design. Using f'_c = 3 ksi and f_y = 60 ksi, and assuming a design moment, M_u = 235 ft-k, find the effective depth of a rectangular beam of width, b = 16", by assuming a steel ratio of 0.00667 (that is, approximately half the maximum steel ratio). Round the answer to the closest inch. It is not necessary to find the steel area or select bars.