ARCH 264/564 Structural Elements

Assignment #3r

Issued April 8, 2008.
Due: April 10, 2008 (not collected or graded)

For problems 1-3, use f'_c = 4 ksi and f_y = 60 ksi.

1. Reinforced concrete beam-columns: design of rectangular section with dimensions known
Find the required steel area and select 4 bars (preferable) for a 16" x 16" beam-column supporting a design load, P_u = 768 k; and a design moment, M_u = 136.53 ft-k. Assume 3" of concrete cover measured to the longitudinal steel centerline, and choose the closest value for ϒ. Check bar fit using "column" charts in Table A-4.11.

2. Reinforced concrete beam-columns: design of circular section with dimensions known
Find the required steel area and select 8 bars (preferable) for a 16"-diameter beam-column supporting a design load, P_u = 502.6 k; and a design moment, M_u = 107.23 ft-k. Assume 3" of concrete cover measured to the longitudinal steel centerline, and choose the closest value for ϒ. Check bar fit using "column" charts in Table A-4.11.

3. Reinforced concrete beam-columns: design of rectangular section with one dimension and reinforcement ratio known
Find the missing dimension, b, and the required steel area; and select 16 bars (preferable; may be split equally between 2 sizes) for a beam-column with dimension, h = 42", supporting a design load, P_u = 3,150 k; and a design moment, M_u = 1,764 ft-k. Use reinforcement ratio, ρ_g = 0.04. Assume 2-1/2" of concrete cover measured to the longitudinal steel centerline, and choose the closest value for ϒ. Check bar fit using "column" charts in Table A-4.11, based on the largest rebars used.

4. Reinforced concrete diagonal tension (shear)
For this problem only, assume f'_c = 3 ksi and f_y = 60 ksi. Use No. 3 stirrups.
A continuous beam with clear spans of 22 feet supports a uniformly-distributed load such that the maximum shear at the face of supports, V_u = 95 k. Consider one such "shear force triangle" defined by this maximum value of 95 k, and a length of one-half the span, or 132 inches. For cross-sectional dimensions of b = 14" and d = 27", find the following:

Minimum stirrup spacing.
Maximum stirrup spacing, and location (distance from beam centerline where this maximum spacing may begin)
Value of shear where no stirrups are needed and location (distance from beam centerline where "no stirrups" may begin)

5. Reinforced concrete diagonal tension (shear)
For this problem only, assume f'_c = 5 ksi and f_y = 60 ksi. Use No. 4 stirrups.
A simply-supported beam with a clear span of 30 feet supports a single concentrated design load at mid-span, P_u = 200 k. Neglecting the weight of the beam itself, find the spacing and distribution of web steel (stirrups). The cross-sectional dimensions are b = 16" and d = 29".