CIVE 447/847 - Spring 2022 Homework #4 Due: 03/11/24 Alignment Chart 1. Use the alignment chart to determine the effective length factors for Columns AB and BC of the unbraced

frame. Assume that the beams are 12-in. × 18-in. and the columns are 12-in. × 12-in. Use the ACI code for calculating the moment of inertia (Columns will have 70% and beams will have 35% of the moment of inertia for gross cross sections). Use = 10 for the hinged base. Use the alignment chart provided. C B 30' 30' 30' 12' 12' 2. The following structure is being designed. To control the drift in the structure, the engineer of record has decided to stiffen the beams in one of the bays as shown. This beam can be considered to be rigid. Determine if slenderness needs to be considered for Column A. Use the alignment chart provided. Structural Information: f=4,000 (psi), and fy= 60 (ksi) Columns: 14-in. × 14-in. Elevation view of structure: Rigid Beam Column A Beams: 14"x20" 20' 16' Beams: 14"x24" 16' Beams: 14"x24" # 30' 30' 20' 20' Sway Frame Design 3. A six-floor (six-story) reinforced concrete frame building is supported on columns placed on a grid spaced 30 ft in the N-S direction and 20 ft in the E-W direction. At the first level, the distance from the top of the footings to the top of the first story is 18 ft. For other levels, the story height measured from the top of bottom slab to the top of the slab above is 14 ft. The columns are 20 in. by 20 in. Columns are connected in both directions by beams with an overall depth of 2 ft and a web width of 1 ft. The slab thickness is 6 in. for all floors. The standard compressive strength of concrete used in this building is 4,000 (psi). (4---- 6" (3) (2) ---- N B All Columns 20" x 20" 3@20'-0"-60'-0" 6" 30'-0" 30'-0" 30'-0" Plan View of the Building a) What is the moment of inertia of the beams? (Note: the effective width of the beams with flanges is 48 in.) 24" 48" 12" Typical Beam Section ✓ I 6" slab 6" Assume that the frame is unbraced and bending is about the E-W axis. In addition, assume that footings provide absolute ideal fixity at the base of the building. b) What is the effective length factor in Column B2 at the third level? c) What is the effective length factor in Column B1 at the third level? d) Assuming that there are no sustained loads on the columns, what is the effective length in Column B2 at the first level? f) e) What is the buckling load for all columns about the E-W axis bending at the first level? If the dead load is 0.1 kip/ft² and the live load is 0.06 kip/ft² on floors and the roof, what is the total factored axial load at the first level? (Use Load Combination of 1.2D + 1.0W + 1.0L) g) If the unfactored wind load is 30 lbf/ft² and the first-story column drift is 0.3 in., what would be the Q factor in ACI 318 at the first level? (Assume that the foundation carries half of the first story's wind load) h) What would be the moment magnifier using the Q factor calculated in (g) for the first level? i) What would be the moment magnifier if buckling strength of all columns at the first level is used in calculation for the sway frame system? If the owner and designer of the building decided to add a wall to the six-story building so that the building is braced, j) What would be effective length factor for bending about the E-W axis in Column B2 at the first level? k) If the unfactored axial forces from dead and live loads a particular column are 200 kips and 50 kips, respectively, what is the value of Bans? Note: For the calculation of 1 to compute the effective length factor, use the column height provided. For the calculation of buckling load, the unsupported length should be the height with beam depth subtracted from the column height.