Design a rectangular section for the beam using the loads and a steel ratio of half the rho balanced. Beam weights are not included in the loads given. Show sketches of cross sections including bar sizes, arrangements, and spacing. Assume concrete weighs 23.5 kN/m3, fy = 420 MPa, and f’c = 28 MPa.

Calculate the uniform load w (in addition to the beam weight) that will cause the section shown to begin to crack if used as a 28-ft simply supported beam. Use normal weight concrete with L=4000 psi. f = 60,000 psi, E₁=29,000 ksi, and the reinforced concrete weight = 150 lb/ft³. 4 in. 28 ft 4 in. 22 in. 30 in. 2 in. 2 in. 3 #9 ● ||—12 in—-|

Given the concrete (f c=6000 psi) I-beam shown in Figure 1 for the given loading: -draw the shear & moment diagrams -determine Vmax & Mmax -using ASD (Allowable Stress Design) method, check to see if the given loading produces stresses within the given allowable range (check both Omax & Vmax) Using ACI 318-99, allowable stresses are -for flexure, f = .45f'c -for shear, v. = 1.1√f. (HINTS: 8² -note that the beam is symmetric about both axes -Ix for a triangle is (1/36)bh³+Ad² ) 30 kips 16' 10 kip/ft 22' 20 kips 3'-4' -1-6 -1'-6" Figure 1 1'-

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