A beam cross-section is limited to the size shown. Determine the required area of reinforcement for service load moments Mp = 400 ft-kips and ML = 250 ft-kips. Check crack control requirements f' = 4000 psi (normalweight) f = 60,000 psi d'=2.5" b = 12" A's d₂= 32"

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Combined Stresses Given Hollow Steel Section (HSS) that is 4"x6" and 1/2" thick, with axial and transverse loading shown, determine the total normal stress at a. The 5k load on the bottom of the beam b. At the mid-span in the middle of the beam C. At the 10k load on top of the beam 5k 10k A 5' 10' 5' B CENTROID 4" 5 k 3k 8k 6" 2' 6.25k 8.75k +6.25k SECTION +1.25k 'V" -8.75k +43.75k-ft. +31.25k-ft. 'M' 8k 5 k + tension P = Ok %3D

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'-