Design of Beams for Moment

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Design of Beams for Moment

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1. Design of Beams for Moment Moayyad Al Nasra, PhD, PE 1 (c) Al Nasra

2. Design of Beams for Moment Full-Lateral Support of the Top Flange Procedure Calculate the max. Factored moment, Mu Calculate the required plastic modulus, “Z” Zrequired= Mu/FbFy, Fb=0.90 Select the lightest section from AISC tables Check Compactness 2 (c) Al Nasra

3. 3 (c) Al Nasra

4. Compactness A compact section is a section that is capable of developing a fully plastic stress distribution before buckling A non-compact section is a section in which the yield stress can be reached in some, but not all, of its compression elements before buckling occurs. 4 (c) Al Nasra

5. Example Select the lightest W beam to support the following loads 4 in. concrete slab 20 psf dead load 40 psf live load Fy= 50 ksi 5 (c) Al Nasra

6. 6 (c) Al Nasra

7. Solution Dead load = 20psf(10-ft)+(4/12 ft)(150 pcf)(10-ft) = 700 lb/ft Assume beam self weight = 50 lb/ft Total dead load =750 lb/ft Live load = 40 (10) = 400 lb/ft Wu= 1.2(750)+1.6(400) =1540 lb/ft Mu= wul2/8 = (1540 lb/ft)(20ft)2/8 = 77000 lb.ft =77 k.ft Zx,required= Mu/FbFy = (77 k.ft)(12 in./ft)/(0.90(50)) = 20.53 in3 Select a section using AISC steel design manual, 13th edition, LRFD part PP. 1-24 , pick a section with Zx= 21.67 > Zx, required= 20.53 in3, select W10X19 PP. 3-75, under beam for 20-ft length Pick W10x19, Load = 32.4k > 1.54 k/ft(20-ft)=30.8 k PP. 3-129 under beam , locate Mu = 77 k.ft, and unbraced length lb=0, read up and to the right, read W10x19. 7 (c) Al Nasra

8. PP. 1-24 , pick a section with Zx= 21.67 > Zx, required= 20.53 in3, select W10X19 W shapes, Dimensions, Table 1-1, AISC, 13th edition, PP. 1-24 8 (c) Al Nasra

9. under beam for 20-ft length Pick W10x19, Load = 32.4 > 1.54(20)=30.8 k Maximum Total Uniform Loads, Kips, W shapes, Table 3-6, AISC 13 ed., pp. 3-75, Fy=50 ksi, PP. 3-75, 9 (c) Al Nasra

10. PP. 3-129 under beam , locate Mu = 77 k.ft, and unbraced length lb=0, read up and to the right, read W10x19. Available Moment vs. Unbraced length, W shaped, Table 3-10, AISC, Fy=50 ksi, Cb=1, PP. 3-129

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