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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