Deflection of Beams In addition to being safe, the structure must be serviceable ; Serviceable structure is one that performs satisfactorily, not causing.

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Presentation transcript:

Deflection of Beams In addition to being safe, the structure must be serviceable ; Serviceable structure is one that performs satisfactorily, not causing any discomfort such as excessive deflection, vibrations, cracking of plaster or glass, etc. AISC provides little guidance on deflection in chapter (L), but other building codes provides the following criteria: Plastered construction Unplastered floor const. Unplastered roof const. When L = span length (preferably in inches), and the deflection is combined effect of service dead load and service live load (un factored deflection) = s B-26

Example on Deflection Criteria Example B – 9 Select a standard W-shape of Fy = 50 ksi steel to support 5 k/ft live load. Lateral support is continuous. The permission live load deflection is L/360 Solution: 30' 5k/ft live load L w L/2  Assume beam wt. = 100 lb/ft Wu = 1.2 WD + 1.6 WL = 1.2  0.1 + 1.6  5 = 8.12 k/ft. Since fall lateral bracing, assume compact section:- b Mn = b Mp = b Fy Zx  Mu Check deflection: Select W27 x 84 from table (3.2) page (3-15). B-27

Example on Deflection Criteria Example (contd.) Since deflection control the design, we select a section for deflection criteria from (table 3.3) as follows: From table (3 – 3) page (3 – 21) Select W 30  90 with Ix = 3610 in4 Note: Deflection of beams is not a function of the grade of steel used, rather it is a function of load, span and section moment of Inertia. B-28

Unbraced beam Selection Example Select a W shape made of A572-Gr 50 steel to support live loads as shown below. The maximum deflection shall not exceed L/240. Lateral support at ends only. Solution :- If we ignore self wt. of beam, then MA = MB = MC = Mmax = 620 = 120 k·ft. Cb = 1 Mu = 1.6  Mmax=1.6  120 = 192 k·ft Enter selection charts with Lb = 24 ft. Select W12  53 b Mn = 208k·ft > 192k·ft OK. include beam weight: Mu = 192+(1.2)⅛0.053  (24)2 = 197 k·ft OK 24' 6' 20k A B C x B-29

Unbraced beam Selection Example (contd.) Check Deflection: Maximum permissible deflection = From beam tables (case (9) table 3 – 23 page 3 – 213) where: Evan if dead load deflection is considered, P = 20k (service live load) a = (6  12) in. l = (24  12) in. = span = 1.11 in < 1.2 in O.K. B-30