Dr. Mohammed E. Haque, P.E. (Deflection) Page 1 of 4 DEFLECTION A st - PDF document

1 | Page DEFLECTION r. Haque’s Lecture Notes DEFLECTION A structure must be serviceable in addition to being safe. A serviceable structure performs satisfactorily without causing any discomfort or perceptions of un - safety for the occupants or users of the structure. For a beam, being serviceable usually means that the deformation (primaril y vertical sag) must be limited. According to International Building Code (I B C 20 15 ), some of the typical deflection limits (ref: TABLE 1604.3 DEFLECTION LIMITS) are : Members Max. Live Load defl. Max. dead+live load defl. Max. Snow or Wind Load defl. Roof Beam: Supporting plaster ceiling l / 360 l / 240 l / 360 Supporting non - plaster ceiling l / 240 l / 180 l / 240 Not supporting a ceiling l / 180 l / 120 l / 180 Floor Beam l / 360 l / 240 ---------- Farm buildings --------- l / 180 ---------- Greenhouses --------- l / 120 ---------- Note: l = Span Length The limits shown above for deflection due to dead + live loads do not apply to steel beams, because the dead load deflection is usually compensated by cambering . Camber is a curvature in the opposite direction of the dead load deflection curve. When the dead load is applied to a cambered beam, the curvature is removed and beam becomes level. Therefore, the live load deflection is of concern in the completed structure. 2 | Page r. Haque’s Lecture Notes DEFLECTION EXAMPLE 1: Compute the dead load and live load deflections for the floor beam, W 18X35 as shown in fig. Check whether the floor beam is satisfactory considering deflection criterion according to IBC. SOLUTION:  D = (5/384) [(0.5+0.035)/12] (30x12) 4 /(29000x510) = 0.659 in  L = (5/384) [0.55/12] (30x12) 4 /(29000x510) = 0.678 in Total deflection = 0.659+0.678 = 1.337 in The max. permissible live load deflection = l /360 = (30x12)/360 = 1.0 in� 0.678 in. OK The max. permissible dead + live load deflection = l /240 = (30x12)/240 = 1.5 in� 1.337 in. OK [ Note: For a cambered steel beam, no need to check the dead +live lo ad deflection criteria] The beam satisfies the deflection criterion. Service D = 500 lb/ft.; Service L =550 lb/ft. l = 30 ft. W 18 X 35 w l 4 E I 5 384  = 3 | Page DEFLECTION r. Haque’s Lecture Notes 1/3 l P l 3 E I 0.0357  max = M max l 2 E I  max = 0.5 l P l 3 E I 1 48  max = M max l 2 E I 1 12  max = l /4 P l 3 E I  max = M max l 2 E I  max = l w l 4 E I 5 384  max = M max l 2 E I 5 48  max = Maximum Deflection for some common loading conditions w 0.5 l P P P 1/3 l 1/3 l 0.107 P P P l /4 l /4 l /4 0.0495 0.099 4 | Page r. Haque’s Lecture Notes DEFLECTION EXAMPLE 2 : (a) Check whether the floor beam is satisfactory considering deflection criterion according to IBC. (Max. Live Load defl ection = l /360)  L = (5/384) [0.55/12] (30x12) 4 /(29000x510) + 0.0357[5x(30x12) 3 ] /(29000x510) = 0.6777 + 0.563 1 = 1.2 408 in The max. permissible live load deflection = l /360 = (30x12)/360 = 1.0 in .2 408 in. NG The beam DOES NOT satisfy the deflection criterion. (b) Select a W - shape to satisfy the live load deflection criteria. Find required moment of inertia, I 1.2408 x 510/(I) = 1.0 I = 632.82 in 4 Look for I = 632.8 2 or slightly above in AISC Table, W 18 X 46 (I=712);  L = (5/384) [0.55/12] (30x12) 4 /(29000x712) + 0.0357[5x(30x12) 3 ] /(29000x712) = 0.485 + 0.403 = 0.888 in The max. permissible live load deflection = l /360 = (30x12)/360 = 1.0 in� 0.888 in. O K. Service L=550 lb/ft. l = 30 ft. W 18 X 35 10 ft. 10 ft. L= 5 kips L = 5 kips