General. Eqn. 1. where, F b-bbf = Allowable bending stress at the bottom of the beam bottom flange, ksi.
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1 COMPUERS AND SRUCURES, INC., BERKELEY, CALIORNIA DECEMBER 2001 COMPOSIE BEAM DESIGN AISC-ASD89 echnical Note Allowale Bending Stesses Geneal his echnical Note descies how the pogam detemines the allowale ending stesses using the AISC-ASD89 specification fo composite eams. he methodologies fo detemining the allowale ending stess fo oth the steel eam alone and the composite eam ae descied. Impotant note concening cove plates: his section descies how the allowale ending stesses ae detemined fo steel eams. When a cove plate is pesent, the pogam detemines the allowale stesses fo the eam as if the cove plate wee not pesent, except as noted in Note fo ale 1. Based on the allowale ending stess at the ottom of the eam ottom flange, -f, which the pogam detemines as descied in this echnical Note, the allowale ending stess at the ottom of the cove plate, -cp is taken as shown in Equation 1. whee, cp -cp f Eqn. 1 -f Allowale ending stess at the ottom of the eam ottom flange, ksi. -cp Allowale ending stess at the ottom of the cove plate, ksi. Yield stess of eam, ksi. cp Yield stess of cove plate, ksi. Geneal Page 1 of 7
2 Allowale Bending Stesses Allowale Bending Stess fo Steel Beam Alone his section documents the allowale ending stesses that the pogam uses when the steel eam alone (noncomposite) esists the ending. Allowale ending stesses ae povided fo oth compession and tension. Note: Allowale stesses fo composite eams ae descied in the section entitled Allowale Bending Stesses fo Positive Bending in the Composite Beam late in this echnical Note. he allowale ending stess fo the steel eam alone depends on the tpe of eam section, whethe the compession flange and the we ae, the ield stess of the eam and the unsuppoted length of the compession flange, L. ale 1 identifies the equations that ae used to calculate the allowale ending stess of the steel eam alone fo vaious conditions. ale 1 is ased on the equiements of Chapte, Section 1 in the AISC- ASD89 specification. he compact and equiements that the pogame uses fo the flanges, we and the cove plate (if it exists and is in compession) ae pesented in echnical Note Width-to-hickness Checks Composite Beam Design AISC-ASD89. In the lange and Cove Plate column of ale 1, if the flange o the cove plate is, the column ent is. Both the flange and the cove plate must e compact fo the ent to e compact. Allowale Bending Stess fo Steel Beam Alone Page 2 of 7
3 Allowale Bending Stesses ale 1 Equations Used the Pogam fo Allowale Bending Stess fo Steel Beam Alone pe of Beam Section Rolled I-shaped o channel section fom the pogam dataase Use defined (welded) section that is I-shaped o a channel lange and Cove Plate We Beam Unsuppoted Length of Compession lange 1 compact compact 5 ksi Lc compact compact > 5 ksi Lc compact No limit Lc compact 5 ksi Lc compact > 5 ksi Lc No limit Lc No limit > Lc compact compact 5 ksi Lc compact compact > 5 ksi Lc compact No limit Lc ale Desciptive Notes: 5 ksi Lc > 5 ksi Lc No limit > Lc Equation(s) fo, the Allowale Bending Stess 4 fo tension; lage of 7 o 8, as applicale and 9 fo compession 2 5 fo tension; lage of 7 o 8, as applicale and 9 fo compession 2, 1. See Equation 2 fo L c. 2. Equations 7 and 8 do not appl to channels.. o I-shaped eams, Equation 9 does not appl if the aea of the compession flange is less than the aea of the tension flange. o this check the aea of the cove plate is included as pat of the flange aea. Allowale Bending Stess fo Steel Beam Alone Page of 7
4 Allowale Bending Stesses In the fifth column of ale 1, the unsuppoted length of the compession flange is compaed to L c. he length L c is defined in Equation 2. 7 f L c smalle of Eqn. 2 and ( d A f ) he A f and f tems in Equation 2 ae the aea and width of the eam compession flange (not including cove plate even if it exists), espectivel. hese tems ae neve ased on the cove plate dimensions. he tem is the ield stess of the eam (not cove plate) he equations efeed to in the last column of ale 1 ae listed elow. whee 0. Eqn. f Eqn. 4 2t f f Eqn. 5 2t f k c 4.05 k, fo h/t w > 70, othewise k c 1 Eqn. 5a c ( h t ) 0.4 w 0.0 Eqn. In Equation, the pogam takes as the ield stess of the compession flange fo hid eams. When 102 * 10 C ( l ) 2 2 1,50 * 10 l C 510 * C Eqn. 7 Allowale Bending Stess fo Steel Beam Alone Page 4 of 7
5 Allowale Bending Stesses When l > 170 * 10 ( l ) 2 C 510 * 10 C 0.0 Eqn * 10 C 0.0 f Eqn. 9 ( ld A ) In Equations 7 and 8, the l tem in l/ is the unaced length of the compession flange. he tem is ased on the compession flange of the eam. his is significant when the dimensions of the top and ottom flanges ae diffeent. o olled sections, the tem is taken fom the pogam dataase. o usedefined (welded) sections, the tem is calculated using Equation 10a o 10. Equation 10a applies fo positive ending and Equation 10 applies fo negative ending. If it exists, the cove plate is ignoed when calculating. o positive ending: o negative ending: ( d t ) f topt f top ae f top t w 12 Eqn. 10a ( d ae t f top ) t w f topt f top ( t ) f ott f ot ae f ot t w 12 Eqn. 10 ( ae t f ot ) t w f ott f ot he C tem in Equations 7, 8 and 9 is defined in "Bacing (C) a and Bacing a" in echnical Note Ovewites Composite Beam Design AISC-ASC89. In Equation 9 A f is the aea of the compession flange (not including the cove plate even if it exists). Allowale Bending Stess fo Steel Beam Alone Page 5 of 7
6 Allowale Bending Stesses he deivation of ae is povided in "Popeties of Steel Beam (Plus Cove Plate) Alone" in echnical Note ansfomed Section Moment of Inetia Composite Beam Design AISC-ASD89. Allowale Bending Stesses fo Positive Bending in the Composite Beam Note: Allowale stesses when composite connection is not consideed is descied ealie in this echnical Note in the section entitled Allowale Bending Stess fo Steel Beam Alone. igue 1 shows a tpical composite eam. When thee is positive ending in the eam thee is compession at the top of the concete and tension at the ottom of the eam. o positive ending in a composite eam, the pogam checks the stesses at the following locations: Compession stess at the top of the concete. his stess is limited to 0.45 f c '. ension o compession at the top of the top flange of the eam. See ale 2 fo the allowale stess. ension o compession at the ottom of the ottom flange of the eam. In pactice, it is unlikel that the ottom flange of the eam will eve e in compession fo positive ending. It would equie an extemel lage cove plate, eond the ounds of pacticalit. See ale 2 fo the allowale stess. ension at the ottom of the cove plate. See ale 2 and the section entitled Geneal at the eginning of this echnical Note fo the allowale stess. ale 2 defines the equations that ae used to calculate the allowale ending stess fo the steel eam potion of a composite eam section fo vaious conditions. he equation used depends on whethe the eam we is compact and whethe the ield stess is less than o equal to 5 ksi. Allowale Bending Stesses fo Positive Bending in the Composite Beam Page of 7
7 Allowale Bending Stesses Concete sla h t c Metal deck d Steel eam Cove plate cp t cp igue 1 Composite Beam ale 2: Equations the Pogam Uses to Calculate the Allowale Bending Stess in the Steel Beam Potion of a Composite Beam pe of Beam Equations Used fo Allowale Stesses Section We Beam Compession ension An composite eam compact 5 ksi ksi > 5 ksi Eqn Eqn. 12 Allowale Bending Stesses fo Positive Bending in the Composite Beam Page 7 of 7
Overview. Overview Page 1 of 8
COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIORNIA DECEMBER 2001 COMPOSITE BEAM DESIGN AISC-LRD93 Tecnical Noe Compac and Noncompac Requiemens Tis Tecnical Noe descibes o e pogam cecks e AISC-LRD93 specificaion
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