Design Aids for Unreinforced Web Openings in Steel and Composite Beams with W-Shapes

Design Aids for Unreinforced Web Openings in Steel and Composite Beams with W-Shapes GUSTAVO DE SOUZA VERÍSSIMO Assistant professor in the Civil Engineering Department Federal University of Viçosa, Viçosa, MG, Brazil. RICARDO HALLAL FAKURY Professor of strctral steel design in the Strctres Engineering Department Federal University of Minas Gerais, Belo Horizonte, MG, Brazil. JOSÉ CARLOS LOPES RIBEIRO Civil Engineering, gradate research assistant Federal University of Minas Gerais, MG, Brazil Introdction Several factors can impose height limitations in mltistory bildings, sch as zoning reglations, economic reqirements and aesthetic considerations. To minimize floor height, a common soltion is to ct openings into steel beam webs in order to pass tilities throgh (see Figre 1). If these openings are nreinforced, they can significantly redce the flexral and shear capacity of the beams. d t b f t f D o h o d t w a o a) nreinforced opening d t t f b) reinforced opening Fig. 1. Openings in steel beams. In the 60s, 70s, and 80s, stdies on different web opening configrations were completed in the United States and Canada, inclding sqare, rectanglar, circlar, concentric, and eccentric openings in both non-composite and composite steel beams. In the late 80s, Darwin and Donahey (88), Darwin and Lcas (90) and Darwin (90) demonstrated that it is possible to prodce a nified procedre embodying the different cases that are freqently sed in steel bilding strctres. 1

Some national standards, sch as the British Standard (BSI, 00) and the Canadian Standard (CSA, 01), provide simplified rles for opening design in order to avoid weaening of the beam. However, these rles cover a wide range of possibilities, and, therefore, they are very conservative and, in general, restrict the openings to the middle third of the beam depth and to the two central qarters of the beam span. By fixing some parameters, it wold be possible to get more flexible and economical reslts for typical sitations in the floors of bildings. This wor presents the reslts of comptational simlations in non-composite and composite steel beams with web openings, based on a nified procedre developed by Darwin (90), and it is limited to W-shape sections. Design aids are provided that allow the identification of the beam region where nreinforced openings with specific characteristics do not redce the member capacity. Application of these design aids avoids the se of complex and expensive analytical calclation methods. The design aids are compatible with the Load and Resistance Factor Design Specification for Strctral Steel Bildings (AISC, 99-a) and can serve as a spplemental reference to that specification. Range of application The design aids were developed for non-composite and composite steel W-shape sections with the followings limitations: d b f > 1. (1) h t E 3.76 () w F y b f t f E 0.38 (3) F y where d = overall depth of steel section h = clear distance between flanges less the corner radis t w = web thicness b f = flange width t f = flange thicness E = modls of elasticity of steel F y = yield stress of the steel The beams shall be simply spported and sbject to a factored niformly distribted load. They mst have appropriate lateral bracing to avoid lateral-torsional bcling. The steel shall have maximm yield strength of 50 si (350 MPa). In composite beams, the slab can be normal weight concrete or lightweight concrete with a specified compressive strength, f c, of not more than 6.5 si (45 MPa). In addition, the slab shall have total thicness not greater than 6.3 in. (0 mm) and effective width not greater than 8 in. (00 mm). These restrictions are applied to both solid concrete slab and concrete slab on formed steel dec. The steel-concrete interaction can be fll or partial and the constrction shored or nshored.

The openings considered have the following shapes: sqare, rectanglar with aspect ratio eqal to (length a o eqal to twice the depth h o as shown in Figre 1) and circlar. The span-depth ratio of the beams,, shall be in the range of to. For composite beams, this ratio refers only to steel profile. The corners of sqare and rectanglar openings shold have minimm radii at least twice the thicness of the web, t w, or 5/8 in. ( mm), whichever is greater, in order to avoid fatige cracing de to stress concentration at these points (Darwin, 90). Methodology The principal aim of this paper is to identify, by means of the procedre proposed by Darwin (90), the region where one concentric opening with a certain shape and dimensions does not case redction on the beam strength. Knowing the location of this region, called the netral zone and represented by the hatched area in Figre, it is possible to design web openings withot considering the beam net section, which dispenses of analytical calclation methods. The netral zone depth, h nz, is symmetrically positioned with respect to the centroid of the steel section and can be defined as twice the web opening half-depth pls the opening eccentricity (Figre ). Obviosly, for openings symmetrically positioned with respect to the centroid of the steel section (concentric opening), h nz is the opening depth itself. S netral zone d h nz L L/ L/ L nz L Fig.. Netral zone. The netral zone length, L nz (Figre ), for each case stdied is the beam length where the moment-shear interaction is not considered as critical. For this, the following expression is sed (Darwin, 90): M φ M m 3 V + φv m 3 1 where M = reqired flexral strength at opening centerline V = reqired shear strength at opening centerline M m = maximm nominal flexral strength at the location of an opening nder pre bending; it occrs when V = 0 at opening centerline V m = maximm nominal shear strength at the location of an opening nder pre shear; it occrs when M = 0 at opening centerline φ = resistance factor, eqal to 0.90 for steel beams and 0.85 for composite beams (4) 3

The nominal flexral and shear strengths at the location of an opening, M m and V m, depend on (a) the shape and dimensions of the concentric opening and (b) the nominal flexral and shear strengths, respectively M n and V n, respectively, of the non-composite or composite steel beam with an nperforated web. Darwin (90) spplies the method for obtainment of these vales. The reqired flexral and shear strengths are calclated in several intermediary sections, eqally spaced along midspan, L/, with the following classical eqations from the theory of strctres: M ( z L z ) w z ) = o (5) ( o o L V ( zo ) = w zo (6) where z o = centerline position of a spposed opening (Figre 3) w = niformly distribted load on the simply spported beam. z o L Fig. 3. Opening centerline position. The vale of w can vary from near to zero to a maximm that can be obtained taing into accont the design flexral strength, φ b M n, and the design shear strength φ v V n, of the nperforated section, in accordance with the Load and Resistance Factor Design Specification for Strctral Steel Bildings (AISC, 99-a). Then, w is the smaller vale of the following, the first related to the mid-span and the second to the spport: w 8φb M n (7) L φv Vn w (8) L where L = length of the beam M n = nominal flexral strength φ b = resistance factor for flexre, eqal to 0.90 for steel beams and 0.85 for composite beams V n = nominal shear strength φ v = resistance factor for shear, eqal to 0.90 for non-composite and composite steel beams For composite beams, φ b M n is related to composite section with fll or partial interaction and φ v V n to the failre of the steel section web area, disregarding the contribtion of the concrete slab. 4

With the shape and dimensions of the concentric opening, all the characteristics of the beam and the vale of the niformly distribted load fixed, the moment-shear interaction is verified along the beam mid-span (the same several intermediary sections are considered in which M and V were calclated) in accordance with Eqation 4. The netral zone is obtained delimiting the length in which that expression is satisfied. It is observed that the openings case greater redction of shear strength than of flexral strength, and, for this reason, the netral zone originates in the mid-span and stretches in direction of the beam spports. A compter program was developed to determine the netral zone of non-composite and composite steel beams, according to the range of application presented previosly. Sets of crves were developed for web openings of varios shapes, dimensions, and in varios locations. The envelopes of each of these grops are presented in charts that allow simplified identification of the netral zone. The reslts are presented by plotting crves for different loading rates on a graph relating a variable to the beam span-to-depth ratio. Reslts The following design aids were prepared sing reslts obtained from comptational simlations in accordance with the methodology presented above. It has been determined that one or more nreinforced openings may be located in the web of W-shapes of non- composite and composite steel beams withot considering net section properties when the openings are sitated in the netral zone (Figre ). The depth of the netral zone, h nz, was first considered eqal to 33% of the overall depth of steel section, d, and then, eqal to 50%. These limits cover the most common sitations and they do not lead to significant design restrictions. For practical reasons, Darwin (90) limits the opening depth to 70% of the member depth. The netral zone mst always be considered centered in relation to the depth of the steel beam. The charts in Figres 4 to locate the netral zone for beams with circlar, sqare and rectanglar openings (Figres 1 and ), according to Table 1. For each chart, the inpt data are the ratio between the beam span and the steel section depth,, and the loading rate, R. The otpt data is the parameter, which shall be mltiplied by the beam span, L, to spply the lengths in the two ends of the beam where openings cannot be made (see Figre - the netral zone length stays between these two lengths). 5

Table 1 Charts for Determination of the Netral Zone Length Figre Shape of the Depth of the Opening Netral Zone Beam 4 sqare and circlar d/3 steel 5 rectanglar d/3 steel 6 circlar d/ steel 7 sqare d/ steel 8 rectanglar d/ steel 9 sqare and circlar d/3 composite rectanglar d/3 composite circlar d/ composite sqare d/ composite rectanglar d/ composite The loading rate, R, is the qotient between the reqired strength determined from factored loads and the design strength of the beam withot openings. R shall be obtained from the following condition considering Eqations 7 and 8 for w and Eqations 5 and 6 for M and V R M φb M V φv Vn n (9) 0,50 0,45 0,40 0,35 0, 0, 0, 0, 0, 0,05 0.90 0.95 0,00 Fig. 4. Netral zone for sqare and circlar openings with h o d/3 in steel beams with W-shapes. 6

0,50 0,45 0,40 0,35 0, 0, 0, 0, 0, 0.80 0.90 0.95 0,05 0,00 Fig. 5. Netral zone for rectanglar openings (a o =h o ) with h o d/3 in steel beams with W-shapes. 0,50 0,45 0,40 0,35 0, 0, 0, 0, 0, 0.80 0.90 0,05 0,00 Fig.6. Netral zone for circlar openings with D o d/ in steel beams with W-shapes. 0,50 0,45 0,40 0,35 0, 0, 0, 0.90 0, 0, 0.60 0.80 0,05 0,00 Fig. 7. Netral zone for sqare openings with h o d/ in steel beams with W-shapes. 7

0,50 0,45 0,40 0,35 0, 0, 0, 0, 0, 0.60 0.80 0.90 0,05 0,00 Fig. 8. Netral zone for rectanglar openings (a o =h o ) with h o d/ in steel beam with W-shapes. 0.45 0.40 0.35 0. 0. 0. 0. 0.85 0.80 0. 0.60 0.05 0.00 Fig. 9. Netral zone for sqare and circlar openings with h o d/3 in composite beams with W-shapes. 0.45 0.40 0.35 0. 0. 0. 0. 0. 0.05 0.85 0.80 0.60 0.00 Fig.. Netral zone for rectanglar openings (a o =h o ) with h o d/3 in composite beams with W-shapes. 8

0.45 0.40 0.35 0. 0. 0. 0. 0. 0.05 0.75 0.65 0.60 0.00 Fig.. Netral zone for circlar openings with D o d/ in composite beams with W-shapes. 0.45 0.40 0.35 0. 0. 0. 0. 0. 0.05 0.75 0.60 0.00 Fig. Netral zone for sqare openings (a o =h o ) with h o d/ in composite beams with W-shapes. 0.45 0.40 0.75 0.35 0. 0. 0.60 0. 0. 0. 0.05 0.00 Fig.. Netral zone for rectanglar openings (a o =h o ) with h o d/ in composite beams with W-shapes. 9

When the beam has more than one opening, the minimm spacing between edges of two adjacent openings, S (Figre ), mst be in accordance with the following criterion to avoid interaction between openings (Darwin, 90). For sqare and rectanglar openings S h a o o V φv p V () For circlar openings 1.5 Do S V Do φv p V where V p = plastic shear capacity of an nperforated beam φ = resistance factor, eqal to 0.90 for non-compostite steel beams and 0.85 for composite beams In addition to the spacing reqirements above, openings in composite beams shold be spaced so that S d. () Examples Example 1: Steel Beam Determine the netral zone of a 35-ft (.668 m) span Wx40 (W460 60) steel beam, to mae nreinforced concentric rectanglar openings with depth h o eqal to 6 in. ( mm) and length a o eqal to in. (4 mm). This beam had the design flexral and the design shear strengths determined in the Example 5.1 (Soltion a) of the LRFD Manal of Steel Constrction Part 5: Design of Flexral Members (AISC, 99-b): φ b M n = 4 ip-ft φ v V n = ips (399 N.m) (676 N) The beam is simply spported, with a factored distribted load of 1.6 ips/ft (.34 N/m). Therefore, the reqired flexral and shear strengths are M 1.6 35 = 8 = 5ip- ft 1.6 35 V = = ips (5N) The loading rate R is the larger of: M b φ M n 5 = = 4 0.83 (33N.m)

V and = = 0. φ V v n The netral zone depth, h nz, will be considered eqal to the opening depth itself, h o. Ths, h nz = h o = 6 in. (8 mm) d/3 L = 4 in. (668 mm) d =.9 in. (455 mm) a o = in. (4 mm) = h o =.5 R = 0.83 From Figre 5 (steel beam, a o = h o and h nz = d/3), the vale of for =.5 and R = 0.83 is 0.045. Ths, the netral zone for this case stretches from 0.045L =.9 in. (480 mm) to 401.1 in. (8 mm), having as reference the left spport. Then, concentric rectanglar openings with in. x 6 in. (4 mm mm) can be made in this region, as long as the design criteria are satisfied (Figre ). Wx40.9 in. netral zone = 38. in. 4 in. Fig. Netral zone for a steel W 40 beam. Example : Composite Beam Determine how many circlar nreiforced openings with D o = 9.8 in. and downward eccentricity of 1 in. can be made in a 40-ft. (. m) span Wx55 (W6x8) composite steel section. The yield stress of the steel, F y, is eqal to 50 si. This beam had the design flexral and the design shear strengths determined in the Example 5.6 of LRFD Manal of Steel Constrction Part 5: Design of Flexral Members (AISC, 99-b), as follows: φ b M n = 1,050 ip-ft φ v V n = ips ( N.m) ( N) The beam is simply spported with a total factored distribted load of 3.6 ips/ft (5.5 N/m). The reslting reqired flexral and shear strengths are: M V 3.6 40 = 8 = 7ip - ft 3.6 40 = = 7 ips (3N) (976 N/m)

The loading rate R is the larger vale of: M φ M b n = 7 = 1,055 0.68 V v φ V n 7 = = 0. The biggest vale mst be adopted. Ths, R = 0.68. 1 st step: Find the netral zone. The depth can be calclate as: h nz 9.8 = + 1 =.80 in. (0 mm) This vale is eqal to half of the overall depth of the steel section (.6 in.). The other important dimensions and parameters are: L = 480 in. ( mm) R = 0.68 From Figre chart (composite beam, circlar openings and h nz = d/), the vale of for = and R = 0.69 is near 0.. The netral zone for this case, hence, stretches from 0.L = 7 in. ( mm) to 408 in. (363 mm) from the left spport. Ths, circlar openings can be made in this region, as long as the design criteria are satisfied (Figre ). nd step: Determine the minimm spacing between edges of two adjacent openings. For a Wx55, t w = 0.395 in. and the vale of the plastic shear strength of the beam is (AISC, 99-a) V p = 0.6 F y d t w = 0.6 50.6 0.395 = 0 ips (44 N) For circlar openings: 1. 5 Do = 1. 5 9. 8 =. 7 in. (373mm) S V 7 Do = 9. 8 = 4. in. φv p V 0. 85 0 7 (8 mm) and, for a composite beam, S d =.6 = 47. in. (00 mm). S is the spacing between edges of two adjacent openings, therefore, the distance between centers of openings will be S + D o = 47. + 9.8 = 57 in. (48 mm) The length of the netral zone is (Figre ): L NZ = 480 (7) = 336 in. (8534 mm)

Ths, the nmber of spaces of 57 in. (48 mm) possible to fit in L NZ is given by L NZ D S + D o o 336 9. 8 = = 5. 7 to adopt 5 57 Therefore, the nmber of openings possible to fit in L NZ is 6 (Figre ). Wx55 7 in. 5.5 in. 65 in. 65 in. netral zone length = 336 in. 480 in. Figre Netral zone for a composite beam with Wx55 steel section. Smmary and conclsions Design aids compatible with the Load and Resistance Factor Design Specification for Strctral Steel Bildings (AISC, 99-a) were obtained from comptational analyses based on Darwin (90) to facilitate the design of openings in webs of steel and composite beams with W- shapes. The set of design aids allow to identify the netral zone, a region in the beam web in which openings with some particlar characteristics do not redce the beam strength. This leads to more economical web penetrations. Nomenclatre D o E F y L L nz M M n M m M p R S V V n V m V p a o b f d Diameter (or depth) of circlar opening Modls of elasticity of steel Specified minimm yield stress of the steel Length or span of beam Length of netral zone Reqired flexral strength Nominal flexral strength Maximm nominal flexral strength at the location of an opening nder pre bending; it occrs when V = 0 at opening centerline Plastic bending moment of an nperforated steel beam Loading rate Clear space between openings Reqired shear strength Nominal shear strength Maximm nominal shear strength at the location of an opening nder pre shear; it occrs when M = 0 at opening centerline Plastic shear strength Length of sqare or rectanglar opening Flange width Overall depth of steel section

f c h h nz h o w t f t w z o φ φ b φ v Specified compressive strength of concrete Clear distance between flanges less the corner radis Depth of netral zone Depth of sqare or rectanglar opening Total factored niformly distribted load Flange thicness Web thicness Distance from left spport to opening center line Resistance factor for moment-shear interaction or openings interaction Resistance factor for flexre Resistance factor for shear Acnowledgements The athors are indebted to the Federal University of Viçosa Research Fondation (Arthr Bernardes Fondation) and the National Research Concil of the Brazilian Government (CNPq) for their sponsorship of the research that led to this paper. The athors are also thanfl to Prof. David Darwin, of the University of Kansas, for its opinion regarding the application of the procedres to the composite beams with lightweight concrete. References 1. AISC (99-a), Load and Resistance Factor Design Specification for Strctral Steel Bildings American Institte for Steel Constrction (with errata incorporated as of September 1, 0), American Institte of Steel Constrction, Chicago, IL.. AISC (99-b), LRFD Manal of Steel Constrction Part 5: Design of Flexral Members (with errata incorporated as of September 1, 0), American Institte of Steel Constrction, Chicago, IL. 3. BSI (00), Strctral Use of Steelwor in Bildings Part 1: Code of Practice for Design- Rolled and Welded Sections, BS-5950, British Standards Instittion, UK. 4. CSA (01), Limit States Design of Steel Strctres, S-01, Canadian Standards Association, Toronto, Ontario. 5. Darwin, D. and Donahey, R. C. (88), LFRD for Composite Beams with Unreinforced Web Openings, Jornal of Strctral Engineering, ASCE, Vol. 1, pp. 535-55. 6. Darwin, D. (90), Steel and Composite Beams with Web Openings, Design Gide, American Institte of Steel Constrction, Chicago, IL. 7. Darwin, D. and Lcas, W. C. (90), LFRD for Steel and Composite Beams with Web Openings, Jornal of Strctral Engineering, ASCE, Vol. 6, pp. 79-93.