Bending Analysis of Castellated Beams. By Sahar Elaiwi Boksun Kim Long-Yuan Li

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1 Athens Journ of Technoogy nd Engineering X Y Bending Anysis of Csteted Bems By Shr Eiwi Boksun Kim Long-Yun Li Existing studies hve shown tht the od-crrying cpcity of csteted bems cn be infuenced by the sher stresses prticury those round web openings nd under the T- section, which coud cuse the bem to hve different fiure modes. This pper investigtes the effect of web openings on the trnsverse defection of csteted bems by using both nytic nd numeric methods nd evutes the sher-induced trnsverse defection of csteted bems of different engths nd fnge widths subjected to uniformy distributed trnsverse od. The purpose of deveoping nytic soutions, which dopted the cssic principe of minimum potenti energy is for the design nd prctic use; whie the numeric soutions re deveoped by using the commerci softwre ANSYS for the vidtion of the nytic soutions. Keywords: Csteted Bem, Defection, Energy Method, Finite Eement, Sher Effect. Introduction Engineers nd reserchers hve tried vrious methods to reduce the mteri nd construction costs to hep optimise the use of the stee structur members. The csteted bem is one of the stee members which uses ess mteri, but hs comprbe performnce s the I-bem of the sme size (Atifiisch et. 1957). An exmpe is shown in Figure 1. The csteted bem is fbricted from stndrd univers I-bem or H-coumn by cutting the web on hf hexgon ine down the centre of the bem. The two hves re moved cross by hf unit of spcing nd then re-joined by weding. This process increses the depth of the bem nd thus the bending strength nd stiffness of the bem bout the mjor xis re so enhnced without ddition mteris being dded. This ows csteted bems to be used in ong spn ppictions with ight or moderte oding conditions for supporting foors nd roofs. In ddition, the fbriction process cretes openings on the web, which cn be used to ccommodte services. As resut, the designer does not need to increse the finished foor eve. Thus, despite the increse in the bem depth the over buiding height my ctuy be reduced. When compred with soid web soution where services re provided beneth the bem, the use of csteted bems coud ed to svings in the cdding costs especiy in recent yers, the stee cost becomes higher. Owing to the fct tht the stee mteris hve poor fire resistnce, buidings mde from stee PhD Student, Pymouth University, UK. Pymouth University, UK. Pymouth University, UK. 1

2 Vo. X, No. Y Eiwi et.: Bending Anysis of Csteted Bems structures require to use high quity fireproof mteris to protect stee members from fire, which further increse its cost. Moreover, becuse of its ightweight the csteted bem is more convenient in trnsporttion nd insttion thn the norm I-bem. Literture Review For mny yers, the csteted bem hve been used in construction becuse of its dvntges when considering both the sfety nd servicebiity whie considering function requirements ccording to the use for which the construction is intended. Extensive study hs been done by reserchers who re working in the construction fied to identify the behviour of csteted bems when they re oded with different types of ods. It ws found tht the csteted bem coud fi in vrious different modes depending on the dimensions of the bem nd the type of oding s we s the boundry conditions of the bems. Kerd nd Nethercot (1984) informed the potenti fiure modes, which possiby tke pce in csteted bems. Aso, they expined the resons for the occurrence of these fiure modes. For instnce, sher force nd web wed rupture cuse Vierendee mechnism nd web post-bucking. Additiony, they pointed out tht ny other fiures whether cused by fexur mechnism or tertorsion instbiity is identic to the equivent modes for bems without web opening. The web openings in the csteted bem, however, my reduce the sher resistnce of the bem. The sved evidence, tht the method of nysis nd design for the soid bem my not be suitbe for the csteted bem (Boyer 1964, Kerd nd Nethercot 1984, Demirdjin 1999). Design guidnce on the strength nd stiffness for csteted bems is vibe in some countries. However, gin, most of them do not tke into ccount the sher effect. As fr s the bending strength is concerned, negecting the sher effect my not cuse probems. However, for the bucking nd the ccution of servicebiity, the sher wekness due to web openings in csteted bems coud ffect the performnce of the bems nd thus needs to be crefuy considered. Experiment investigtions (Aminin et. 1, Mek 4, Yun et. 14, Yun et. 16, Zrour nd Redwood, 1996) were crried out nd finite eements methods (Hosin et. 1974, Sherbourne nd Vn Oostrom 197, Sotni et. 1, Sonck et. 15, Srimni nd Ds 1978, Wng et. 14) were so used to predict the defection of csteted bems nd/or to compre the predictions with the resuts from the experiments. The experiment findings (Zrour nd Redwood 1996) demonstrted the possibiity of the occurrence of the bucking of the web posts between web openings. The sher defection of the stright-sided tpering cntiever of the rectngur cross section (Mek 4) ws ccuted by using theoretic method bsed on Timoshenko s bem theory nd virtu work method. Liner genetic progrmming nd integrted serch gorithms (Aminin et. 1) showed tht the use of the mchine erning system is n ctive method to vidte the fiure od of csteted bems. A

3 Athens Journ of Technoogy nd Engineering X Y numeric computer progrmme (Sherbourne nd Vn Oostrom 197) ws deveoped for the nysis of csteted bems considering both estic nd pstic deformtions by using prctic ower imit retionships for sher, moment nd xi force interction of psticity. An nysis on five experiment groups of csteted bems (Srimni nd Ds 1978) ws conducted to determine the defection of the bem. It ws demonstrted (Hosin et. 1974) tht the finite eements method is suitbe method for ccuting the defection of symmetric section csteted bems. The effect of noninerity in mteri nd/or geometry on the fiure mode prediction of csteted bems (Sotni et. 1) ws done by using MSC/NASTRAN softwre to find out bending moments nd sher od cpcity, which re compred with those pubished in iterture. Axi compression bucking of csteted coumns ws investigted (Yun et. 14), in which n nytic soution for critic od is derived bsed on sttionry potenti energy nd considering the effect of the web sher deformtions on the fexur bucking of simpy supported csteted coumn. Recenty, prmetric study on the rge defection nysis of csteted bems t high tempertures (Wng et. 14) ws conducted by using finite eement method to ccute the growth of the end rection force, the midde spn defection, nd the bending moments t susceptibe sections of csteted bems. More recenty, comprehensive comprison between the defection resuts of ceur nd csteted bems obtined from numeric nysis (Sonck et. 15) ws presented, which ws obtined from different simpified design codes. The comprison showed tht the design codes re not ccurte for short spn bems nd conservtive for ong spn bems. The principe of minimum potenti energy ws dopted (Yun et. 16) to derive n nytic method to ccute the defection of csteted/ceur bems with hexgon/circur web openings, subjected to uniformy distributed trnsverse od. The previous reserch efforts show tht there were few of rtices tht det with the defection nysis of csteted bems. Due to the geometric prticurs of the bem, however, it ws remrkbe to note tht most of the theoretic pproximte methods re interested in ccuting the defection of the csteted bems for ong spn bems where the sher effect is negigibe. However, the csteted bems/coumns re used not ony for ong spn bems/coumns but so for short bems/coumns. Owing to the compex of section profie of the csteted bems, the sher-effect cused by the web opening on the defection ccution is not fuy understood. There re no ccurte ccution methods vibe in iterture to perform these nyses. Thus it is importnt to know how the sher ffects the defection of the bem nd on wht kind of spns the sher effect cn be ignored. In ddition, reserchers hve dopted the finite eements method to predict the defection of csteted bems by using different softwre progrms such s MSC/NASTRAN, ABAQUS, nd ANSYS. However, these progrms need efficiency in use becuse ny error coud ed to significnt distortions in resuts. Europen buiding stndrds do not hve formus for the ccution of defections of csteted bems, which incude sher deformtions. This pper presents the nytic method to ccute the estic defection of csteted bems. The defection eqution is to be deveoped bsed on the 3

4 Vo. X, No. Y Eiwi et.: Bending Anysis of Csteted Bems principe of minimum potenti energy. In order to improve the ccurcy nd efficiency of this method, sher rigidity fctor is determined by using suitbe numeric techniques. The nytic resuts were vidted by using the numeric resuts obtined from the finite eement nysis using ANSYS softwre. Anytic Phiosophy of Defection Anysis of Csteted Bems An pproximte method of defection nysis of csteted bems under uniformy distributed trnsverse od is presented herein. The method is derived bsed on the principe of minimum potenti energy of the structur system. Becuse of the presence of web openings, the cross-section of the csteted bem is now decomposed into three prts to ccute the defection nd bending stress, two of which represent the top nd bottom T-sections, one of which represents the mid-prt of the web. The nysis mode is iustrted in Figure 1, in which the fnge width nd thickness re b f nd t f, the web depth nd thickness re h w nd t w, nd the hf depth of hexgons is. The hf of the distnce between the centroids of the two T-sections is e. In this study, the cross-section of the csteted bem is ssumed to be douby symmetric. Under the ction of uniformy distributed trnsverse od, the bem section wi hve xi nd trnsverse dispcement s shown in Figure 1b, where x is the ongitudin coordinte of the bem, z is the cross-section coordinte of the bem, (u 1, w) nd (u, w) re the xi dispcements nd the trnsverse dispcements of the centroids of the upper nd ower T-sections. A points on the section re ssumed to hve the sme trnsverse dispcement becuse of the bem ssumption used in the present pproch (Yun et. 14). The corresponding xi strins 1x in the upper T- section nd x i in the ower T-section re inery distributed nd cn be determined by using the strin-dispcement retion s foows: In the upper T-section: ε 1x x, z = du 1 dx (z + e) d w (1) dx In the ower T-section: ε x x, z = du dx (z e) d w dx () The sher strin γ xz in the midde prt between the two T-sections cn so be determined using the sher strin-dispcement retion s foows: For the midde prt between the two T-sections: γ xz x, z = du dz + dw dx = u 1 u + e dw dx (3) 4

5 Athens Journ of Technoogy nd Engineering X Y e = b f t f h w+t f +t w h w h w + 4 b f t f +t w h w (4) Becuse the upper nd ower T-sections behve ccording to Bernoui's theory, the strin energy of the upper T-section U 1 nd the ower T-section U cused by trnsverse od cn be expressed s foows: h w U 1 = Eb f ε 1x Et w dzdx + ε 1x dzdx ( h w ) (t f + h w ) = 1 EA tee du 1 dx ( h w ) + EI tee d w dx U = Et w ε x Eb f dzdx + ε x dzdx = 1 EA tee du dx (t f + h w ) h w + EI tee d w dx dx dx (5) (6) where E is the Young's moduus of the two T-sections, G is the sher moduus, A tee nd I tee re the re nd the second moment of re of the T- section, which re determined in their own coordinte systems s foows: A tee = b f t f + t w h w (7) 3 b f t f I tee = 1 + b ft h w+t f f e + t 3 w 1 h w + t w h w h w + e 4 (8) The mid-prt of the web of the csteted bem, which is iustrted in Figure 1, is ssumed to behve ccording to Timoshenko s theory (Yun et. 14). Therefore, its strin energy due to the bending nd sher cn be expressed s foows: U b = 1 K b (9) where is the retive dispcement of the upper nd ower T-sections due to pir of sher forces nd cn be expressed s ( = γ xz ). Whie K b is the 5

6 Vo. X, No. Y Eiwi et.: Bending Anysis of Csteted Bems combined stiffness of the mid prt of the web cused by the bending nd sher, nd is determined in terms of Timoshenko bem theory s foows, 1 K b = 3 b GA b + 3 b 1EI b (1) where A b = 3t w is the equivent cross-section re of the mid prt of the web, I b = ( 3) 3 t w /1 is the second moment of re, nd b = is the ength of the Timoshenko bem; herein representing the web post ength. Note tht, the Young's moduus of the two T-sections is E=(1+ν)G nd the Poisson s rtio is tken s v =.3, the vue of the combined stiffness of the mid prt of the web cused by the bending nd sher cn be determined s fow: K b = 3Gt w 4 (11) Thus, the sher strin energy of the web, U sh, due to the sher strin γ xy cn be ccuted s foows: U sh = 3 Gt w γ xz n k=1 3Gt w 6 γ Gt w xz dx = 4 γ xz dx 3 (1) Let the sher rigidity fctor k sh =.5. Substituting Eqs. (3) into (1) gives the tot sher strin energy of the mid-prt of the web: U sh = Gt we k sh dw dx u β e dx (13) Note tht, in the ccution of sher strin energy of Eq. (1) one uses the concept of smer mode, in which the sher strin energy ws ccuted first for web without hoes. Then by ssuming the rtio of the sher strin energies of the webs with nd without hoes is proportion to the voume rtio of the webs with nd without hoes, the sher strin energy of the web with hoes ws evuted, in which k sh =.5 ws obtined (Kim et. 16). However, by using twodimension iner finite eement nysis (Yun et. 16) the vue of the combined stiffness of the mid prt of the web of the csteted bem cused by the bending nd sher, ws found to be K b =.78 3Gt w 4 (14) which is smer thn tht bove-derived from the smer mode. This eds to the sher rigidity fctor k sh =.78x.5. The reson for this is probby due to 6

7 Athens Journ of Technoogy nd Engineering X Y the smer mode used for the ccution of the sher strin energy for the midprt of the web in Eq. (1). Figure 1. () Nottions used in Csteted Bems (b) Dispcements nd (c) Intern Forces However, it shoud be mentioned tht the fctor of.78 in Eq. (14) ws obtined for ony one specific section of csteted bem. It is not known whether this fctor cn so be ppied to other dimensions of the bems. A finite eement nysis mode for determining the sher rigidity fctor k sh is therefore deveoped herein (see Figure c), in which the ength nd depth of the unit re (4/ 3) nd (+/), respectivey. In the unit the retive dispcement cn be ccuted numericy when unit od F is ppied (see Figure c). Hence, the combined rigidity K b =1/ is obtined. Note tht in the unit mode dispcements nd rottion of the bottom ine re ssumed to be zero, wheres the ine where the unit od is ppied is ssumed to hve zero vertic dispcement. The cibrtion of the sher rigidity for bems of different section sizes shows tht the use of the expression beow gives the best resuts nd therefore Eq. (15) is used in the present nytic soutions. K sh =.76 b f 1 4 (15) where is the ength of the bem. Thus the tot potenti energy of the 7

8 Vo. X, No. Y Eiwi et.: Bending Anysis of Csteted Bems csteted bem U T is expressed s foows, U T = U 1 + U + U sh (16) For the simpicity of presenttion, the foowing two new functions re introduced: u 1 u u (17) u 1 u u (18) By using Eqs. (17) nd (18), the tot potenti energy of the csteted bem subjected to uniformy distributed trnsverse od cn be expressed s foows: = EA tee du β dx + Gt we k sh dx +EI tee d w dx dw dx u β e dx dx W (19) where W is the potenti of the uniformy distributed od q mx due to the trnsverse dispcement, which cn be expressed s foows: W = q mx w dx () where q mx is the uniformy distributed od, which cn be expressed in terms of design stress σ y, s foows: q mx = 16 σ yi reduced (h w + t f ) b f h w + t 3 f I reduced = 1 t w 3 1 h w 3 b f t w 1 (1) () 8

9 Athens Journ of Technoogy nd Engineering X Y Figure. Sher Strin Energy Ccution Mode: () Unit Considered, (b) Sher Deformtion Ccution Mode nd (c) Finite Eement Mode of 4/ 3 Length Unit nd (+/) Depth, Loded by Unite Force F Defection of Simpy Supported Csteted Bem with Uniformy Distributed Trnsverse Loding For simpy supported csteted bem u α (x), u β (x) nd w(x) cn be ssumed s foows: u α (x) = A m cos mπx m=1,,.. (3) u β (x) = B m cos mπx m=1,,.. (4) w(x) = C m sin mπx m=1,,.. (5) where A m, B m nd C m re the constnts to be determined. It is obvious tht the dispcement functions ssumed in Eqs. (3)-(5) stisfy the simpy support d w w dx du dx boundry conditions, tht re nd dx t x = nd x =, nd m = 1,, is the integr number. Substituting Eqs. (3), (4) nd (5) into (19) nd () nd ccording to the principe of minimum potenti energy, it yieds, du δu T + U sh W = (6) 9

10 Vo. X, No. Y Eiwi et.: Bending Anysis of Csteted Bems The vrition of Eq. (6) with respect to A m, B m nd C m resuts in foowing three gebric equtions: EA tee mπx EA mπ tee EI mπ tee 4 A m = + Gt wk sh + Gt we k sh B m Gt wek sh mπ = 1 1 m q mx mπ Mthemticy Eqs. (7) -(9) ed to: mπ C m Gt wek sh C m = mπ B m (7) (8) (9) A m = B m = Gt wek sh EA tee mπ mπ Gt + w k sh (3) C m (31) C m = 1 ( 1)m q 4 mπ 5 e EI tee + EA tee 1 + EA tee mπ Gk sh t w (3) Therefore, the defection of the csteted bem cn be expressed s foows: w(x) = q 4 EI tee + e A tee mπ m=1,,.. e A tee I tee + e A tee EA tee mπ Gk sh t w 1 EI tee mπ mπx Gk sh t w sin e (33) The mximum defection of the simpy supported bem is t the mid of the bem, tht is x=/ nd thus it cn be expressed s foows: 1

11 Athens Journ of Technoogy nd Engineering q 4 w x=/ = EI tee + e A tee k=1,,.. 1 k+1 π 5 k k+1 π k 1 3 EI tee Gk sh t w e k=1,,.. e A tee I tee + e EA tee A tee Gk sh t w 1 k+1 π k 1 k=1,,.. X Y (34) Note tht, mthemticy, the foowing equtions hod, 1 k+1 5 π 5 k 1 5 = 384 k=1,,.. (35) 1 k+1 π 3 k 1 3 = 1 16 (36) k=1,,.. 1 k+1 π k 1 k=1,,.. = 1 (37) Using Eqs. (35), (36) nd (37), the mximum defection of the bem cn be simpified s foows: 5q 4 w x=/ = 384EI tee + e A + q ea tee tee 16Gk sh t w I tee + e A tee 1 EI (38) tee Gk sh t w e It is cer from Eq. (38) tht, the first prt of Eq. (38) represents the defection generted by the bending od, which is deemed s tht given by Bernoui-Euer bem, whie the second prt of Eq. (38) provides the defection generted by the sher force. Moreover, Eq. (38) shows tht the sher-induced defection is proportion to the cross-section re of the two T-sections but inversey proportion to the bem ength. This expins why the sher effect coud be ignored for ong spn bems. If the ccution does not consider the sher effect of web openings, Eq. (38) reduces to the foowing bending defection eqution. w x=/ = 5q 4 384EI reduced (39) Numeric Study In order to vidte the bovementioned nytic soution numeric nysis using the finite eement method is so crried out. The numeric computtion 11

12 Vo. X, No. Y Eiwi et.: Bending Anysis of Csteted Bems uses the ANSYS Progrmming Design Lnguge (APDL). The FEA modeing of the csteted bems is crried out by using 3D iner Qudrtic 4-Node thin she eements (SHELL181). This eement presents four nodes with six DOF per node, i.e., trnstions nd rottions on the X, Y, nd Z xis, respectivey. Hf-ength of the csteted bems is used becuse of the symmetry in geometry. The ter nd trnsverse defections nd rottion re restrined (u y =, u z = nd θ x =) t the simpy supported end, whie the symmetric boundry condition is ppied t the other end by constrining the xi dispcement nd rottions round the two xes within the cross-section (u x =, θ y = nd θ z =). The mteri properties of the csteted bem re ssumed to be iner estic mteri with Young s moduus E = 1 GP nd Poisson s rtio v =.3. A ine od effect is used to mode ppied uniformy distribution od, where the od is ssumed cting on the junction of the fnge nd the web. The equivent nod od is ccuted by mutipy the distribution od with bem s hf-ength nd then divided by the number of the nodes on the junction ine of the fnge nd the web. Discussion Figure 3 shows comprison of the mximum deftions between nytic soutions using different sher rigidity fctors incuding one with zero sher fctor nd FEA numeric soution for four csteted bems of different fnge widths. It cn be seen from the figure tht, the nytic soution using the proposed sher fctor is cosest to the numeric soution, wheres the nytic soutions using other sher fctors is not s good s the present one. This demonstrtes tht the sher fctor is so ffected by the rtio of the fnge width to the bem ength. Aso, it cn be seen from the figure tht, the onger the bem, the coser the nytic soution to the numeric soution; nd the wider the fnges, the coser the nytic soution to the numeric soution. 1

13 Athens Journ of Technoogy nd Engineering X Y Figure 3. Mximum Defections of Simpy Supported Csteted Bems with Uniformy Distributed Lod Obtined using Anytic Soution with Different Sher Rigidity Fctors (Eqs. (38) nd (39)) nd FEA Numeric Soution for Four Csteted Bems of Different Fnge Widths () bf=1mm (b) bf=15mm (c) bf=mm (d) bf=5mm (h w =3mm, t f =1mm, t w =8mm nd =1mm) Figure 4 shows the retive error of ech nytic soution when it is compred with the finite eement soution. From the figure it is evident tht the error of the nytic soutions using the present sher rigidity fctor does not exceed 6.% for of discussed four sections in the bem ength rnge (>3 meter). In contrst, the nytic soution ignoring the sher effect, or considering the sher effect by using smer mode or by using the ength-independent sher rigidity fctor wi hve rge error, prticury when the bem is short. 13

14 Vo. X, No. Y Eiwi et.: Bending Anysis of Csteted Bems Figure 4. Divergence of Mximum Defections of Simpy Supported Csteted Bems with Uniformy Distributed Lod Obtined using Anytic Soution with Different Sher Rigidity Fctors (Eqs. (38) nd (39)) nd FEA Numeric Soution for Four Csteted Bems of Different Fnge Widths () bf=1mm (b) bf=15mm (c) bf=mm (d) bf=5mm (h w =3mm, t f =1mm, t w =8mm nd =1mm) Concusions This study hs reported the theoretic nd numeric soutions for ccuting the defection of hexgon csteted bems with simpy supported boundry condition, subjected to uniformy distributed trnsverse od. The nysis is bsed on the tot potenti energy method, by tking into ccount the infuence of web sher deformtions. The min novety of the present nytic soution for 14

15 Athens Journ of Technoogy nd Engineering X Y the ccution of defection is it considers the sher effect of web openings more ccurtey. Both the nytic nd numeric soutions re empoyed for wide spectrum of geometric dimensions of I-shped csteted bems in order to evute the nytic resuts. From the present study, the min concusions cn be summrized s foows: 1. The present nytic resuts re in exceent greement with those obtined from the finite eement nysis, which demonstrtes the ppropriteness of proposed pproch.. Sher effect on the defection of csteted bems is very importnt, prticury for short nd medium ength bems with nrrow or wide section. Ignoring the sher effect coud ed to n under-estimtion of the defection. 3. Divergence between nytic nd numeric soutions does not exceed 6.% even for short spn csteted bem with nrrow or wide section. 4. The effect of web sher on the defection reduces when csteted bem ength increses. 5. Despite tht the numeric soution bsed on FEA hs been widey used in the nysis of csteted bems; it is usuy time-consuming nd imited to specific geometric dimensions. Thus, simpified ccution soution tht is be to deiver resonbe resuts but requires ess computtion effort woud be hepfu for both reserchers nd designers. Acknowedgments The first uthor wishes to thnk the Ministry of Higher Eduction in Irq Trust for funding her PhD study in the University of Pymouth. References Atifiisch MD, Cooke RB, Toprc AA (1957) An Investigtion of Open Web Expnded Bems. Weding Reserch Counci Buetin, New York 47: Aminin P, Niroomnd H, Gndomi AH, Avi AH, Arb Esmeii M (1) New Design Equtions for Assessment of Lod Crrying Cpcity of Csteted Stee Bems: A Mchine Lerning Approch. Neur Computing nd Appictions 3(1): Boyer JP (1964) Csteted Bem- A New Deveopment Csteted Bems-New Deveopments. AISC Engineering 1(3): Demirdjin S (1999) Stbiity of Csteted Bem Webs. (PhD), McGi University Montre, Cnd. Hosin M, Cheng W, Neis V (1974) Defection Anysis of Expnded Open-Web Stee Bems. Computers & Structures 4(): Kerd D, Nethercot D (1984) Fiure Modes for Csteted Bems. Journ of Construction Stee Reserch 4(4):

16 Vo. X, No. Y Eiwi et.: Bending Anysis of Csteted Bems Kim B, Li L-Y, Edmonds A (16) Anytic Soutions of Lter Torsion Bucking of Csteted Bems. Interntion Journ of Structur Stbiity nd Dynmics, Mek S (4) Sher Defections of Tpered Timoshenko Bems. Interntion Journ of Mechnic Sciences 46(5): Sherbourne A, Vn Oostrom J (197) Pstic Anysis of Csteted Bems Interction of Moment, Sher nd Axi Force. Computers & Structures (1): Sotni MR, Bouchïr A, Mimoune M (1) Noniner FE Anysis of the Utimte Behvior of Stee Csteted Bems. Journ of Construction Stee Reserch 7: Sonck D, Kinget L, Beis J (15) Defections of Ceur nd Csteted Bems. Pper presented t the Future Visions (Interntion Assocition for She nd Spti Structures) (IASS15). Srimni SS, Ds P (1978) Finite Eement Anysis of Csteted Bems. Computers & Structures 9(): Wng P, Wng X, M N (14) Vertic Sher Bucking Cpcity of Web-Posts in Csteted Stee Bems with Fiet Corner Hexgon Web Openings. Engineering Structures 75: Yun W-B, Kim B, Li L-Y (14) Bucking of Axiy Loded Csteted Stee Coumns. Journ of Construction Stee Reserch 9: j.jcsr Yun W-B, Yu N-T, Bo Z-S, Wu L-P (16) Defection of Csteted Bems Subjected to Uniformy Distributed Trnsverse Loding. Interntion Journ of Stee Structures 16(3): Zrour W, Redwood R (1996) Web Bucking in Thin Webbed Csteted Bems. Journ of Structur Engineering 1(8):