Desigrn in stuchucrl steelwork to BS 5950

BENDING STRENGTHFrom Table 4. 17, relevant compressive strength values for bucHing about the x - x axis are obtainedfrom Table 27 ft) (Table 4- 18) and from Table 27 (c) (Table 4.19)-for bending about the y - y axis.

Lx= LElrx=595O/89 = 66.8Frcm Table 4.18, pc= 208 N *rrr- 2

?vy = Lr/ry = 5950/51.6 = I I 5.3From Table 4' 19, pc = 103 N

-*-

2. Hence critical compressive strength of column, pg, ispc:103 N mm-2

OVERALL BUCKUNG CHECK

lr-r=@-o.5x7ooo - . .otY-=--5TF-=o/ 'u

From Table 4'15, p6 = 193 N *-- 2. Buckling resistance moment capacity of column, d46, is givenby

Ms =psSx = 193 x 568 x 103 = 1O9.6 x lO6 N mmHence for stability,

F mMx ntMo

Aer* Mb * nzv

= t

z8o x to366.4x tO2 x 103

, 1x7.8x106-;25;n4x ro3

,1x40.6x1061O9.6 x 106

50 min75 max

Beinforcement

Characleristics'rength of concrele ) 20 N/mm2

Fig.427 Cased tJC section. Reinforcement: steelfabrb type?9! (BS 4483) or > S mm di.amiter bngitudinaib,ars andlinks at a maximum spacing of 200 mm.

r38

= 0.41 + O-37 + 0.16 = 0.94 < ITherefore, the 203 x2O3xlZIUC section is suitable.

Longitudinalbars 4,9,5 DESIGN OF CASED COII]MNS

As discussed in section 45, steel columns are some_times cased in concreteforfire protection. However,the concrete also increases thi strengdr of the sec_tion, a fact which can be used to advaitage in designprovided that the conditions stated in cliuse 4.14.1of BS 5950 are met. Some of these conditions areillustrated in Fig. 4.27.

BS 5950 gves guidance on the design of UCsections encased in concrete for the foiloftng load_ing conditions which are discussed below: 1i) axiattyloaded columns and (ii) columns subjeci to axialload and bending.

4.9.5.1 Ar<icrlly loaded columnsThe design procedure for this case is summarized inFig. 4.28.

IIIIIItIt

Design of compression members

the cased section about the x-x axis, r3, is assumedto be equal to the radius of gyratio; of the un_cased steel section about the x-x axis.

3. Th: compression resistance of the cased section,Ps, is given by

e"= (e*94 ^

)0"(4.2e)

Fig. 4.28 Design procedure for axially loaded cased columns.

Nbtbs to Fig.4.28.

1. The efective length, lp, sho^uld not exceed theleast of (i) 40Dc; (ii) l}}bc"ld< and (iii) 250r,where bc and dc are as indicated in Frg. 4-22 andr is the minimum radius of gyration of the un_case{ UC section, i.e. ry.

2. Theradius of gyration of the cased section aboutthe y-y axis, ry, is taken as 0.20c but not morethan 0.2(B + 150) mm. The radius of gyration of

PROPERTIES OF UC SECTIONArea of UC section (lg)Radius of gyration (ta)Radius of gyration (r)Design strength (py)Effective len$h (Ls)

However, this should not be greater than theshort strut capacity of the section, pcs, which isgrven by

. O.25fc,r/1c\ , (4-3O)Po=(Ae+-f f )A \ '\ - Py ) '

where lc is the groqs sectional area of the con-crete but neglecting any casing in excess of Z5mm from the overall dimensions of the UCsection or any applied finish, Agthe gross sec-t ional area of the UC secl ion, /su thecharacteristic strength of the concrete whichshould not be greater than 40 N mm- 2, p" *recompressive strength of the IJC section deter_mined as discussed for uncased columns (section4.9. 1) blut using ry and ry for the cased section(9ee_19te 2 above) and fo the design suength ofthe U"C section which should not exceed af S Nmm -.

Excrnple 4.13 Encqsed steel colunn reslsting crn cDrial loqdCalculate the compression resistance of a 3o5x3o5 x l18 kg rn- I UC column if it is encased inconcrete of compressive strength 20 N mm-'io th. manner rrr""*" below. Assume *rat the effectivelength of t}le column about both axes is 3.5 m.

dc: 425

= 15 000 mm2,= 136 mm-- 77 -5 mm=265N**-2=3.5m

x 305 x 118 kg m-l UC

(Appendix B)

(since T= 18.7 mm)

calculate ef fect ive length'1, L,

calculate radii of gyration of cased section'2, ry and r;

calculate compression resislance of column*3, p"

II

Deslgrn in skuchnol steelwork to BS 5950

EFFECITiTE TENGTHCheck that the effective length of column (= 3500 mm) does not exceed the least of:

4Obg= 40 x 425 = 17 000 mm

roob? fio x 4252e

=- -iis - = 42 5oo mm

25ory = 25O x77.5 = 19 375 mm OK

RADII OF GYRATION FOR TFIE CASED SECNONFor the cased section rx is same as for the rJC secrion = 136 mm. For the cased sectio n ry = o.2bc=O.2x425 =85 mm > g.Z@ + 150) =O-2(3O6.8 + 150) = 91.36 mm OKFlence ry = 85 mm and rx = 136 mm.

COMPRESSION RESISTANCESlendemess rcrtio

" ls 3500,tx= r*

= 136

=25.7 <l8O

^ LE 35ooAv=-' ry85

= 41.2 < 180

Compressive strengrthFrom Table 4' 17, relivarrt compressive strength values for buckling about the x-x axis are obtained

["fiIi:T:;SJrBS 5e50 (iabte4-1o andfromTabre 27 (.>

'rbs sssririoii+Jsfo,u.,,ai,,gFor l"x = 25.7 and py =,265 \mm-

2 "orrp."rsive

strength (pc) = 257 I;"g- 1- (Table4.18). For Iy

;1i,'*1fr; 265-N. mm- z compressive strength (?;) = i;6 N mm- ' <r"ob' q.-i;i. H.r,.., p" ii

Compression resistsrceAe = 15 OO0 mm2Ac = dcbc= 425x!25 = 180 625 mm2h = 265 { *- i (since T= 18.7 mm)

fi=33'"i#;'Compression resistance of encased column, ps, is given by

' o.=ln"*!!$f o.LPvl-

=[,, ooo * O-45 x 2O x 180 625

lr^ = n.r,x 106N265

TIItt!IT

IIIIII

il

; lI

I

Desigrn ol compression mem.berswhich sbould not be greater than the short strut capacity, pss, given by

*,=[r,.rY]^=ft , ooo no'25x2ox

L 265180 62

=4.g7 x t06N OKHence the compression resistance of the encased column is 4.g1 x 106 N. comparing this with thecompression resistance ofthe'ncased column tzxamete a1,jl;o:*G"t trr.load capacity ofthe columnhas been increased from 3357 to 481 0 klr{, which r.pro.no * i.ro""r" of approxima tely 45(r/o.

4'9'5'2 columns subiect to csdcl locd ond where Fc is the compressive force due to axial load,bending L--- :^ ^:-:r^- ^- ^r

P" the compression resistance of the cased sectionThe design procedure here is similar to that when c"q""ti"" i.2g), pcstrr" ,ton,t-rrt capacity (equa--$e column is axially loaded but also involves check- aio" alaol,'aa- , My the applied moment about theng for local capacitv and buckling resistance using *"ioi *'d minor ;., .J$;;.iu.ty, Mq, Mgy thedle following relationships: moment capaciry of the uc section about the x - x\- l-ocalcapacity. and y - y axes r-espectivelR z is the equivalent

*.# *p =, @ 31) ffl:f*:"13T;',#ff i;'.i"JTi:1,.,::r cs tYtcx lvrcy resrstance mo.r l lent of the cased column ]

?. Buchling resistance- Sxpu) l.5Mu for the uncased section. To determine

Fc . mMx, mMv - . (4.32) t*J:"'f:It.1*'":"I?;lt'jrffiT'r;;,'nir"

P"" Mb *MJ=t

B : 306.8

=l00kNm=2OkNm

305 x 305 x 118.kg m- ' UC

t4 l

Excnnple 4.14 Encqsed steel column resisting cr c,xicrl loodcrnd bending11 Example 4.l l itwas found that a 305 x 305 xthe below design load and moments:

Design axial loadDesign moment about the x-x axisDesign moment about the y-y axis

fr,'J$:efJi"*-fffi*H:'-":I^::.i#i:.g.*;;"; berow, determine its suitab'ity.The effective length of tle column "u""i

u",rr axes is 7 m.

I l8 kg m-' UC column was incapable of resisting

Desigrn in stucttucrl steelwork to BS 5950

PROPERNES OF UC SECTIONArea of UC section (lg)Radius of gyration: x-x axis (4)Radius of gyration: y-y axis (r)Elastic modulus: x-x axis (Zx)Elastic modulus: y-y axis (Zy)Plastic modulus: x-x axis (Sx)Design strength (py)Effective tength (tr)

LOCAI CAPACIWAxial load (Fc)Applied moment: x-x axis (Mx)Applied moment: y_y axis (My)

Short strut capacity, pss, is givenby

= 15 000 mm2= 136 mm= 77.5 mm= 176O x 103 mm3= 587 x 103 mm3= 1950 x 103 mm3=265 N mm-2 1rirr.. 7= l8.Z mm)=7m

= 200O klr{= 100 kl.I m= 20 kI.I m

265

= 4.878x 106 N = 4g7g k].{Moment capacity of column, Mcx, is given by

Mcx: fuZx=265 x 1?60 x lO3 = 466.4x 106 N mm = 466.4 kNI mMoment capacity of column, M(:lpis gven by

M.y = fuZy = 265 x587 x lO3 = 155.6 x 106 N mm = I 55.6 kI.I m

F" Mx Mv - 2ooo + loo * 2o

P** M".* 6 =t:;:. ::f .', ,T: 3 .75 < |Ffence, the local capacity ofthe section is satisfactory

BUCKLING MSISTANCERodii of gryrcrlion lor cqsed sec[onFor the cased section rx is same as for the IJC section = 136 mm. For ttre cased section ry = e.ll.=0.2x425 =85mm> 0.2 (B+ 150)=0.2 (306.8+ f50)=91.36mm OKHence ry = 85 mm and rx = 136 mm.

Slendemess rqtio

*,=[r , . ' * ]*

= [,,

ooo *

, t "=t l=#= 51.5 < l8o

^r=E=t:*=82.4<r8oCompressive stengrthFlt^\=5f.5anqry- ZOf Nrm--2"o*pr".. ivesrength (F")=226N;o--2 TToblr4.Ig).ForLy= 82..4

"e- 265_r mm-' compressive strengrh ,(p) = ir N *-- 2 gatti +.tt1. Hence2" is

equal to 153 N mm-'.

zl- l

l2Ox 425265

O.25x

ITIIIIIII

Compression resistcrrceAe = 15 000 mm2Ac = 425 x 425 =

^180 625 mm2

h =265Nmm-1Pc: l53Nmm-2fc.u :20 N mm- 2

Compression resistance of encased column, ps, is given by

n"=le"*o nt{y.f ;.L- h r

=f rs ooo *o'45x20.\r80625] , r r=3.233x 106NL 265 J^

which is not greater than short strut capacity, pcs: 4g7g kl.{ (see above) OK.

Buckling resistcrrceFor the uncased section.

xy=b=9=90ry 77.5

Nx=9A116.2=5.5

From Table 4-14 zt = 0.79 and

)'LT = nudty= I x 0.851 x 0.79 x 90 = 6lHence pu = 205 N *-- 2 t:om Table 4.15.

rMu = Sxpr = 1950 x 103 x 2A5 = AOOx 106 N mm = 400 kN mFor the cased section.

" Le _ 7000 =R) /Lb=-rv 85

From Tabre 4.14'=0.gl and Nx=824116'2 = 5'08

?q:r = rum\ry = I x 0.851 x 0.81 x g2.4 = 56.gHencep6 = 214 N

-*-2 fromTable 4.15.

Mu=Sxpu= 1950x lO3 x 214 = 4l7x 106 N mm =417 kN m

|f9nce Mt(for casedUC section=417 kl.{m) } 1.5Mu (foruncasedUC section= 1.5 x40o= 600l<}.{ m).

CbecL buckling reslstcsrceFrom clause 4.7.7 of BS 5950, m = l.O for cased columns:

Fc mMx mlwe -2ooo -* I x 100 *1x20P,* Mo * M; =t?::.o.r:nTo.ru3i$.,

Hence, the section is now just adequate to resist the desigTr axial load of 2000 lN and design momentsabout the x-x and y-y ues of 100 and 20 kNI * ,.rp""i".iy. - ---

I=l

IIItI

Desigrn of compression members

Design in struch.ual steelwork to BS 5950

a: greater projectionb.' lesser projection

bkr{

I

4.9,6 DESIGNI OF COLUMN BASEPLAIESClause 4.1V.2 of BS 5950 gives guidance on thedesign of concentrically loaded slab baseplates,which covers most practical design situations (Frg.

4.29)- The plan area of the baseplate is given by

Plan area ofbaseplate =axial load (4.33)

bearing strengthStanchion

+T,

where bearing strength = 0.4/cu for concrete founda-

tions. The baseplate thickness, r, is given by

, =lTt 6' - o3u'1f"d flange thickness ({f 'un)

Lpyp I

where a is the greater proiection of the plate beyond

the column (Fis. 4.29)' b the smaller proiection ofthe plate beyond the column (FiS. 4.29), ar thepressure on the underside of the plate assuming auniform distribution (N mm-') andp]? the designstrength of the platewhich maybe taken fromTable6 of BS p95O (Table 4.3), but not greater rhan 270N mm- ".

Plan

Pressuae N mm-2

Elevation

Fig.4.29 cle

l .

Excrmple 4,15 Desigrn of cr steel colurnn bcrseplcrte

Plan area ofbaseplate =axial load

bearing strength

Design a baseplate for the axially loaded column shown belolr, assuming that the foundations are of

.orr"i"a" of compressive characieristic strength 30 N mm- ' and the design strengh of the plate is

265 N mm-' .

I Axial load = 3O0O kN

Y305 x 305 x 118 kg m-' UC f'n

\1| ,1, I r=18.7mml ry l r

r-l--+--l-1 t r----r---T'I

[- 'lf o| i l t tTI l i l 11314.5

l r i l l lbt ' ' t - _t ' t

a 306.8 a

=#flf, =2.5xlo5mm2

Asguming that the baseplate is square, the minimum length of the sides of tlle baseplate is V(2-5 x

l0)) : 500 mm. Pressure on the underside of baseplate, zo, is given by

F-tii#.FrrF.ilII

J,l-33)

-=***=: :L lou=12N__-2ptan area )uu_Baseplate thickness, r, is given by

, =l# o, - o.z*l]* n u,n ,thickness

fz.sxtz n - lh=l

26s (96.6" _ 0.3 x sz.ts21l

= 27 .6mm > flange thickness = l g.7 mmwhere a=r/2 (500- 306.9) = 96.6mm and b= t /z(500_ 3t4.5) =92.75 mm.Hence provide baseplate 500 x 500 x 30 mm_

4.10 Design ol connections

Desigrn o{ @nnections

Web plale

I

IItIII

is

There are two- principal methods for connectingtogether steel elements of structure, and the variouscleats, end plates, etc. also required:

l. Bolting_,^using ordinary or high strengrh frictiongrip @ISFG) bolts, is the pincipat-_.tfroa of_c_o_nnefting together elements on iit..

2. Velding, principally elecric arc welding, is analtemadve way of connecdng elemehts on site,but most welfing usually t"t-.* pt".. in factoryconditions. End plates and fixing .ilr.,

"r"welded to the elements in the faUri-caton yara.The elements are then detiv.reJio .ii". _rr.r"they are bolted together in position.

Figure 4-30 shows some typical connecdons used insteel structures.The aim of this section is to describe the designofsomecomr.nonly used types of b"ill;;Jwetded

connections in steel stntctures. However, at theoutset, it is worth while reiterating som.'generalgotpp^re_l g tin g to connecti on desi gn-give,

-i., .t

".rr.6 ofBS 5950.

The first sentence is vitally important _ .Connec_tions should b-e designed ,ri ,fr. U"ri, of a realisticassumption of the disribution of intemat forces,h1y-g regard ro retarive stiftress., il;i; any de-tailed- design is embarked

";";;; iefor., aconsideration of how forces will Ue iiansmltteathrough the ioint is essential.

'loints should be designed to act in accordance

* *^--t ::rumptions already maae irrtfr-Ja.rigrr.,rr, ror rnstance, the structure- is designed in .simllec-onstruction', the beam_column i6int strouta Uedesigned accordingly to accept rotations rather than

T"Ilil t-rigid joint woutd be completerv *rr;g

rn uus sltuation) as it would tend to generate amoment in the column for which it has" not beendesigned.

. 'The ductiliry-of steel assists in the distribution ofrorces generated within a joint,, This means thatresidual forces due to initial lack of nt,", J"" to bolttightening, do not normally have to Ue .or,siO.r"a.

4.10.1 BOLTED CONNECTIONSAs mentioned above, two types of bolts commonlv

Boltedend-plate

===J=.F(IILJ

JL

Flangecover plate

j

Boltedweb cleat

I.l

I

(a)

Fig. 4.30 Tjpical connections: (a) beam m column; (b) beam to beam.

(b)

145