Client: Client No 1. Location: Location No 1

Transcription

1 1 of 3 JOINT CONIGURATION AND DIMENSIONS: bolted ed plate coectio (ustiffeed) Referece clauses: Resistaces for the exteded ed plate coectio. Assumptio: The desig momets i the to beams are equal ad opposite. No axial compressio i the beams (N Ed = 0). Colum UC 54 x 54 x 107 Beam 1 UB 533 x 10 x 9 8 Beam UB 533 x 10 x x 50 x x 50 x 5 Colum: UC 54 x 54 x 107 i S 75 (EN 1005-) RESISTANCE O JOINT Beams: UB 533 x 10 x 9 i S 75 (EN 1005-) Bedig momet: M j,rd = 44 knm Ed plate: 670 x 50 x 5 i S 75 (EN 1005-) Vertical shear: V j,rd = 499 knm Bolts: M4 o preloaded class 8.8 bolts ISO 4016 ISO ISO 7089/7091 Welds: illet elds. Assumed eld sized: s f = 1mm (flage) s = 8 mm (eb) Bolt spacigs S = D = C = = 75 mm 100 mm R1 = e x = 50 mm R11 + R = p 1- = 100 mm (spacig ro 1-) R11 = x = 40 mm R = 60 mm R3 = p -3 = 90 mm (spacig ro -3) R3 = 90 mm Techical Refereces: Joits i Steel Costructio: Momet-Resistig Joits to Eurocode 3. Publicatio P398. The Steel Costructio Istitute..steel-sci.com The British Costructioal Steelork Associatio Limited..steelcostructio.org

2 of 3 DIMENSIONS AND SECTION PROPERTIES Referece clauses: Colum rom data tables for UC 54 x 54 x 107: Depth h c = 66,7 mm Width b c = 58,8 mm Web thickess t c = 1,8 mm lage thickess t fc = 0,5 mm Root radius r c = 1,7 mm Depth betee fillets d c = 00,3 mm Area A c = mm² = 136,4 cm² Beams rom data tables for UB 533 x 10 x 9: Depth h b = 533,1 mm Width b b = 09,3 mm Web thickess t b = 10,1 mm lage thickess t fb = 15,6 mm Root radius r b = 1,7 mm Depth betee fillets d b = 476,5 mm Area A b = mm² = 117,4 cm² Ed plates Depth h p = 670 mm Width b p = 50 mm Thickess t p = 5 mm Bolts M4 o preloaded class 8.8 bolts Diameter of bolt shak d = 4 mm Diameter of hole d 0 = 6 mm Shear area A s = 353 mm² Diameter of asher d = 44 mm (ISO 7089/7091) Bolts spacigs Colum Ed distace (ro 1 from colum edge) e 1 = 1000 mm Spacig (guage) = 100 mm Edge distace e c = 79,4 mm Spacig ro 1- p 1- = 100 mm Spacig ro -3 p -3 = 90 mm Ed plate Ed distace e x = 50 mm Spacig (guage) = 100 mm Edge distace e p = 75 mm Spacig ro 1 above beam flage x = 40 mm Spacig ro 1- p 1- = 100 mm Spacig ro -3 p -3 = 90 mm igure 6.8 igure 6.10 igure 6.13

3 3 of 3 MATERIAL STRENGTHS Referece clauses: Steel stregth BS EN NA..4 or buildig the omial values of the yield stregth (f y ) ad the ultimate stregth (f u ) for structural steel should be those obtaied from the product stadard. Where a rage is give, the loest omial value should be used. S 75 (EN 1005-) EN Table 7 or t 16 mm f y = R eh = 75 N/mm² or 16 mm < t 40 mm f y = R eh = 65 N/mm² or 3 mm t 100 mm f u = R eh = 410 N/mm² Hece: Beam yield stregth f y,b = 75 N/mm² Beam ultimate stregth f u,b = 410 N/mm² Colum yield stregth f y,c = 65 N/mm² Colum ultimate stregth f u,c = 410 N/mm² Ed plate yield stregth f y,p = 65 N/mm² Ed plate ultimate stregth f u,p = 410 N/mm² Bolt stregth Table 3.1 Nomial yield stregth f yb = 640 N/mm² Nomial ultimate stregth f ub = 800 N/mm² PARTIAL ACTORS OR RESISTANCE EN Structural steel Table.1 (see NA) = 1,00 M1 = 1,00 M = 1,10 Parts i coectio Table.1 (see NA) M = 1,5 (bolts, elds, plates i bearig).

4 4 of 3 TENSION ZONE T-STUBS Whe pryig forces may develop, the desig tesio resistace ( T,Rd ) of a T-stub flage should be take as the smallest EN value for the 3 possible failure models i Table 6. () (6) BOLT ROW 1 Colum flage i bedig (o backig plate) Cosider bolt ro 1 to be actig aloe. The key dimesios are sho belo. Determie e mi, m ad l eff for the ustiffed colum flage EN m t 0.8r c c mc () 0,5 x [100 1,8 x 0,8 x 1,7] = 33,4 mm e mi = mi[e p ; e c ] = mi(75; 79,4] = 75 mm EN igure 6.8 or Mode 1, l eff,1 is the lesser of l eff,c ad l eff,cp Table 6.6 l eff,cp = πm = x 3,14 x 33,4 = 10 mm l eff,c = 4m + 1.5e c = 4 x 33,4 + 1,5 x 79,4 = 33 mm l eff,1 = mi[l eff,c ; l eff,cp ] = mi[33; 10] = 10 mm or failure Mode, l eff, = l eff,c STEP 1 Therefore l eff, = l eff,c = 33 mm Mode 1 resistace or Mode 1, ithout backig plates, usig Method : 8 e m e m EN Table 6. m = m c = 33,4 mm = mi[e mi ; 1.5m] = mi[75; (1.5 x 33,4)] = mi[75; 41,8] = 41,8 mm (cot'd)

5 5 of leff,1 tfcfy,c [0,5 x 10 x (0,5)² x 65]/1,00 = 5847 x 10³ Nmm = 5,85 knm Diameter of the asher (for M4 o preloaded class 8.8 bolts): d = 44 mm e = d /4 = (44)/4 = 11 mm Therefore, 8 e m e m [(8 x 41,8 x 11) x 5847 x 10³]/{10³ x [ x 33,4 x 41,8 11 x (33,4 + 41,8)]} = 98,1 kn Mode resistace or Mode T,,Rd Mpl,,Rd m [ x (6487 x 10³) + 41,8 x 406,7 x 10³)/(33,4 + 41,8) = 398,4 kn EN Table 6. 0,5 leff, t fcfy,c Mpl,,Rd [0,5 x 33 x (0,5)² x 65]/1 = 6487 x 10³ Nmm = 6,49 knm is the total value of for all the bolts i the ro, kf A 0.9f A ub s ub s M M or bolts i the ro (0,9 x 800 x 353)/1,5 = 03,3 x 10³ N = 03,3 kn (for a sigle bolt) EN Table 3.4 = x 03,3 x 10³ = 406,7 x 10³ N = 406,7 kn Mode 3 resistace (bolt failure) T,3,Rd = = 406,7 kn EN Table 6. Resistace of colum flage i bedig t,fc,rd = mi[ ; T,,Rd ; T,3,Rd ] = mi[98,1; 398,4; 406,7] = 398,4 kn EN (6) Colum eb i trasverse tesio The desig resistace of a ustiffeed colum eb to trasverse tesio is determied from: EN (1) t,c,rd b t f eff,t,c c y,c Eq. (6.15) here ω is a reductio factor that allos for the iteractio ith shear i the colum eb pael.

6 6 of 3 Trasformatio parameter β = 0,0 [-] Reductio factor: 0 β 0.5 ω = 1,00 Table 5.4 Table 6.3 Here, as mi[ ; T,,Rd ] = [98,1; 398,4] = 398,4 kn ith: l eff,1 = l eff, = 10 mm 33 mm for a bolted coectio the effective idth of the colum eb i tesio is cosidered to be: b eff,t,c = 33 mm. f y,c = f y,c = 65 N/mm² ω = 1,00 [-] Thus, t,c,rd = [(1,00 x 33 x 1,8 x 65)/1,00]/10³ = 790,4 kn Ed plate i bedig STEP 1 Bolt ro 1 is outside the tesio flage of the beam. The key dimesios for the T-stub are sho belo igure 6.10 The values of m x, e x, ad e for the T-stub are: e = e p = e x = 75 mm 50 mm m x = x 0.8s f = 40 0,8 x 1 = 30,4 mm or Mode 1, l eff,1 is the lesser of l eff,c ad l eff,cp Table 6.6 l eff,cp = mi[πm x ; πm x + ; πm x + e] = mi[(π x 30,4); (π x 30, ); (π x 30,4 + x 75)] = mi[191; 196; 46] = 191 mm l eff,c = mi[4m x + 1.5e x ; e + m x e x ; 0.5b p ; m x e x ] = mi[(4 x 30, x 50); (75 + x 30, x 50); (0.5 x 50); (0.5 x x 30, x 50)] = Table 6.6 l eff,c = mi[184; 167; 15; 14] = 15 mm

7 7 of 3 l eff,1 = mi[l eff,c ; l eff,cp ] = mi[15; 191] = 15 mm or Mode, l eff, = l eff,c = 15 mm Mode 1 resistace or Mode 1 failure, usig Method : Table 6. 8 e m e m = e mi = mi[e x ; 1.5m x ] = mi[50; 1.5 x 30,4] = 38,3 mm m = m x = 30,4 mm Sheet 6 e = 11,0 mm Sheet 5 f y = f y,p = t = t p = 65 N/mm² 5 mm 0.5 leff,1 tp fy,p (0.5 x 15 x 5² x 65)/1 = x 10³ = Nmm = 5, knm 8 e m e m (8 x 38,3 x 11,0) x x 10³/{10³ x [ x 30,4 x 38,3 11,0 x (30,4 + 38,3]} = 936 kn Mode resistace T,,Rd Mpl,,Rd m Table leff,tpfy,p Mpl,,Rd (0.5 x 15 x 5² x 65)/1 = x 10³ = Nmm = 5, knm l eff, = 15 mm = 407 x 10³ N = 407 kn Sheet 5 Therefore, T,,Rd = ( x x 10³ + 38,3 x 407 x 10³)/{10³ x (30,4 + 38,3)} = 377 kn Mode 3 resistace (bolt failure) T,3,Rd = = 407 kn Resistace of ed plate i bedig t,ep,rd = mi[ ; T,,Rd ; T,3,Rd ] = mi[936; 377; 407] = 377 kn (6) Beam eb i tesio As bolt ro 1 is i the extesio of the ed plate, the resistace of the beam eb i tesio is ot applicable tothis bolt ro.

8 8 of 3 SUMMARY: RESISTANCE O T-STUB OR BOLT ROW 1 Resistace of bolt ro 1 is the smallest value of: Colum flage i bedig t,fc,rd = 398 kn Colum eb i tesio: t,c,rd = 790 kn Ed plate i bedig: t,ep,rd = 377 kn Therefore, the resistace of bolt ro 1 is: t1,rd = mi[ t,fc,rd ; t,c,rd ; t,ep,rd ] = mi[398; 790; 377] = 377 kn BOLT ROW irstly, cosider ro aloe. Colum flage i bedig The resistace of the colum flage i bedig is as calculated for bolt ro 1 (Mode ): STEP 1 t,fc,rd = 398 kn Sheet 5 Colum eb i trasverse tesio The colum eb resistace to trasverse tesio ill also be as calculated for bolt ro 1. STEP 1B Therefore: t,c,rd = 790 kn Sheet 6 Ed plate i bedig STEP 1 Bolt ro is the first bolt ro belo the beam flage, cosidered as "first bolt-ro belo tesio flage of beam" i Table 6.6. The key dimesios for the T-stub are as sho for the colum flage T-stub for ro 1 ad as sho belo (i elevatio) for ro. Sheet 4 tb 0.8s m mp e = e p = 75 mm (100 10,1 x 0.8 x 8)/ = 38,6 mm m = R t fb 0.8s f = 60 15,6 (0.8 x 1) = 34,8 mm α is obtaied from igure 6.11 (reproduced i, Appedix G as igure G.1) Parameters required to determie α: m 1 m e ad m m e

9 9 of 3 λ 1 = 38,6/(38,6 + 75) = 0,34 λ = 34,8/(38,6 + 75) = 0,31 Thus, by iterpolatio (see, igure 6.11), = 7,3 [-] igure 6.11 Table 6.6 l eff,cp = πm = l eff,c = m = l eff, = l eff,c = x π x 38,6 = 4 mm 7,3 x 38,6 = 83 mm 83 mm l eff,1 = mi[l eff,cp ; l eff,c ] = mi[4; 83] = 4 mm Mode 1 resistace Table 6. or Mode 1, usig Method : 8 e m e m SHEET 4 = mi[e mi ; 1.5m] = mi[75; (1.5 x 38,6)] = 48, mm SHEETS 5//3 e = 11,0 mm t p = 5 mm f y,p = 65 N/mm² 0.5 leff,1 tp fy,p 8 e m e m (0,5 x 4 x 5² x 65)/1,00 = 10,0 x 10³ x 10³ Nmm [(8 x 48, x 11,0) x 10³]/[( x 38,6 x 48,) 11,0 x (38,6 + 48,)] = 1.30 kn Table 6. SHEET 5 Mode resistace T,Rd Mpl,,Rd m = 03 kn 0.5 leff, tp fy,p Mpl,,Rd (0,5 x 83 x 5² x 65)/1,00 = 11,7 x 10³ x 10³ Nmm = x 03 = 407 kn T,,Rd Mpl,,Rd m ( x 11,7 x 10³ + 48, x 407)/(38,6 + 48,) = 496 kn Mode 3 resistace (bolt failure) T,3,Rd = = 407 kn

10 10 of 3 Resistace of ed plate i bedig t,ep,rd = mi[ ; T,,Rd ; T,3,Rd ] = [1.30; 496; 407] = 407 kn (6) Beam eb i tesio STEP 1B The desig tesio resistace of the eb is determied from: (1) beff,t,btbfy,b t,b,rd Eq. (6.) b eff,t,b = mi[l eff,1 ; l eff, ] = 4 mm (coservatively, cosider the smallest l eff from earlier calculatios) () t b = 10,1 mm SHEET ω = 1,00 [-] SHEET 6 Therefore: t,b,rd b t f eff,t,b b y,b [(1,00 x 4 x 10,1 x 75)/1,00]/10³ = 673 kn The above resitaces for ro all cosider the resistace of the ro actig aloe. Hoever, o the colum side, the resistace may be limited by the resistace of the group of ros 1 ad. That group resistace is o cosidered. ROWS 1 AND COMBINED Colum flage i bedig e c = m c = p -3 = 79,4 mm SHEET 33,4 mm SHEET mm SHEET e 1 = 1000 mm SHEET 3 or bolt ro 1 combied ith ro i the colum flage, both ros are cosidered as ''ed bolt ro'' i Table 6.4. or bolt ro 1: l eff,c = mi[(m e + 0.5p); (e p)] = mi[( x 33, x 79, x 100); ( x 100)] = 167 mm l eff,cp = mi[(πm + p); (e 1 + p)] = mi[(π x 33, ); ( x )] = 05 mm The effective leghts for bolt ro, as a bottom ro of a group, are the same as for ro 1: l eff,c = l eff,cp = x 167 = 333 mm x 05 = 410 mm

11 11 of 3 The effective legths for the group of bolts is: Mode 1 Table 6.4 l eff,1 = mi[ l eff,c ; l eff,cp ] = mi[333; 410] = 333 mm Mode : Table 6.4 l eff, = l eff,c = 333 mm Mode 1 resistace 8 e m e m Table 6. m = 33,4 mm SHEET 4 = 41,8 mm SHEET 4 e = 11,0 mm SHEET leff,1 tfc fy,c 8 e m e m (0.5 x 333 x 0,5² x 65)/1,00 = 9,7 x 10³ x 10³ Nmm [(8 x 41,8 x 11,0) x 9,7 x 10³ x 10³)/{10³ x [ x 33,4 x 41,8 11,0 x (33,4 + 41,8)]} = 1.47 kn Mode resistace T,,Rd Mpl,,Rd m Table 6. = 03 kn SHEET 5 = 4 x 03 = 813 kn 0.5 leff,tfcfy,c Mpl,,Rd T,,Rd Mpl,,Rd m (0.5 x 333 x 0,5² x 65)/1,00 = 9,7 x 10³ x 10³ Nmm ( x 9,7 x 10³ + 41,8 x 813)/(33,4 + 41,8) = 698 kn Mode 3 resistace (bolt failure) T,3,Rd = = 4 x 03 = 813 kn Table 6. Resistace of colum flage i bedig t,fc,rd = mi[ ; T,,Rd ; T,3,Rd ] = mi[1.47; 698; 813] = 698 kn (6) Colum eb i trasverse tesio STEP 1B The desig resistace of a ustiffed colum eb i trasverse tesio is: beff,t,ctc fy,c t,c,rd here b eff,t,c is the equivalete T-stub represetig the colum flage from Sec (). Coservatively use the (3) lesser of the values of effective legths for Mode 1 ad Mode : SHEET 10 (cot'd)

12 1 of 3 b eff,t,c = l eff, = 333 mm ith t c = 1,8 mm; f y,c = 65 N/mm² The equatio to use to calculate ω depeds o β. As before, β = 0,0 ad therefore ω = 1,00: SHEET 6 t,c,rd b t f eff,t,c c y,c (1,00 x 333 x 1,8 x 65/1,00)/10³ = kn Ed plate i bedig There is o group mode for the ed plate. SUMMARY: RESISTANCE O BOLT ROWS 1 AND COMBINED Resistace of bolt ro 1 ad combied, o the colum side, is the smaller value of: Colum flage i bedig: Colum eb i tesio: Therefore, the resistace of bolts 1 ad combied is: t,fc,rd = t,c,rd = t,1-,rd = 698 kn kn 698 kn The resistace of bolt ro o the colum side is therefore limited to: t,c,rd = t,1-,rd t1,rd = ( ) = 31 kn SHEET 8 SUMMARY: RESISTANCE O BOLT ROW Resistace of bolt ro is the smallest value of: Colum flage i bedig: t,fc,rd = 398 kn SHEET 8 Colum eb i tesio: t,c,rd = 790 kn SHEETS 6/8 Beam eb i tesio: t,b,rd = 673 kn SHEET 10 Ed plate i bedig: t,ep,rd = 407 kn SHEET 10 Colum side, as part of a group (see above): t,c,rd = 31 kn Therefore, the resistace of bolt ro is: t,,rd = 31 kn BOLT ROW 3 irst, cosider ro 3 aloe. Colum flage i bedig STEP 1 The colum flage i bedig resistace is the same as bolt ros 1 ad therefore: Colum eb i trasverse tesio t,fc,rd = 398 kn STEP 1B The colum eb resistace to trasverse tesio is as calculated for bolt ros 1 ad. Therefore: t,c,rd = 790 kn SHEET 6 Ed plate i bedig STEP 1 Bolt ro 3 is the secod bolt ro belo the beam's tesio flage, cosidered as a ''other ed bolt-ro'' i Table 6.6. The key dimesios are as oted above for bolt ro. Determie m, e ad l eff : e = e p = 75 mm m = 38,6 mm SHEETS /8 l eff,cp = πm = x π x 38,6 = 4 mm

13 13 of 3 l eff,c = 4m + 1.5e = l eff,1 = mi[l eff,cp ; l eff,c ] = 4 x 38, x 75 = 48 mm mi[4; 48] = 4 mm l eff, = l eff,c = 48 mm Mode 1 resistace or Mode 1, usig Method : 8 e m e m Table 6. = 48, mm ad m = 38,6 (as for ro ) SHEETS 8/9 = 11,0 mm SHEET leff,1t pfy,p 8 e m e m (0.5 x 4 x 5² x 65)/1,00 = 10,0 x 10³ x 10³ Nmm = 10,0 knm [(8 x 48, x 11,0) x 10,0 x 10³]/{[ x 38,6 x 48, 11,0 x (38,6 + 48,)]} = 1.30 kn Mode resistace M T,,Rd pl,,rd Mpl,,Rd m 0.5 l t f eff, p y,p t p = 5 mm = 03 kn = x 03 = 407 kn 0.5 leff,tpfy,p Mpl,,Rd T,,Rd Mpl,,Rd m (0.5 x 48 x 5² x 65)/1,00 = 10,3 x 10³ x 10³ Nmm = 10,3 knm ( x 10,3 x 10³ + 48, x 407)/(38,6 + 48,) = 463 kn Mode 3 resistace (bolt failure) t,3,rd = Σ = 407 kn Resistace of ed plate i bedig (6) t,ep,rd = mi[ ; T,,Rd ; T,3,Rd ] = mi[1.30; 463; 407] = 407 kn Beam eb i tesio T,b,Rd b t f eff,t,b b y,b STEP 1B (1) Eq. (6.) b eff,t,b = l eff

14 14 of 3 Coservatively, cosider miimum l eff. Therefore: b eff,t,b = l eff = mi[l eff,1 ; l eff, ] = mi[4; 48] = 4 mm. SHEET 13 t b = 10,1 mm. Therefore, b t f eff,t,b b y,b T,b,Rd [(4 x 10,1 x 75)/10³]/1,0 = 673 kn The above resistaces for ro 3 all cosider the resistace of the ro actig aloe. Hoever, o the colum side the resistace may be limited by the resistace of the group of ros 1,, ad 3 or by the group of ros ad 3. O the beam side, the resistace may be limited by groups of ros ad 3. Those group resistaces are o cosidered. ROWS 1, AND 3 COMBINED Colum flage i bedig STEP 1 Circular ad o-circular yield lie patters are: ROW 1 ROW ROW 3 The effective legth for bolt ro 1, as part of a group, is the same as that determied as part of the group of ros 1 a. Thus: Ro 1: l eff,c = 167 mm SHEET 10 l eff,cp = 05 mm Ro 3 is also a "ed bolt ro", similar to ro 1, but the value of bolt spacig p is differet. p = p -3 = 90 mm Thus: l eff,c = m e + 0.5p = ( x 33,4) + (0.65 x 79,4) + (0.5 x 90) = 16 mm l eff,cp = πm + p = (π x 33,4) + 90 = 195 mm or this group, bolt ro is a "other ier bolt ro". Therefore: l eff,cp = p l eff,c = p Here, the vertical spacig betee bolts above ad belo ro is differet, therefore use: p 1 p p 3 (100/) + (90/) = 95 mm l eff,cp = p = x 95 = 190 mm l eff,c = p = 95 mm Therefore, the total effective legths for this group of ros are: l eff,c = = 43 mm

15 15 of 3 l eff,cp = = 590 mm Therefore, assume: l eff, = l eff,1 = 43 mm ( l eff, = l eff,c = l eff,1 l eff,cp ) Table 6.4 Mode 1 resistace or Mode 1, usig Method : 8 e m e m m = 33,4 mm SHEET 4 = 41,8 mm SHEET 4 e = 11,0 mm SHEET leff,1 tf fy,c 8 e m e m (0,5 x 43 x 0,5² x 65)/1,0 = 11,8 x 10³ x 10³ Nmm = 11,8 knm [(8 x 41,8 x 11,0) x 11,8 x 10³]/[( x 33,4 x 41,8) 11,0 x (33,4 + 41,8)] = kn Mode resistace T,,Rd Mpl,,Rd m = 03 kn SHEET 5 = 6 x 03 = 1.0 kn 0,5 leff,,rd t f fy,c Mpl,,Rd Here, as l eff, = l eff,1, M pl,,rd = M pl,1,rd : T,,Rd Mpl,,Rd m ( x 11,8 x 10³ + 41,8 x 1.0)/(33,4 + 41,8) = 991 kn Mode 3 resistace (bolt failure) T,3,Rd = = 6 x 03 = 1.0 kn Table 6. Resistace of colum flage i bedig t,fc,rd = mi[ ; T,,Rd ; T,3,Rd ] = Colum eb i trasverse tesio mi[1.870; 991; 1.0] = 991 kn (6) STEP 1B The desig resistace of a ustiffeed colum eb i traverse tesio is: (1) beff,t,c tc fy,c t,c,rd Eq. (6.15) beff,t,c is the effective legth of the equivalet T-stub represetig the colum flage from As the failure is Mode (see sheet 15) take: (3) b eff,t,c = l eff, = 43 mm SHEET 15

16 16 of 3 The equatio to use to calculate depeds o. As before, ith = 0,00 [-] therefore: = 1,00 [-] SHEET 6 t,c,rd b t f eff,t,c c y,c [(1,0 x 43 x 1,8 x 65)/10³]/1,0 = kn Summary: resistace of bolts ros 1, ad 3 combied Resistace of bolt ros 1, ad 3 combied, o the colum side, is the smaller value of: colum flage i bedig: colum eb i tesio: t,fc,rd = t,c,rd = 991 kn kn Therefore, the resistace of bolt ro 1, ad 3 combied is: t,1-3,rd = 991 kn The resistace of bolt ro 3 o the colum side is therefore limited to: t3,c,rd = ( t,1-3,rd t,1-,rd ) = ( ) = 93 kn ROWS AND 3 COMBINED Colum side-flage i bedig olloig the same process as for ro 1, ad 3 combied, l eff,cp = πm + p = x π x 33,4 + x 90 = 390 mm l eff,c = 4m + 1.5e + p = 4 x 33,4 + 1,5 x 79, = 33 mm Therefore, l eff, = l eff,1 = 33 mm Mode 1 resistace 0,5 leff,1 t f fy,c 8 e m e m (0,5 x 33 x 0,5² x 65)/1,0 = 9,0 x 10³ x 10³ Nmm = 9,0 knm Table 6. [(8 x 41,8 x 11,0) x 9,0 x 10³]/[( x 33,4 x 41,8) 11,0 x (33,4 + 41,8)] = 1.48 kn Mode resistace Here, as l eff, = l eff,1, M pl,,rd = M pl,1,rd : Mpl,,Rd ( x 9,0 x 10³ + 41,8 x 4 x 03)/(33,4 + 41,8) = 691 kn Table 6. T,,Rd m Mode 3 resistace (bolt failure) T,3,Rd = = (6 x 03) = 1.0 kn Table 6. Colum eb i trasverse tesio (1) b eff,t,c = 33 mm Eq. (6.15) The equatio to use to calculate depeds o. As before, ith = 0,00 [-] therefore: = 1,00 [-] SHEET 6 t,c,rd b t f eff,t,c c y,c [(1,0 x 33 x 1,8 x 65)/10³]/1,0 = kn

17 17 of 3 Beam side-ed plate i bedig O the beam side, ro 1 is ot part of a group but the resistace of ro 3 may be limited by the resistace of ros ad 3 as a group. Determie the effective legths for ros ad 3 combied: Ro is a "first bolt-ro belo tesio flage of beam" i Table 6.6. l eff,cp = πm + p Here: p = p -3 = 90 mm = 48, m = 38,6 (as for ro aloe) l eff,cp = πm + p = (π x 38,6) + 90 = 11 mm STEP 1 A Obtai a from igure (or Aex G ) usig (see sheet 9): λ 1 = 0,3395 λ = 0,30647 rom igure 6.11 = 7,3 [-] l eff,c = 0.5p + m (m e) = 0,5 x ,3 x 38,6 [ x 38,6 + (0.65 x 75)] = 04 mm Ro 3 is a "other ed bolt-ro" i Table 6.6 l eff,cp = πm + p = (π x 38,6) + 90 = 11 mm STEP 1 A l eff,c = m e + 0.5p = ( x 38,6) + (0.65 x 75) + (0.5 x 90) = 169 mm Therefore, the total effective legths for this group of ros are: l eff,c = l eff,cp = = 373 mm = 4 mm Hece, l eff, = l eff,1 = 373 mm Mode 1 resistace (ros + 3) or Mode 1 failure, usig Method : Table 6. 8 e m e m = 48, mm SHEET 9 e = 11,0 mm SHEET leff,1 tp fy,p 0.5 x 373 x 5² x 65/1,0 = 15,4 x 10³ x 10³ Nmm = 15,4 knm m = 38,6 mm SHEET 8 8 e m e m [(8 x 48, x 11,0) x 15,4 x 10³]/[ x 38,6 x 48, 11,0 x (38,6 + 48,)] =.034 kn

18 18 of 3 Mode resistace (ros + 3) T,,Rd Mpl,,Rd m = 03 kn = 4 x 03 = 813 kn M pl,,rd 0.5 l t f eff, f y,p Here, as l eff, = l eff,1 : M pl,,rd = M pl,1,rd = 15,4 knm T,,Rd Mpl,,Rd m ( x 15,4 x 10³ + 48, x 813)/(38,6 + 48,) = 808 kn Mode 3 resistace (bolt failure) (ros + 3) T,3,Rd = = 4 x 03 = 813 kn Resistace of ed plate i bedig t,ep,rd = mi[ ; T,,Rd ; T,3,Rd ] = mi[.034; 808; 813] = 808 kn (6) Beam eb i tesio This verificatio is ot applicable as the beam flage (stiffer) is ithi the tesio legth. (*) Summary: resistace of bolt ros ad 3 combied Resistace of bolt ros ad 3 combied, o the beam side, is: Ed plate i bedig: Therefore(*), o the beam side: t,ep,rd = 808 kn t,-3,rd = t,ep,rd = 808 kn The resistace of bolt ro 3 o the beam side is therefore limited to: t3,b,rd = t-3,rd = (808 31) = 487 kn SHEET 1 Resistace of bolts ros ad 3 combied, o the colum side, is: Colum flage i bedig: t,fc,rd = 691 kn SHEET 16 Colum eb i tesio: t,c,rd = kn Therefore, o the colum side: t-3,rd = 691 kn SHEET 16 The resistace of bolt ro 3 o the colum side is therefore limited to: t3,b,rd = t-3,rd = (691 31) = 370 kn Summary: resistace of bolt ro 3 Resistace of bolt ro 3 is the smallest value of: Colum flage i bedig: t,fc,rd = 398 kn SHEET 5/1 Colum eb i tesio: t,c,rd = 790 kn SHEET 6/1 Beam eb i tesio: t,b,rd = 673 kn SHEET 14 Ed plate i bedig: t,ep,rd = 407 kn SHEET 10 (cot'd)

19 19 of 3 (cot'd) Colum side, as part of a group ith & 1: t3,c,rd = 93 kn SHEET 16 Colum side, as part of a group ith : t3,c,rd = 370 kn SHEET 18 Beam side, as part of a group ith : t3,b,rd = 487 kn SHEET 18 Therefore, the resistace of bolt ro 3 is: t3,rd = 93 kn. SUMMARY O TENSION RESISTANCES The above derivatio of effective resistaces of the tesio ros may be summarized i tabular form, as sho belo. Resistaces of ros tr,rd [kn] Colum Colum Ed Beam MIN Effect. flage eb plate eb resist. ROW 1, aloe N/A ROW 1 (mi) ROW, aloe ROW N/A N/A 698 ROW (effect.) ( ) 300 ROW (mi) ROW 3, aloe ROW N/A N/A 991 ROW 3 (effect. a) ( ) 93 ROW N/A 691 ROW 3 (effect. b) (691 31) 370 COMPRESSION ZONE T-STUBS 93 ROW 3 (mi) Colum eb i trasverse compressio STEP The desig resistace of a ustiffed colum eb i trasverse compressio is determied from: c,c,rd k b t f c eff,c,c c y,c (crushig resistace) 6..6,(1) Eq. (6.9) but: c,c,rd kc beff,c,c tc fy,c M1 (bucklig resistace) or a bolted ed plate: b eff,c,c = t fb + a p + 5 (t fc + s) + s p = t fb + s f + 5 (t fc + s) + s p Eq. (6.11) or rolled I ad H colum sectio s = r c. Thus: s = r c = 1,7 mm SHEET s p is the legth obtaied by dispersio at 45 through the ed plate: 0.5s p = 5 mm SHEET t p = 5 mm " Beam flage h p = 670 mm (Ed-plate depth) s f = 1 mm " Ed-plate t fc = 0,5 mm " t fb = 15,6 mm "

20 0 of 3 s p = t p = x 5 = 50 mm Verify that the depth of the ed plate (h p ) is sufficiet to allo the dispersio of the force. Miimum h p required is: h p e x + x + h b + s f + t p = ( , ) = 660,1 mm h p = 670 mm SHEET As 670 mm 660,1, the depth of the ed plate is sufficiet. [Satisfactory] Therefore: b eff,c,c = t fb + a p + 5 (t fc + s) + s p = t fb + s f + 5 (t fc + s) + s p = 15,6 + x x (0,5 + 1,7) + 50 = 55,6 mm. ρ is the reductio factor for plate bucklig If If p p p p p is the plate slederess: Eq. (6.13a) Eq. (6.13b) 0.93 b d f eff,c,c c y,c p Etc 0.93 x {(55,6 x 00,3 x 65)/(10 x 10³ + 1,8²)} = 0,59 [-] Eq. (6.13c) As 0,59 mm 0.7 Eq. (6.13a) gives: 1,00 [-] is determied from Table 6.3 based o (see sheet ). The equatio to use to calculate depeds o. As before, ith = 0,00 [-] therefore: = 1,00 [-] SHEET 6 k c is a reductio factor that takes accout of compressio i the colum eb. Note to Here, it is assumed that k c = 1,00 [-] 6..6.() c,c,rd k b t f c eff,c,c c y,c k b t f c eff,c,c c y,c M1 (1,00 x 1,00 x 55,6 x 1,8 x 65/1,0)/10³ = 867 kn 867 x (1,00/1,00) x 1,00 = 867 kn Therefore: c,c,rd = 867 kn (crushig resistace govers). Beam flage ad eb i compressio The resultat of the desig resistace of a beam flage ad adjacet compressio zoe of the eb is determied usig: (1) Mc,Rd c,fb,rd Eq. (6.1) h t fb M c,rd is the desig resistace of the beam At this stage, assume that the desig shear force i the beam does ot reduce M c,rd. Therefore: M c,rd b fb b fb y,b y,b c,fb,rd bbtfb hb tfb hb tfb bt h t f / f (approximated, coservative)

21 1 of 3 y,b c,fb,rd 1.3 bbtfb f 1,3 x (75/1,0) x 09,3 x 15,6 = x 10³ N = kn Summary: resistace of compressio zoe Colum eb i trasverse compressio: Beam flage ad eb i compressio: c,c,rd = 867 kn c,fb,rd = kn Compressio resistace: c,rd = mi[ c,c,rd ; c,fb,rd ] = mi[867; 1.167] = 867 kn Resistace of colum eb pael i shear STEP 3 The plastic shear resistace of a ustiffeed eb is give by: V p,rd 0,9fy,cA 3 vc (1) Eq. (6.7) The resistace is ot evaluated here, sice there is o desig shear i the eb because the momets for the beams are equal ad opposite. MOMENT RESISTANCE EECTIVE RESISTANCE O BOLTS ROWS STEP 4 The resistaces of each of the three bolt ros i the tesio zoe are: SHEET 19 t1,rd = 377 kn (for ROW 1) = 300 kn (for ROW ) t3,rd = 93 kn (for ROW 3) The UK NA states that the effective resistaces should be reduced he either the resistace of oe of the higher ros exceeds 1.9 UK NA (here: 1.9 = 1,9 x 03 = 386 kn 377 mm) (o reductio is ecessary accordig to UK NA). SHEET 5 or (o reductio is also ecessary): Note d f tp 1.9 f ub y,p or d f tfc 1.9 f ub y,c

22 of 3 I this case, the limitig thickess are respectively: UK NA t p 1,9 mm ith t p = 5 mm (reductio is ecessary). t fc 1,9 mm ith t fc = 0,5 mm (o reductio is ecessary). (No reductio is applied accordig to UK NA: a plastic distributio ca be assumed). Reductio factors: h /h x = 0,83 [-] (for ROW ) h 3 /h x = 0,664 [-] (for ROW 3) = 565,3 mm SHEET 1 h = h x (R11 + R) = 465,3 mm " h 3 = h R3 = 375,3 mm " NOTE - UK NA statemets: o reductio applied. The effective resistaces of each of the three bolt ros i the tesio zoe are: t1,rd = 377 kn (for ROW 1) = 300 kn (for ROW ) t3,rd = 93 kn (for ROW 3) EQUILIBRIUM O ORCES The sum of the tesile forces, together ith ay axial compressio i the beam, caot exceed the resistace of the compressio zoe. Similarly, the desig shear caot exceed the shear resistace of the colum eb pael; thisi is ot relevat i thi case as the momets i the idetical beams are equal ad opposite. or horizotal equilibrium: tr,rd + N Ed = c,rd I this case there is o axial compressio/tesio i the beam (N Ed = 0) Therefore, for equilibrium of forces: tr,rd = c,rd Effective resistaces to achieve equilibrium: t1,rd = 377 kn + = 300 kn t3,rd = 190 kn = c,rd = 867 kn

23 3 of 3 Reductio do Tesio Ro orce NOTE The tesio forces i the bolts ros ad the compressio force at bottom flage level must be i equilibrium ith ay axial force i the beam. The forces caot exceed the compressio resistace of the joit, or, here applicable, the shear resistace of the eb pael. Whe the sum of the effective desig tesio resistaces ti,rd exceeds ( c,rd N Ed ), a allocatio of reduced bot forces must be determied that satisfies equilibrium. To achieve a set of bolt ro forces that is i equilibrium, the effective tesio resistaces should be reduced from the values calculated i step 4, startig ith the bottom ro ad orkig up progressively, util equilibrium is achieved. This allocatio achieves the maximum value of momet resistace that ca be realised. MOMENT RESISTANCE O JOINT The momet resistace of the beam to colum joit (M j,rd ) may be determied usig: M h j,rd r tr,rd r 6..7.(1) Eq. (6.5) Takig the cetre of compressio to be at the mid-thickess of the compressio flage of the beam: h r1 = 565 mm h r = 465 mm h r3 = 375 mm Thus, the momet resistace of the beam to colum joit is: M h h h h j,rd r tr,rd r1 t1,rd r r3 t3,rd r = (565 x x x 190)/10³ = 44 knm. VERTICAL SHEAR RESISTANCE Resistace of bolt group The shear resistace of a o-preloaded M4 class 8.8 bolt i sigle shear is: v,rd = 136 kn. b,rd = 59 kn (ed bolts i 0,5 mm ply, bearig resistace). Hece 135,6 kn govers: Rd = mi[ v,rd ; b,rd ] = mi[136; 59] = 136 kn The shear resistace of the upper ros may be take coservatively as 8% of the shear resistace ithout tesio (this assumes STEP 5 that these bolts are fully utilized i tesio) ad thus the shear resistace of all 4 ros is: V j,rd = ( + 6 x 0.8) x 136 = 3.68 x 136 = 499 kn. WELD DESIGN The simple approach requires that the elds to the tesio flage ad the eb should be full stregth ad the eld to the compressio flage is of omial size oly, assumig that it has bee prepared ith a sa cut ed. BEAM TENSION LANGE WELDS A full stregth eld is provided by symmetrical fillet elds ith a total throat thickess at least equal to the flage thickess. Required throat size: Weld throat provided: t fb / = 15,6/ = 7,8 mm. a f = 1/ = 8,5 mm, hich is adequate. BEAM COMPRESSION LANGE WELDS Provide a omial fillet eld either side of the beam flage. A 8 mm leg legth fillet eld ill be satisfactory. BEAM TENSION LANGE WELDS or coveiece, a full stregth eld is provided to the eb: Required throat size: Weld throat provided: t f / = 10,1/ = 5,1 mm. a p = 8/ = 5,7 mm, hich is adequate.