3.300 m m m m m m 0 m m m 0 m 0 m m m he m T m 1.50 m N/ N

3.300 m 0.500 m 0.300 m 0.300 m 0.300 m 0.500 m 0 m 1.000 m 2.000 m 0 m 0 m 0.300 m 0.300 m -0.200 he 0.400 m T 0.200 m 1.50 m 0.16 2 24.5 N/ 3 18.0 N/ 3 28.0 18.7 18.7 14.0 14.0 X(m) 1.000 2.000 20 Y(m) 0 0.500 0.500 (kn/m2) 5.000 10

kn N/m y P = m xp = m b p = m σ ck = 21 N/mm 2 σ ca = 7 N/mm 2 τ ca = 0.7 N/mm 2 σ sa = 180 N/mm 2 τ a 2.1 N/mm 2 X P P y p 0.26 N/mm 2 t(mm) U(mm) 16 13 250 60 1301 360 16 250 60 794 200 16 250 60 794 200 19 250 60 1146 240 No X Y Xn+1 - Xn-1 1 0 0-3.500 0 2 0 0.300 1.000 0.300 3 1.000 0.500 1.000 0.500 4 1.000 0.500 0 0 5 1.000 3.800 0.300 1.140 6 1.300 3.800 0.482 1.831 7 1.482 0.770 0.482 0.371 8 1.782 0.470 2.018 0.949 9 3.500 0.300 1.718 0.515 10 3.500 0-3.500 0 5.606 5.606 /2 2.803 m2 γc 2.803 24.50 68.674 kn, ) Σ i ( i 2/3 i)} i Σ i ( i 1/3 i)} i i

318.5 6.90 mm (SKK400) 533 25.00 (SS400) L 8.0 m L 7.8 m 1.00 mm EP 200000 N/mm2 σsta 140 N/mm2 σs 90 N/mm2 0.013(L/D)0.53 0.720 δa 1.5 cm 2.0 cm EL(m) m) 2.000 0 1.000 1.000 l 7.800 m -6.800 8.800 533.0 mm 1-6.267 8.267 1-7.333 9.333 4 m 8.796 1 1.000 1.000 1.000 2.0 2 1.000 2.000 0 0.0 3 1.000 3.000-1.000 3.0 4 1.000 4.000-2.000 5.0 5 1.000 5.000-3.000 6.0 6 1.000 6.000-4.000 4.0 7 1.000 7.000-5.000 7.0 8 1.000 8.000-6.000 10.0 9 1.000 9.000-7.000 15.0 10 1.000 10-8.000 15.0 11 1.000 11.000-9.000 20.0 12 1.000 12.000-10 50.0 13 1.000 13.000-11.000 50.0 14 1.000 14.000-12.000 40.0 15 1.000 15.000-13.000 50.0 16 0 15.000-13.000 17 0 15.000-13.000 18 0 15.000-13.000 19 0 15.000-13.000 20 0 15.000-13.000

1 3.000-1.000 2.000 1.3 2.6 5.2 2 7.000-5.000 4.000 5.0 10.0 40.0 3 11.000-9.000 4.000 13.4 26.8 48.2 4 15.000-13.000 4.000 43.8 87.6 0.0 5 0.0 6 0.0 7 0.0 8 0.0 9 0.0 10 0.0 Σ 14.000 93.4 250 0 114.5 250 kn/m2 1 1 N kn/m2 13.7 8.267 9.333m 14.1 4 m / 4/533 1000= 0.0 533 mm 250 kn/m2 kn/m2 RuqdA Σi i 3525 0.1511.001 93.4 625.8 (N/) u: (N) p : (m2) e: π ²/4 π0.319 2 /4 0.533 ² 0.319 ² )/4 0.151 m 2 0.0717252 qd: (n/m2) : () π π 0.319 1.001 i: () i: ( /2)

(kn) (m) (knm) 0 0.600 0 68.672 1.064 73.067 134.047 2.094 280.694 1 5.000 1.400 7.000 2 2.000 3.000 6.000 209.719 366.761 δ= 18.667 () 0 j= 0 () α= 54 () 120.904 kn 0 kn a 53.438 kn KA=2 Pa/(γs h 2 ) = 0.321 KH=Ka cos(δ ) = 0.304 KV=Ka sin(δ ) = 0.103

(kn) PH=1/2 h^2 γs KH 50.589 (m) (knm) 1.433 My=PH Y 72.494 PV=1/2 h^2 γs KV 17.140 3.100 Mx=PV X 53.134 QwH=Qw h KH 13.072 2.150 My=QwH Y 28.105 QwV=Qw h KV 4.429 3.100 Mx=QwV X 13.730 h : 4.300 m PH : PV : QwH : QwV : Σ 231.29 kn Σ 63.66 kn M 333.03 kn ( M : A ) 333.026 N m 1.800 m (2 LAB+LBC)/3 1.400 m 0 m 0-1.400 (m) 1.400 ( ' 63.66 y 1.580 0 100.60 50.59 y 1.433 0 72.49 3.500 3.500 333.03 231.29 0.400-0.090 m 306.30 219.86 0.400-0.043 m Σwi 231.29 ΣMr -433.63 Σre 9.22 Σwi' 219.86 ΣMr' -378.79 Σre' -1.51 ΣA 433.63 F 4.31 1.5 0 100.60 ΣA' F' 0' 378.79 72.49 5.23 1.5

2. 1.0 (mm D 316.5 5.9 (mm) d 304.7 (mm) Apπ (D 2 d 2 )4 5757 mm2 Ipπ (D 4 d 4 )64 6.945E+07 mm4 Zpπ (D 4 d 4 )/(32 D) 439000 mm3 A 6.9E+07 10 6 + 5757 2 1400 6.946E+13 B 6.9E+07 10 6 + 5757 2 0 6.945E+13 C 6.9E+07 10 6 + 5757 2 1400 6.946E+13 2.084E+14 mm4 o 208.373 m4 1 Ip=Io/3 69.458 m4 1.0 (mm D t L n Ep Ip Ap (mm) (mm) (m) () (N/mm2) (mm4) (mm2) 316.50 5.90 7.800 1.000 2.000E+05 6.945E+07 5757 k1.7 2.212 m Kv p p/l 0.720 5757 200000 / 7800 106283 (N/mm) 106283 N/m a 1/n u1/6 93.5 0.0 15.6 kn n: 6 u Σi i π0.533 93.4 93.5 kn Bh D 0.3165 0.8368 β 0.452 Kh Kho(Bh/0.3) -3/4 15,867 0.8368 / 0.3 ) -3/4 = 7,351 kn/m 3 = 74 N/mm2 Kh 0 =1/0.3αEo 1/0.3 1.00 4,760 = 15,867 kn/m 3 α 1.00 E 0 2800N 2800 1.7 = 4,760 kn/m 2 m β 4 KhD 7,351 4EI 4 4 0.3165 13890 m-1 0.452 EI 200000 6.945E+07 1.389E+13 Nmm2 13890 knm2

a h D 7,351 0.3165 δa β 0.452 0.015 77 kn δa β 0.452 7.8 3.526 3 K1 4 β 3 5131 1.00 5131 K2 3 2 β 2 5676 1.00 5676 K4 2 β 12557 1.00 12557 θi0 xxσ 1cos2θi vsinθi 15393 xy yxσ v 1sinθicosθi 0 xa axσ{ v 1xisinθicosθi 2cosθi} -17028 yyσ vcos 2 θi 1sin 2 θi} 318849 ya ayσ{ vcos 2 θi 1sin 2 θi}xi 2sinθi} 0 aaσ{ vcos 2 θi 1sin 2 θi}xi 2 (2 3xisinθi 4 454301 15393 δx -17028 α 63.66 50.59 318849 δy 231.29 219.86-17028 δx 454301 α 9.22-1.51-410679 δx 454301 α -1698-410679 δx 454301 α ### δx -393651 0 α -1708-393651 δx 0 α ### δx 434 342 m 0.65 0.51 cm δy 073 069 m 0.11 0.10 cm α 018 013 rad 027 019 rad Ni vδyi Hi 1δxi 2α ti 3δxi + 4α δxi δxcosθi(δyαxi)sinθi δyi δxsinθi(δyαxi)cosθi 231.29 63.66-66.99 76.202 9.212 xi θi δxi δyi Ni Hi ti nixi 1.400 0 434 098 104.31 21.22-22.33 146.034 0 0 434 073 77.1 21.22-22.33 0-1.400 0 434 047 49.88 21.22-22.33-69.832 xi θi 1.400 0 0 0-1.400 0 219.86 50.58 δxi 342 342 342-53.61 52.094 δyi Ni 086 91.89 069 73.29 051 54.68-1.516 Hi ti -17.87-17.87 16.86 16.86 16.86-17.87 128.646 0-76.552

kn/m) 1 1 1 p p' ' max min max min 21.22 16.86 31.83 25.29 104.31 49.88 156.47 74.82-33.50-26.81 a 77 (kn) a 625.8 /3 208.6 (kn) a -15.6 (kn) /βe -βx (βhocosβx(1βho)sinβx) /2e -βx sinβx 31.83 kni -33.50 N β 0.452 m -1 ho t/-1.052 (Nnm) 0 33.50 1.000 8.91-19.57 1.738-1.11-22.70 2.000 3.000 3.368 4.000 5.000 6.000 7.000 8.000 9.000 10 11.000 12.000 13.000 14.000 15.000 16.000 17.000 18.000 19.000 max -3.36-7.46-7.69-7.18-5.20-3.04-1.38-0.35 0.16 0.32 0.31 0.22 0.13 0.06 0.01-0.01-0.01-0.01-0.01 33.50-22.41-17.73-15.35-11.22-5.67-1.95 0.07 0.87 0.96 0.75 0.47 0.24 0.08-0.01-0.04-0.04-0.03-0.02-0.01 22.70 33 0 8.9 20 1.1 23 3.4 22 7.5 18 7.7 15 7.2 11 5.2 5.7 3 1.9 1.4 0.1 0.3 0.9 0.2 1 0.3 0.8 0.3 0.5 0.2 0.2 0.1 0.1 0.1 0 0 0 0 0 0 0 0 0 0 0 /2β{(1+2βho)2+1)e -βlm -7.69 Nm lm1/βtan -1 1/(1+2βho)3.368 m /βe -π/4 sinπ/4) -22.70 Nm lmπ/4β1.738 m

max σ e Z 156470 5757 33500000 439000 103.5 N/mm2 σsta 140 N/mm2 σ e 74820 Z 5757 33500000 439000-63.3 N/mm2 σsta -140 N/mm2

18.667 3.4682 50 102.436 kn 18.886 kn = 45.448 0.464 0.430 0.175 P= 0 kn y P = 3.300 m ( ) b p = 0 m 1m P u = 0 kn/m 58.065 knm/m 49.239 kn/m 27.544 kn 14.620 knm/m 19.780 kn/m

( D16@250 D13@250 B2 = 500 mm b = 1000 mm i = 60 mm d = 440 mm A s = 1301 mm 2 U = 360 mm b σ c x/3 x=kd M C h A s d z=jd T=σ s A s E A S S n = = 15 np = n = Ec b d 0.04435 k = 2 k ( np) + 2np np = 0.257 j = 1 = 3 0.914 M= 5.81E+07 Nmm S= 4.92E+04 N 2.6 N/mm 2 7.0 N/mm 2 110.9 N/mm 2 σsa= 180.0 N/mm 2 0.112 N/mm 2 τca= 0.70 N/mm 2 0.340 τca= 2.10 d = 361 mm D16@250 M= 1.46E+07 Nmm A s = 794 mm 2 S= 1.98E+04 N U = 200 mm K = 0.226 j = 0.925 1.1 N/mm 2 7.0 N/mm 2 55.1 N/mm 2 σsa= 180.0 N/mm 2 0.055 N/mm 2 τca= 0.70 N/mm 2 0.296 N/mm τa= 2.10

l lh2/2 l 0.250m e= 0.4 m LAB= 1.400 m LBC= 1.400 m a= 0.600 m b= -0.800 m -2.200 m a= -0.150 m b= -1.550 m -2.950 m H3 = 0.300 m H2 = 0.500 m B= 3.500 m HS = 0.450 m l m =B5 = 1.000 m l s = 0.750 m W1=H3γc 7.35 kn/m 7.35 kn/m2 W2=H2γc12.25 kn/m 12.25 kn/m2 W 3 W 1 (W 2 W 1 )l s B5 11.03 kn/m2 11.03 104.31 77.10 49.88 kn kn kn 104.31 0 kn/m2 kn/m -6.89 L l m 2 2W1 W2 58.09 knm/m 6

D19@250 T = 500 450 mm b = 1000 1000 mm i = 60 60 mm d = A s = U = 440 794 200 390 794 200 mm mm 2 mm ES A n = = 15 np = n S = Ec b d 0.02707 2 ( ) = k = np + 2np np 0.207 k j = 1 3 = 0.931 M= 58094333.33 Nmm S= 6890.625 N 3.1 7.0 N/mm 2 N/mm 2 178.6 N/mm 2 σsa= 180.0 N/mm 2 d = 390 mm 0.018 N/mm 2 τca= 0.70 N/mm 2 0.095 N/mm² τca= 2.10

lh2/2 l 0.250m B6l 1.750m A B C 0.400 m 1.400 m 1.400 m -1.100 0 0.300 1.700 1.700 0.300 Ee=2Pv/L l 0.475 0.470 4.429 Ex=Ee/B6l 0.554 0.664 Ev=1/2(Ex+Ee)(B6-l) 4.36 4.456 17.14 Ex=Ee/B6l 2.143 Ev=1/2(Ex+Ee)(B6-l) 16.873 kn N kn kn kn 19.60 0.92 17.97 16.61 16.04 2.32 0.97 0.09 0.09 0.01 128.09 1.04 133.60 114.19 110.83 21.09 1 4.00 0.40 1.60 2.75 4.50 2.00 2 2.00 1.90 3.80 2.00 4.43 1.33 5.91 4.36 4.46 7.17 17.14 1.33 22.85 16.87 16.75 4.76-77.10 0.30-23.13-77.10-49.88 1.70-84.80-49.88-49.88 49.26 77.89 29.82 102.69 37.33 49.256 29.819 102.692 37.329 M w = 58.07 knm/m 49.24 Smax = 102.69 kn l 0.47 m

D19@250 T = 500 b = 1000 i = 60 d = 440 A s = 1146 U = 240 470 1000 60 410 1146 240 mm mm mm mm mm 2 mm ES A n = = 15 np = n S = Ec b d 0.03907 2 ( ) = k = np + 2np np 0.243 k j = 1 3 = 0.919 M= 5.81E+07 Nmm S= 1.03E+05 N 2.7 N/mm 2 7.0 N/mm 2 125.3 N/mm 2 σsa= 180.0 N/mm 2 d = 410 mm 0.250 N/mm 2 τca= 0.70 N/mm 2 1.136 N/mm² τca= 2.10

(kn) (m) (knm) 0 0.600 0 68.672 1.064 73.067 134.047 2.094 280.694 202.719 353.761 (kn) (m) (knm) 0 3.800 0 10.988 1.063 11.680 21.447 2.222 47.656 32.435 59.336 14.000 0.38383 0 48 0.3365 9.090 149.836 19.6655 0 00 151.742 = 74.181 kn 0.446 0.433 0.108

(kn) PH=1/2 h^2 γs KH 72.056 (m) (knm) 1.433 My=PH Y 103.256 PV=1/2 h^2 γs KV 17.972 3.100 Mx=PV X 55.713 QwH=Qw h KH 0 2.150 My=QwH Y 0 QwV=Qw h KV 0 3.100 Mx=QwV X 0 4.300 m Σ 220.69 kn Σ 104.49 kn M 246.88 kn 1.800 m (2 LAB+LBC)/3 1.400 m 0 m 0-1.400 m 1.400 104.49 y 0.988 0 103.26 3.500 /2 246.882/ 220.691 0.400 0.231 m Σwi 220.69 ΣMr -350.14 Σre -62.01 ΣA 350.14 F 0 103.26 3.39 1.2

2. K1 4 β 3 5131 K2 3 2 β 5676 K4 2 β12557 15393 δx -17028 α 104.49 318849 δy 220.69-17028 δx 454301 α -62.01-410679 δx 454301 α -2788-410679 δx 454301 α 0 δx -393651 0 α -2726-393651 δx 0 α 0 δx 692 1.04 cm/ δy 069 0.10 cm/ α 012 rad 018 rad/ Ni vδyi Hi 1δxi 2α ti 3δxi + 4α δxi δxcosθi(δyαxi)sinθi 220.69 104.49-113.28 51.254 δyi δxsinθi(δyαxi)cosθi -62.026 xi θi δxi δyi Ni Hi ti 1.400 0 692 086 91.87 34.83-37.76 0 0 692 069 73.56 34.83-37.76-1.400 0 692 052 55.26 34.83-37.76 nixi 128.618 0-77.364 kn/m) 1 1 1 p 34.83 52.25 max 91.87 min 55.26 137.81 82.89 max -56.64 7,351 0.3165 a h D δa 0.020 103 kn β 0.452 δa a Ru/2 625.8 /2 312.9 kn a -31.2 N a 1/n u1/3 93.5 0 31.2 kn

2 /βe -βx (βhocosβx(1βho)sinβx) /2e -βx sinβx 52.25 kni -56.64 N β 0.452 m -1 ho t/-1.084 (Nnm) 0 56.64 57 0 1.000 16.04-32.13 16 32 1.738-0.75-37.27 0.7 37 2.000-4.58-36.78 4.6 37 3.000-11.73-29.10 12 29 3.431-12.26-24.51 12 25 4.000-11.58-18.43 12 18 5.000-8.51-9.31 8.5 9.3 6.000-5.05-3.20 5 3.2 7.000-2.34 0.11 2.3 0.1 8.000-0.63 1.42 0.6 1.4 9.000 0.22 1.58 0.2 1.6 10 0.51 1.24 0.5 1.2 11.000 0.50 0.77 0.5 0.8 12.000 0.36 0.39 0.4 0.4 13.000 0.21 0.13 0.2 0.1 14.000 0.10-0.01 0.1 0 15.000 0.02-0.06 0 0.1 16.000-0.01-0.07 0 0.1 17.000-0.02-0.05 0 0.1 18.000-0.02-0.03 0 0 19.000-0.02-0.02 0 0 max 56.64 37.27 /2β{(1+2βho)2+1)e -βlm -12.26 Nm lm1/βtan -1 1/(1+βho) 3.431 m /βe -π/4 sinπ/4) -37.27 Nm lmπ/4β 1.738 m max σ e 137810 56640000 Z 5757 439000 153.0 (N/mm2) σsta 210 (N/mm2) σ e 137810 Z 5757 56640000 439000-105.1 (N/mm2) σsta -210 (N/mm2)

14 3.4682 45 9.090 123.346 0 124.915 54.938 kn 0.561 0.535 0.168 P= 0 kn y P = 3.300 m ( ) b p = 0 m 1m P u = 0 kn/m 5.174 kn 1.513 m 65.507 knm/m 57.609 kn/m 2.826 kn 0.944 m 0.421m 33.296 kn 15.508 knm/m 22.086 kn/m

D16@250 D13@250 B2 = 500 mm b = 1000 mm i = 60 mm d = 440 mm A s = 1301 mm 2 U = 360 mm b σ c x/3 x=kd M C h A s d z=jd T=σ s A s E S A n = = 15 np = n S = Ec b d 0.04435 k = ( np) k + 2np np = 0.257 j = 1 3 = M= 6.55E+07 Nmm 0.914 S= 5.76E+04 N 2.9 N/mm 2 10.5 N/mm 2 125.1 N/mm 2 σsa= 270.0 N/mm 2 0.131 N/mm 2 τca= 1.05 N/mm 2 0.398 N/mm τa= 3.15 d = 361 mm D16@250 M= 1.33E+07 Nmm A s = 794 mm 2 S= 1.88E+04 N U = 200 mm K = 0.226 j = 0.925 1.0 N/mm 2 10.5 N/mm 2 50.3 N/mm 2 σsa= 270.0 N/mm 2 0.052 N/mm 2 τca= 1.05 N/mm 2 0.282 N/mm τa= 3.15

lh2/2 l 0.250m l e= 0.4 m LAB= 1.400 m LBC= 1.400 m a= 0.600 m b= -0.800 m Lc= -2.200 m a= -0.150 m b= -1.550 m Lc= -2.950 m H3= 0.300 m H2= 0.500 m B= 3.500 m HS= 0.450 m l m =B5= 1.000 m l s = 0.750 m W1=H3γc 7.35 kn/m2 7.35 W2=H2γc12.25 kn/m2 12.25 kn/m2 kn/m2 W 3 W 1 (W 2W 1 )l s 11.025 kn/m2 B5 0 11.03 kn/m2 91.87 73.56 55.26 kn kn kn 91.87 ls/2w1w3-6.89 kn/m l m 2 L 2W1 W2 50.63 6 knm/m

D19@250 T = 500 450 mm b = 1000 1000 mm i = 60 60 mm d = A s = U = 440 794 200 390 794 200 mm mm 2 mm ES A n = = 15 np = n S = Ec b d 0.02707 2 ( ) = k = np + 2np np k 0.207 j = 1 = 0.931 3 M= 50630333.33 Nmm S= 6890.625 N 2.7 N/mm 2 10.5 N/mm 2 155.7 N/mm 2 σsa= 270.0 N/mm 2 d = 390 mm 0.018 N/mm 2 τca= 1.05 N/mm 2 0.095 N/mm² τca= 3.15

lh2/2 l 0.250m B6l 1.750m A B C 0.400 m LAB= 1.400 m 1.400 m -1.100 0 0.300 1.700 1.700 0.300 Ee=2Pv/L l 0.475 0.470 0.330 0 Ex=Ee/B6l 0 0 0 Ev=1/2(Ex+Ee)(B6-l) 0 0 0 17.972 Ex=Ee/B6l 2.247 2.696 15.276 Ev=1/2(Ex+Ee)(B6-l) 17.692 17.568 4.987 kn N kn 19.60 0.92 17.97 16.61 0.97 0.09 0.09 0.01 128.09 1.04 133.60 114.19 0 0 1.33 17.97 1.33 23.96 17.69 kn 16.04 110.83 17.57-73.56 0.30-22.07-73.56-55.26 1.70-93.94-55.26-55.26 37.82 59.61 19.69 89.17 37.819 19.688 89.17 M w = 65.51 knm/m 57.61 kn 2.32 21.09 4.99 28.39 28.39 Smax = 89.17 kn l 0.47 m

D19@250 T = 500 470 mm b = 1000 1000 mm i = 60 60 mm d = A s = U = 440 1146 240 410 1146 240 mm mm 2 mm ES A n = = 15 np = n S = Ec b d 0.03907 2 ( ) = k = np + 2np np k 0.243 j = 1 = 0.919 3 M= 5.96E+07 Nmm S= 8.92E+04 N 2.8 N/mm 2 10.5 N/mm 2 128.7 N/mm 2 σsa= 270.0 N/mm 2 d = 410 mm 0.217 N/mm 2 τca= 1.05 N/mm 2 0.986 N/mm² τca= 3.15

4.31 1.50 31.83 77.0 156.47 208.6 74.82-15.60 7.00 0.26 18 0.70 2.10 2.55 110.93 0.11 0.34 1.07 55.14 0.05 0.30 3.11 178.62 0.02 0.09 2.68 125.31 0.25 1.14 103.5 140-63.3-140 0.65 1.5 3.39 1.20 52.25 103.0 137.81 312.9 55.26-31.2 10.50 0.39 27 1.05 3.15 2.88 125.15 0.13 0.40 0.98 50.25 0.05 0.28 2.71 155.67 0.02 0.09 2.76 128.65 0.22 0.99 153.0 210-105.1-210 1.04 2.0