ν := 0.3 MPa := fy := 235 N s := 30. N t := 120 N := N

Examen Berekening van Bouwkundige Constructies III Plooien van plaatvelden restart; a:=1500*mm;b:=1500*mm;alpha:=a/b;tp:=12*mm; a := 1500 mm b := 1500 mm α := 1 tp := 12 mm E:=210000*N/mm^2;nu:=0.3;MPa:=N/mm^2;fy:=235*N/mm^2; E := 210000 N s:=30.*n/mm^2; t:=120*n/mm^2; ν := 0.3 MPa := N fy := 235 N s := 30. N t := 120 N sigma[eff]:=sqrt((s/mpa)^2+3*(t/mpa)^2)*mpa; σ eff := 210.0000000 N ks:=4.;kt:=9.34; ks := 4. kt := 9.34 sigma[0,cr]:=ks*evalf(pi)^2*e/(12*(1-nu^2))*(tp/b)^2; σ 0, cr := 48.58882169 N tau[0,cr]:=sigma[0,cr]/ks*kt; τ 0, cr := 113.4548986 N eq:=(zeta*s/sigma[0,cr]+(zeta*t/tau[0,cr])^2)=1;zeta:=solve(eq, zeta); eq := 0.6174259625 ζc1.118706053 ζ 2 = 1 (1.1) (1.2) (1.3) (1.4) (1.5) (1.6) (1.7) (1.8)

ζ := 0.7089513160, K1.260862125 (1.9) eq:=zet*(2/4*s/sigma[0,cr]+sqrt((2/4*s/sigma[0,cr])^2+(t/tau[0, cr])^2))=1;zeta:=solve(eq,zet); eq := 1.410534091 zet = 1 ζ := 0.7089513159 sigma[eff,cr,ideëel]:=zeta*sigma[eff]; σ eff, cr, ideëel := 148.8797763 N lambda:=sqrt(fy/sigma[eff,cr,ideëel]); λ := 1.256365718 temp:=sigma[eff,cr,ideëel]/fy; temp := 0.6335309630 if temp <= 0.8 then sigma[eff,cr]:=sigma[eff,cr,ideëel] else eta:=(20+sqrt(25-15*lambda^4))/(25+lambda^4); sigma[eff,cr]:= eta*fy; end if; σ eff, cr := 148.8797763 N mu[sigma]:=1.05-0.22;mu[tau]:=1.05; µ σ := 0.83 (1.10) (1.11) (1.12) (1.13) (1.14) µ τ := 1.05 mu:=sqrt((mu[sigma]*(s/sigma[0,cr])^2+mu[tau]*(t/tau[0,cr])^2)/ ((s/sigma[0,cr])^2+(t/tau[0,cr])^2)); µ := 0.9970383864 grenswaarde:=mu*sigma[eff,cr]; grenswaarde := 148.4388519 N if sigma[eff]/grenswaarde <=1 then print("het plaatveld plooit niet") else print("pas ontwerp aan") end if; "Pas ontwerp aan" (1.15) (1.16) (1.17) (1.18) Halve veld ks:=(b/(a/2)+a/2/b)^2.;kt:=4+5.34/(a/2/b)^2; ks := 6.250000000 kt := 25.36 sigma[0,cr]:=ks*evalf(pi)^2*e/(12*(1-nu^2))*(tp/b)^2; σ 0, cr := 75.92003387 N tau[0,cr]:=sigma[0,cr]/ks*kt; τ 0, cr := 308.0531295 N eq1:=(zeta1*s/sigma[0,cr]+(zeta1*t/tau[0,cr])^2)=1;zeta1:= solve(eq1,zeta1); eq1 := 0.3951526161 ζ1c0.1517439000 ζ1 2 = 1 (1.1.1) (1.1.2) (1.1.3)

ζ1 := 1.576391089, K4.180466878 zeta1 := 1.576391089; ζ1 := 1.576391089 sigma[eff,cr,ideëel]:=zeta1*sigma[eff]; σ eff, cr, ideëel := 331.0421287 N lambda:=sqrt(fy/sigma[eff,cr,ideëel]); λ := 0.8425434334 temp:=sigma[eff,cr,ideëel]/fy; temp := 1.408689909 (1.1.4) (1.1.5) (1.1.6) (1.1.7) (1.1.8) if temp <= 0.8 then sigma[eff,cr]:=sigma[eff,cr,ideëel] else eta:=(20+sqrt(25-15*lambda^4))/(25+lambda^4); sigma[eff,cr]:= eta*fy; end if; η := 0.9479422018 σ eff, cr := 222.7664174 N mu[sigma]:=0.83;mu[tau]:=1.05; µ σ := 0.83 µ τ := 1.05 (1.1.9) (1.1.10) mu:=sqrt((mu[sigma]*(s/sigma[0,cr])^2+mu[tau]*(t/tau[0,cr]) ^2)/((s/sigma[0,cr])^2+(t/tau[0,cr])^2)); µ := 0.9687246273 grenswaarde:=mu*sigma[eff,cr]; grenswaarde := 215.7993147 N if sigma[eff]/grenswaarde <=1 then print("het halve plaatveld plooit niet") else print("pas ontwerp aan") end if; "Het halve plaatveld plooit niet" (1.1.11) (1.1.12) (1.1.13) Ontwerp van de starre dwarsverstijver unprotect(gamma); gamma[0,tau]:=5.4*(2+2.5-1-1); γ 0, τ := 13.50 (1.2.1) gamma[0,sigma]:=4*(4-1/4.)/evalf(pi)^2/(1-evalf(pi^2)/(12-48) ); γ 0, σ := 1.192803815 (1.2.2) T0:=4*gamma[0,tau]*1/12/(1-nu^2)*tp^3*b; T0 := 1.281758242 10 7 mm 4 ts:=10*mm;beff:=ts+15*tp*2;h:=2*c;c:=xi*mm; ts := 10 mm beff := 370 mm h := 2 c (1.2.3)

c :=ξ mm As:=c*ts+h*ts+beff*tp; As := 30 ξ C4440 Ss:=c*ts*ts/2+h*ts*(ts+h/2)+beff*tp*(ts+h+tp/2); Ss := 50 ξ mm 3 C20 ξ 10 mmcξ mm C4440 16 mmc2 ξ mm xg:=ss/as; xg := 50 ξ mm3 C20 ξ 10 mmcξ mm C4440 16 mmc2 ξ mm 30 ξ C4440 T:=c*ts^3/12+c*ts*(xG-ts/2)^2+ts*h^3/12+h*ts*(xG-ts-h/2)^2+ beff*tp^3/12+beff*tp*(ts+h+tp/2-xg)^2; T := 250 3 ξ mm 4 C10 ξ 50 ξ mm 3 C20 ξ 10 mmcξ mm C4440 16 mmc2 ξ mm 30 ξ C4440 K5 mm 2 C20 ξ C 20 3 mm4 ξ 3 50 ξ mm 3 C20 ξ 10 mmcξ mm C4440 16 mmc2 ξ mm 30 ξ C4440 K10 mmkξ mm 2 C53280 mm 4 C4440 16 mmc2 ξ mm (1.2.4) (1.2.5) (1.2.6) (1.2.7) (1.2.8) K 50 ξ mm3 C20 ξ 10 mmcξ mm C4440 16 mmc2 ξ mm 30 ξ C4440 eq:=simplify(t/t0)=1;xi:=solve(eq,xi); eq := 2.600594421 10-7 4. ξ 4 C2980. ξ 3 C30267. ξ 2 C1.05376 10 5 ξc2.365632 10 6 ξc148. = 1 ξ := 59.62159476, K35.65988003C44.37380662 I, K733.3018347, K35.65988003 K44.37380662 I c:=mm*xi[1];h:=2*c; c := 59.62159476 mm h := 119.2431895 mm 2 (1.2.9) (1.2.10) Samengestelde drukstaven restart;

Divergentie bij buiging om de materiaalsnijdende as h:=24*cm;b:=12*cm;af:=30.12*cm^2;iy:=3892*cm^4;iz:=283.6* cm^4;wply:=366.6*cm^3;wplz:=73.92*cm^3;fy:=35.5*kn/cm^2;e:= 21000*kN/cm^2;nu:=0.3;L:=600*cm; h := 24 cm b := 12 cm Af := 30.12 cm 2 (2.1.3) (2.1.5) (2.1.6) (2.1.8) eq:=nbrd/af+nbrd*w0/(1-nbrd/ncry)/wply=fy;w0:=solve(eq,w0); 30.24671617 kn 4.187714465 kn w0 35.5 kn eq := cm 2 C cm 3 = cm 2 w0 := 1.254451294 cm (2.1.9) Sterktevoorwaarde bij samengestelde buiging e:=10*cm; (2.1.10) Iy := 3892 cm 4 Iz := 283.6 cm 4 Wply := 366.6 cm 3 Wplz := 73.92 cm 3 35.5 kn fy := cm 2 21000 kn E := cm 2 ν := 0.3 L := 600 cm Bepaal de ideële vormfout Ncry:=evalf(Pi^2)*E*Iy/L^2; Ncry := 2240.729187 kn Npl:=Af*fy; Npl := 1069.260 kn lambda:=sqrt(npl/ncry); λ := 0.6907914835 alpha:=0.21; α := 0.21 phi:=0.5*(1+alpha*(lambda-0.2)+lambda^2); φ := 0.7901295426 chi:=1/(phi+(phi^2-lambda^2)^0.5); χ := 0.8520201735 NbRd:=chi*Af*fy; NbRd := 911.0310909 kn e := 10 cm eq:=n/af+(n*e+n*w0)/(1-n/ncry)/wply=fy; (2.1.1) (2.1.2) (2.1.4) (2.1.7) (2.1.11)

eq := 0.03320053121 N 0.03069953980 N cm 2 C cm 2 1K 0.0004462832929 N kn Nu:=solve(eq,N)*2; Ν := 9784.358376 kn, 979.4907332 kn Nuy:=Nu[2]; Nuy := 979.4907332 kn = 35.5 kn cm 2 (2.1.11) (2.1.12) (2.1.13) Knik om de materiaalvrije as v0:=l/500.;a:=l/5;bk:=8*cm;tk:=0.7*cm;h:=36*cm;ik:=bk^3*tk* 2/12; v0 := 1.200000000 cm a := 120 cm bk := 8 cm tk := 0.7 cm h := 36 cm Ik := 59.73333333 cm 4 (2.2.1) GAv:=1/(a/12*(h/E/Ik+a/2/E/Iz));1/GAv; GAv := 2579.078993 kn 0.0003877353128 kn Iref:=Af*h^2/2+2*Iz; Iref := 20084.96000 cm 4 i:=sqrt(iref/(2*af)/cm^2)*cm; i := 18.25967334 cm lambda:=l/i; λ := 32.85929539 mu:=1;iref:=iref; µ := 1 (2.2.2) (2.2.3) (2.2.4) (2.2.5) Iref := 20084.96000 cm 4 (2.2.6) Ncrz:=evalf(Pi)^2*E*Iref/L^2/(1+evalf(Pi)^2*E*Iref/L^2/GAv); Ncrz := 2108.749577 kn (2.2.7) Nd:=P/2+P*v0/(1-P/Ncrz)/Iref*h/2*Af; Nd := 1 (2.2.8) 2 PC 0.03239199878 P 1K 0.0004742146772 P kn Knik van de randstaaf aan de concave zijde Ncr:=evalf(Pi^2)*E*Iz/a^2; Ncr := 4081.903888 kn (2.2.1.1)

lambda:=sqrt(npl/ncr); λ := 0.5118117747 alpha:=0.34; α := 0.34 phi:=0.5*(1+alpha*(lambda-0.2)+lambda^2); φ := 0.6839836481 chi:=1/(phi+(phi^2-lambda^2)^0.5); χ := 0.8789460651 NbRd:=chi*Af*fy; NbRd := 939.8218695 kn eq:=nd=nbrd;nuz:=solve(eq,p); eq := 1 2 PC 0.03239199878 P 1K 0.0004742146772 P = 939.8218695 kn kn Nuz := 2601.225655 kn, 1523.780888 kn Nuz:=Nuz[2]; Nuz := 1523.780888 kn Nu:=min(Nuz/kN,Nuy/kN)*kN; Ν := 979.4907332 kn (2.2.1.2) (2.2.1.3) (2.2.1.4) (2.2.1.5) (2.2.1.6) (2.2.1.7) (2.2.1.8) (2.2.1.9) Sterkte van de knikplaten Vd:=evalf(Pi)/L*Nu*v0/(1-Nu/Ncrz);Md:=a*Vd/2; Vd := 11.49242579 kn Md := 689.5455475 cm kn (2.2.2.1) Vpl:=bk*tk*2*fy/sqrt(3.);Mpl:=tk*bk^2/4*2*fy; Vpl := 229.5544670 kn Mpl := 795.2000000 cm kn (2.2.2.2) if (Md/Mpl <= 1) then print('knikplaten_sterk_genoeg') end if; Knikplaten_sterk_genoeg (2.2.2.3) Sterkte van de randstaven Nd:=Nu/2;Md:=a*Vd/4; Nd := 489.7453666 kn Md := 344.7727738 cm kn Npl;Mpl:=Wplz*fy; 1069.260 kn Mpl := 2624.160 cm kn nu:=nd/npl; ν := 0.4580227135 tf:=0.98*cm;a:=(af-2*b*tf)/af; tf := 0.98 cm (2.2.3.1) (2.2.3.2) (2.2.3.3) (2.2.3.4)

a := 0.2191235060 (2.2.3.4) MNzRd:=Mpl*(1-((nu-a)/(1-a))^2); MNzRd := 2378.544919 cm kn (2.2.3.5) if Md/MNzRd <= 1 then print('sterkte_randstaven_ok') end if; Sterkte_randstaven_OK (2.2.3.6) Methode van Gehler restart; H:=10*kN;p:=20*kN/m;L:=5.*m;EI:=400.*kN*m^2; H := 10 kn 20 kn p := m L := 5. m EI := 400. kn m 2 eq:=pab*l+h*l/2-p*l^2/2=0;pab:=solve(eq,pab);pcd:=p*l-pab; eq := 5. PAB mk225.0000000 kn m = 0 PAB := 45. kn PCD := 55. kn MAB:=2*EI/L*(2*phi[A]-3*psi); (3.1) (3.2) (3.3)

MAB := 160.0000000 kn m 2 φ A K3 ψ eq:=mab=0;phi[a]:=solve(eq,phi[a]); eq := 160.0000000 kn m 2 φ A K3 ψ = 0 φ A := 1.500000000 ψ MDC:=2*EI/(L/2)*(2*phi[D]-3*2*psi); MDC := 320.0000000 kn m 2 φ D K6 ψ eq:=mdc=0;phi[d]:=solve(eq,phi[d]); eq := 320.0000000 kn m 2 φ D K6 ψ = 0 φ D := 3. ψ MBA:=2*EI/L*(phi[A]-3*psi); MBA := K240.0000000 kn m ψ MCD:=2*EI/(L/2)*(phi[D]-3*2*psi); MCD := K960.0000000 kn m ψ V[AB]:=-MBA/L;V[CD]:=-MCD/(L/2); V AB := 48.00000000 kn ψ V CD := 384.0000000 kn ψ eq:=v[ab]+v[cd]+h-pab*psi-pcd*2*psi=0; eq := 277.0000000 kn ψc10 kn = 0 psi:=solve(eq,psi); ψ :=K0.03610108303 ub:=-psi*l; ub := 0.1805054152 m MBA:=MBA; MBA := 8.664259927 kn m MCD:=MCD; MCD := 34.65703971 kn m eq:=0.1805=0.1157/(1-100/pcr); eq := 0.1805 = 0.1157 1K 100 Pcr Pcr:=solve(eq,Pcr); Pcr := 278.5493827 (3.3) (3.4) (3.5) (3.6) (3.7) (3.8) (3.9) (3.10) (3.11) (3.12) (3.13) (3.14) (3.15) (3.16)