Finding a value and marking it in a graph
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Shimon Katzman
am 5 Dez. 2019
Kommentiert: VBBV
am 25 Dez. 2022
Hi everyone,
I am trying to find the value of M when epss=epssh=0.009 for every graph (there are 4 of them) and to mark it on the graph unsucssesfully.
Can anyone help me please with this please?
b=400; %mm
d=500; %mm
Asv = [3000 5000 3000 5000]; %mm^2
fckv = [30 30 90 90]; %Mpa
num_fckv = numel(fckv);
epscmv = linspace(0.1, 100, 5000)*1E-3;
num_epscvm = numel(epscmv);
fsolve_opts = optimoptions('fsolve','Display','off');
M = zeros(num_epscvm, num_fckv);
phi = zeros(num_epscvm, num_fckv);
idx = zeros(1, num_fckv);
Mmax = zeros(1, num_fckv);
phiAtMmax = zeros(1, num_fckv);
epsAtMmax = zeros(1, num_fckv);
tic
for k = 1:num_fckv
fck = fckv(k);
Ecshah=57000/145*(fck*145)^0.5; %Mpa
Es=200000; %Mpa
Esh=8500; %Mpa
fy=500; %Mpa
fsu=750; %Mpa
epssh=0.009;
epssu=0.075;
eps0=1.027*10^-7*fck*145+0.00195;
kshah=0.025*fck*10^3;
A=Ecshah*eps0/fck;
P=Esh*((epssu-epssh)/(fsu-fy));
epsy=fy/Es;
As = Asv(k);
c0 = 1000;
c = zeros(1, num_epscvm);
for i=1:num_epscvm
epscm = epscmv(i);
epss=@(c) (d-c)/c*epscm;
funCshah=@(epsc) (1-(1-epsc./eps0).^A) .* (epsc<=eps0) + exp(-kshah*(epsc-eps0).^1.15) .* (epsc>eps0);
compression=@(c) b*fck*c/epscm*integral(funCshah,0,epscm)/1000;
sigmaSteel=@(c) Es*epss(c) .* (epss(c)<=epsy) + fy .* (epss(c)>epsy & epss(c)<=epssh) + (fsu+(fy-fsu)*abs((epssu-epss(c))./(epssu-epssh)).^(1/P)) .* (epss(c)>epssh & epss(c)<=epssu) + 0 .* (epss(c)>epssu);
tension=@(c) sigmaSteel(c).*As/1000;
c(i)=fsolve(@(c) compression(c)-tension(c), c0, fsolve_opts);
c0 = c(i);
funM=@(epsc) (1-(1-epsc./eps0).^A).*(d-c(i)+(c(i)./epscm).*epsc) .* (epsc<=eps0) + exp(-kshah*(epsc-eps0).^1.15).*(d-c(i)+(c(i)./epscm).*epsc) .* (epsc>eps0);
M(i,k)=b*fck*c(i)/epscm*integral(funM,0,epscm)/1000000;
phi(i,k)=epscm/c(i);
epss1(k,i)= (d-c(i))/c(i)*epscm;
sigmaSteel1(k,i)= Es*epss1(k,i) .* (epss1(k,i)<=epsy) + fy .* (epss1(k,i)>epsy & epss1(k,i)<=epssh) + (fsu+(fy-fsu)*abs((epssu-epss1(k,i))./(epssu-epssh)).^(1/P)) .* (epss1(k,i)>epssh & epss1(k,i)<=epssu) + 0 .* (epss1(k,i)>epssu);
c_mtx(i,k) = c(i);
end
idx(k) = find(diff(M(:,k)) < 0, 1, 'first')
[Mmax(k),idx(k)]=max(M(:,k)) %[kNm]
phiAtMmax(k)=phi(idx(k),k) %[1/mm]
epsAtMmax(k)=epscmv(idx(k))*1000 %[promil]
end
toc
% epss_c = fsolve(@(c) epss(c)-epssh, 100, fsolve_opts)
% c_idx = find(c >= epss_c, 1, 'first')
% epscm_exact = interp1(c([-5 5]+c_idx), epscmv([-5 5]+c_idx), epss_c)
figure
hold all
hp = zeros(1, num_fckv);
lgdstr = cell(1, num_fckv);
for k = 1:num_fckv
hp(k) = plot(phi(1:idx(k)+50,k), M(1:idx(k)+50,k));
% plot([1 1]*epss_c, ylim, ':k')
lgdstr{k} = sprintf('fck = %2d [Mpa], As = %4d [mm^2]',fckv(k), Asv(k));
plot(phi(idx(k),k),M(idx(k),k),'r*') % marking the Mmax
end
hold off
grid on
xlabel('phi [1/mm]')
ylabel('Moment [kNm]')
hl = legend(hp,lgdstr);
hl.FontSize = 7;
% text(epss_c, 400, sprintf('\\leftarrow epss_c = %.1f', epss_c), 'HorizontalAlignment','left')
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Akzeptierte Antwort
Star Strider
am 5 Dez. 2019
The only way I can see to calculate ‘M’ where ‘epss’ is equal to 0.009 is to duplicate the first nested loop, defining:
epss = @(c) epssh;
If you do that:
for k = 1:numel(fckv)
fck = fckv(k);
Ecshah=57000/145*(fck*145)^0.5; %Mpa
Es=200000; %Mpa
Esh=8500; %Mpa
fy=500; %Mpa
fsu=750; %Mpa
epssh=0.009;
epssu=0.075;
eps0=1.027*10^-7*fck*145+0.00195;
kshah=0.025*fck*10^3;
A=Ecshah*eps0/fck;
P=Esh*((epssu-epssh)/(fsu-fy));
epsy=fy/Es;
epscmv = linspace(0.1, 100, 5000)*1E-3;
As = Asv(k);
for i=1:numel(epscmv);
epscm = epscmv(i);
epss = @(c) epssh;
% epss=@(c) (d-c)/c*epscm;
funCshah=@(epsc) (1-(1-epsc./eps0).^A) .* (epsc<=eps0) + exp(-kshah*(epsc-eps0).^1.15) .* (epsc>eps0);
compression=@(c) b*fck*c/epscm*integral(funCshah,0,epscm)/1000;
sigmaSteel=@(c) Es*epss(c) .* (epss(c)<=epsy) + fy .* (epss(c)>epsy & epss(c)<=epssh) + (fsu+(fy-fsu)*abs((epssu-epss(c))./(epssu-epssh)).^(1/P)) .* (epss(c)>epssh & epss(c)<=epssu) + 0 .* (epss(c)>epssu);
tension=@(c) sigmaSteel(c).*As/1000;
c(i)=fsolve(@(c) compression(c)-tension(c),1000);
funM=@(epsc) (1-(1-epsc./eps0).^A).*(d-c(i)+(c(i)./epscm).*epsc) .* (epsc<=eps0) + exp(-kshah*(epsc-eps0).^1.15).*(d-c(i)+(c(i)./epscm).*epsc) .* (epsc>eps0);
M009(i,k)=b*fck*c(i)/epscm*integral(funM,0,epscm)/1000000;
phi(i,k)=epscm/c(i);
c_mtx(i,k) = c(i);
end
end
toc
figure
mesh(M009)
grid on
and also do the surface plot, you can see the result.
I have no idea what to do with this result, so I leave that to you.
11 Kommentare
VBBV
am 25 Dez. 2022
b=400; %mm
d=500; %mm
Asv = [3000 5000 3000 5000]; %mm^2
fckv = [30 30 90 90]; %Mpa
num_fckv = numel(fckv);
fsolve_opts = optimoptions('fsolve','Display','off');
c0 = 100;
tic
for k = 1:num_fckv
fck = fckv(k);
Ecshah=57000/145*(fck*145)^0.5; %Mpa
Es=200000; %Mpa
Esh=8500; %Mpa
fy=500; %Mpa
fsu=750; %Mpa
epssh=0.009;
epssu=0.075;
eps0=1.027*10^-7*fck*145+0.00195;
kshah=0.025*fck*10^3;
A=Ecshah*eps0/fck;
P=Esh*((epssu-epssh)/(fsu-fy));
epsy=fy/Es;
As = Asv(k);
%Values at yield
epssAtMy= epsy;
epscmAtMy=@(cAtMy) epssAtMy*cAtMy./(d-cAtMy);
funCshahAtMy=@(epsc) (1-(1-epsc./eps0).^A) .* (epsc<=eps0) + exp(-kshah*(epsc-eps0).^1.15) .* (epsc>eps0);
compressionAtMy=@(cAtMy) b*fck*cAtMy/epscmAtMy(cAtMy)*integral(funCshahAtMy,0,epscmAtMy(cAtMy))/1000;
%compressionAtMy=@(cAtMy) b*fck*cAtMy/epscmAtMy*integral(funCshahAtMy,0,epscmAtMy)/1000;
sigmaSteelAtMy= fy;
tensionAtMy= sigmaSteelAtMy*As/1000;
cAtMy(k)=fsolve(@(cAtMy) compressionAtMy(cAtMy)-tensionAtMy, c0, fsolve_opts);
c0=cAtMy(k);
funM=@(epsc) (1-(1-epsc./eps0).^A).*(d-c0+(c0./epscmAtMy(c0)).*epsc) .* (epsc<=eps0) + exp(-kshah*(epsc-eps0).^1.15).*(d-c0+(c0./epscmAtMy(c0)).*epsc) .* (epsc>eps0);
K = integral(funM,0,epscmAtMy(c0));
M(k)=b*fck*cAtMy(k)/epscmAtMy(c0)*K/1000000;
end
M
toc
you need to provide input value to variable to the function epscmAtMy defined using function handle when calling it in the lines
funM=@(epsc) (1-(1-epsc./eps0).^A).*(d-c0+(c0./epscmAtMy(c0)).*epsc) .* (epsc<=eps0) + exp(-kshah*(epsc-eps0).^1.15).*(d-c0+(c0./epscmAtMy(c0)).*epsc) .* (epsc>eps0);
M(k)=b*fck*cAtMy(k)/epscmAtMy(c0)*K/1000000;
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