📄 lresp.for
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**********************************
* Program res_spec.f
* Generates the RESPONSE SPECTRA of a LINEAR
* Undamped SDOF System to any arbitrary applied load
**********************************
* The program uses the Newmark-B integration scheme
* to evaluate the response at each discrete time step
**********************************
* Program Author : Sanjoy Chakraborty : 09CE
**********************************
program res_spec
implicit real *8 (a-h,o-z)
real *8 k,m
character *12 fout
dimension x(200000),x1(200000),x2(200000),ft(100),tt(100),
1 p(200000)
data pi/3.141592654/
call input(m,c,rm,tt,ft,nfor,tend,h,td,
1 trat1,trat2,trath)
call inter_f(nfor,tt,ft,p,h,tend,pmax)
**********************************
* Loop for computing the value of maximum DISPLACEMENT
* response for successive values of system TIME-Period
**********************************
write(*,'(//a)')' Output File Name :'
read(*,'(a)')fout
open(2,file=fout,status='unknown')
do 701 trat=trat1,trat2,trath
t=td/trat
k=m*(2.*pi/t)**2
cc=c*sqrt(2.*k*m)
call resp(x,x1,x2,m,cc,k,h,tend,rm,p,ic)
call output(m,cc,k,rm,tt,ft,nfor,tend,h,ic,x,x1,x2,
1 trat,t,pmax)
701 continue
stop
end
**********************************
subroutine input(m,c,rm,tt,ft,nfor,tend,h,
1 td,trat1,trat2,trath)
**********************************
* Used to input the system parameters and forcing
* function from the input file fin
**********************************
implicit real *8 (a-h,o-z)
real *8 k,m
character *12 fin
dimension tt(100),ft(100)
rm=0.1e12
write(*,115)
115 format(//,' Program to Generate Load Response Spectra',
1 //,' Program Author : Sanjoy Chakraborty, Auburn University',
2 ///,' Input File Name :')
read(*,'(a)')fin
open(1,file=fin,status='old')
read(1,*)m,c,tend,h
read(1,*)td,trat1,trat2,trath
nfor=1
110 continue
read(1,*,err=111)tt(nfor),ft(nfor)
nfor=nfor+1
goto 110
111 nfor=nfor-1
close(1)
return
end
**********************************
subroutine inter_f(nf,tt,ft,p,h,tend,pmax)
**********************************
* Used to interpolate for the forcing function values
* at the times at which the solution is sought
**********************************
implicit real *8 (a-h,o-z)
dimension tt(100),ft(100),p(200000)
ic=1
do 1001 t=0.,tend,h
do 1002 i=1,nf-1
if(t.ge.tt(i).and.t.le.tt(i+1))then
p(ic)=ft(i)+(ft(i+1)-ft(i))*(t-tt(i))/(tt(i+1)-tt(i))
goto 1003
endif
1002 continue
1003 ic=ic+1
1001 continue
pmax=abs(ft(1))
do 1005 i=2,nf
if(abs(ft(i)).gt.pmax)pmax=abs(ft(i))
1005 continue
return
end
**********************************
subroutine resp(x,x1,x2,m,c,k,h,tend,rm,p,ic)
**********************************
* Computes the system response (displacement, velocity
* and acceleration) at each time step
**********************************
* The loop (=i) parameter is used to determine the
* exact location of the system on the hysteretic loop
* describing the resistance function Rm
* loop =1 --> elastic loading stage
* loop =2 --> plastic loading stage
* loop =3 --> elastic rebound stage
* loop =4 --> plastic rebound stage
* xmax, xmin, and xlim are parameters used to control
* the physical route of the resistance function along
* the hysteretic loop
* xmax = max. +ve plastic deformation (loop=2)
* xmin = max. -ve plastic deformation (loop=4)
**********************************
implicit real *8 (a-h,o-z)
real *8 k,m,kelas,kplas
dimension x(200000),x1(200000),x2(200000),p(200000)
x(1)=0.
x1(1)=0.
x2(1)=p(1)/m
xel=rm/k
a1=3./h
a2=6./h
a3=h/2.
a4=6./h**2
kelas=k+a4*m+a1*c
kplas=a4*m+a1*c
xlim=xel
xmin=-xel
loop=1
ic=2
do 501 t=h,tend,h
if(loop.eq.1)then
call res1(kelas,p,x,x1,x2,m,c,ic,a2,a3,a1)
r=-rm-(xmin-x(ic))*k
x2(ic)=(p(ic)-c*x1(ic)-r)/m
if(x(ic).ge.xlim)then
loop=2
endif
ic=ic+1
goto 501
elseif(loop.eq.2)then
call res1(kplas,p,x,x1,x2,m,c,ic,a2,a3,a1)
r=rm
x2(ic)=(p(ic)-c*x1(ic)-r)/m
if(x1(ic).le.0.)then
loop=3
xmax=x(ic)
xlim=x(ic)-2.*xel
endif
ic=ic+1
goto 501
elseif(loop.eq.3)then
call res1(kelas,p,x,x1,x2,m,c,ic,a2,a3,a1)
r=rm-(xmax-x(ic))*k
x2(ic)=(p(ic)-c*x1(ic)-r)/m
if(x(ic).le.xlim)then
loop=4
endif
ic=ic+1
goto 501
elseif(loop.eq.4)then
call res1(kplas,p,x,x1,x2,m,c,ic,a2,a3,a1)
r=-rm
x2(ic)=(p(ic)-c*x1(ic)-r)/m
if(x1(ic).ge.0.)then
loop=1
xlim=x(ic)+2.*xel
xmin=x(ic)
endif
ic=ic+1
goto 501
endif
501 continue
return
end
**********************************
subroutine res1(k,p,x,x1,x2,m,c,ic,a2,a3,a1)
**********************************
* Used to compute displacement and velocity
* at any time step
**********************************
implicit real *8 (a-h,o-z)
real *8 k,m
dimension p(200000),x(200000),x1(200000),x2(200000)
dps=p(ic)-p(ic-1)+x1(ic-1)*(a2*m+3.*c)+x2(ic-1)*
1 (3.*m+a3*c)
dx=dps/k
dx1=a1*dx-3.*x1(ic-1)-a3*x2(ic-1)
x(ic)=x(ic-1)+dx
x1(ic)=x1(ic-1)+dx1
return
end
**********************************
subroutine output(m,c,k,rm,tt,ft,nfor,tend,h,ic,
1 x,x1,x2,trat,t,pmax)
**********************************
* Computes the value of Maximum Response at each value
* of TIME PERIOD of the system, then writes the output
* to Unit:3 in the format Td/T vs. (DLF)max
**********************************
implicit real *8 (a-h,o-z)
real *8 m,k
dimension tt(100),ft(100),x(200000),x1(200000),x2(200000)
xm=x(1)
txm=0.
x1m=x1(1)
tx1m=0.
x2m=x2(1)
tx2m=0.
do 605 i=2,ic-1
if(abs(x(i)).gt.abs(xm))then
xm=x(i)
txm=float(i-1)*h
endif
if(abs(x1(i)).gt.abs(x1m))then
x1m=x1(i)
tx1m=float(i-1)*h
endif
if(abs(x2(i)).gt.abs(x2m))then
x2m=x2(i)
tx2m=float(i-1)*h
endif
605 continue
xstat=pmax/k
dlf=abs(xm)/xstat
write(2,'(2e14.7)')trat,dlf
return
end
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