In [1]:

```
from math import pi,atan,sqrt,cos,sin
#variable declaration
#summation of all horizontal forces is zero & vertical forces is zero.
P1=float(10) #Vertical down Load at 4m from A,KN
P2=float(15) #Inclined down Load at angle 30° at 6m from A,KN
P3=float(20) #Inclined down Load at angle 45° at 10m from A,KN
theta2=30
theta3=45
#horizontal,vertical component at A is Ha,Va respectively.
Ha=P2*cos(theta2*pi/180)+P3*cos(theta3*pi/180)
Rb=(P1*4+P2*6*sin(theta2*pi/180)+P3*10*sin(theta3*pi/180))/12 #reaction at B point,KN
print "RB=",round(Rb,4),"KN"
#now vertical component
Va=P2*sin(theta2*pi/180)+P3*sin(theta3*pi/180)+P1-Rb
Ra=sqrt(pow(Ha,2)+pow(Va,2))
print "RA=",round(Ra,4),"KN"
alpha=(atan(Va/Ha))*180/pi
print "alpha=",round(alpha,2),"°"
```

In [2]:

```
from math import pi,atan,sqrt,cos,sin
#variable declaration
#summation of all horizontal forces is zero & vertical forces is zero.
P1=float(60) #inclined down to right Load at angle 60 at 1m from A,KN
P2=float(80) #Inclined down to left Load at angle 75° at 3m from A,KN
P3=float(50) #Inclined down to left Load at angle 60° at 5.5m from A,KN
theta1=60
theta2=75
theta3=60
thetaRb=60
#horizontal,vertical component at A is Ha,Va respectively.
Rb=(P1*1*sin(theta1*pi/180)+P2*3*sin(theta2*pi/180)+P3*5.5*sin(theta3*pi/180))/(6*sin(thetaRb*pi/180)) #reaction at B point,KN
Ha=-P1*cos(theta1*pi/180)+P2*cos(theta2*pi/180)-P3*cos(theta3*pi/180)+Rb*cos(thetaRb*pi/180)
print "RB=",round(Rb,4),"KN"
#now vertical component
Va=P1*sin(theta1*pi/180)+P2*sin(theta2*pi/180)+P3*sin(theta3*pi/180)-Rb*sin(thetaRb*pi/180)
Ra=sqrt(pow(Ha,2)+pow(Va,2))
print "RA=",round(Ra,4),"KN"
alpha=(atan(Va/Ha))*180/pi
print "alpha=",round(alpha,2),"°"
```

In [3]:

```
from math import pi,atan,sqrt,cos,sin
#variable declaration
#summation of all horizontal forces is zero & vertical forces is zero.
P1=float(20) #vertical down Load at 2m from A,KN
P2=float(30) #uniform distributed load from 2m to 6m from A,KN/m(in 4m of span)
P3=float(60) #Inclined down to right Load at angle 45° at 7m from A,KN
theta3=45
#horizontal,vertical component at B is Hb,Vb respectively.
Ra=(P1*7+P2*4*5+P3*2*sin(theta3*pi/180))/(9) #reaction at B point,KN
print "RA=",round(Ra,4),"KN"
Hb=P3*cos(theta3*pi/180)
print "HB=",round(Hb,4),"KN"
#now vertical component
Vb=P1+P2*4+P3*sin(theta3*pi/180)-Ra
print "VB=",round(Vb,4),"KN"
Rb=sqrt(pow(Hb,2)+pow(Vb,2))
print "RB=",round(Rb,4),"KN"
alpha=(atan(Vb/Hb))*180/pi
print "alpha=",round(alpha,2),"°"
```

In [4]:

```
#variable declaration
#Let the reactions at A be Ha, Va and Ma
#summation of all horizontal forces is zero & vertical forces is zero.
P1=float(20) #vertical down Load at 2m from A,KN
P2=float(12) #vertical down Load at 3m from A,KN
P3=float(10) #vertical down Load at 4m from A,KN
Pu=float(16) #uniform distributed load from A to 2m from A,KN/m(in 2m of span)
##horizontal,vertical component at A is Ha,Va respectively.
print"no horizontal force ","HA=0"
Va=Pu*2+P1+P2+P3
print "VA=", round(Va,2),"KN"
Ma=Pu*2*1+P1*2+P2*3+P3*4
print "MA=", round(Ma,2),"KN-m"
```

In [5]:

```
#variable declaration
#Let the reactions at A be Va and Ma
#summation of all horizontal forces is zero & vertical forces is zero.
P1=float(15) #vertical down Load at 3m from A,KN
P2=float(10) #vertical down Load at 5m from A,KN
M=float(30) #CW moment at 4m distance from A, KN-m
Pu=float(20) #uniform distributed load from A to 2m from A,KN/m(in 2m of span)
##horizontal,vertical component at A is Ha,Va respectively.
print"no horizontal force ","HA=0"
Va=Pu*2+P1+P2
print "VA=", round(Va,2),"KN"
Ma=Pu*2*1+P1*3+P2*5+M
print "MA=", round(Ma,2),"KN-m"
```

In [6]:

```
#variable declaration
#As supports A and B are simple supports and loading is only in vertical direction, the reactions RA and RB are in vertical directions only.
#summation of all horizontal forces is zero & vertical forces is zero.
P1=float(30) #vertical down Load at 1m from A,KN
P2=float(40) #vertical down Load at 6.5m from A,KN
Pu=float(20) #uniform distributed load from 2m to 5m from A,KN/m(in 3m of span).
Rb=(Pu*3*3.5+P1*1+P2*6.5)/5
print "RB=", round(Rb,2),"KN"
Ra=Pu*3+P1+P2-Rb
print "RA=", round(Ra,2),"KN"
```

In [7]:

```
#variable declaration
#Let the reactions at A be Va and Ma.
#summation of all horizontal forces is zero & vertical forces is zero.
P1=float(60) #vertical down Load at 4m from A to right,KN
P2=float(20) #vertical down Load at 11m from A to right,KN
M=float(30) #CW moment at 7m distance from A to right, KN-m
Pu=float(20) #uniform distributed load from A to 2m from A to left ,KN/m(in 2m of span)
##horizontal,vertical component at A is Ha,Va respectively.
print"no horizontal force ","HA=0"
Vb=(-Pu*2*1+P1*4+P2*11+M)/9
print "VB=", round(Vb,2),"KN"
Va=Pu*2+P1+P2-Vb
print "VA=", round(Va,2),"KN"
```

In [8]:

```
from math import pi,atan,sqrt,cos,sin
#variable declaration
#summation of all horizontal forces is zero & vertical forces is zero.
P1=float(30) #Inclined down Load at angle 45° to left at 5m from A,KN
Pu=float(20) #uniformly distributed load from 6m to 8m from A ,KN,(2m of span)
theta1=45
M=40 #ACW moment at 3m from A, KN-m
#horizontal,vertical component at A is Ha,Va respectively.
Rb=(M+P1*5*sin(theta1*pi/180)+Pu*2*7)/6 #reaction at B point,KN
print "RB=",round(Rb,4),"KN"
Ha=P1*cos(theta1*pi/180)
#now vertical component
Va=P1*sin(theta1*pi/180)-Rb+Pu*2
Ra=sqrt(pow(Ha,2)+pow(Va,2))
print "(Negative sign show that the assumed direction of VA is wrong. In other words, VA is acting vertically downwards). "
Va1=-1*Va
print "RA=",round(Ra,4),"KN"
alpha=(atan(Va1/Ha))*180/pi
print "alpha=",round(alpha,2),"°"
```

In [9]:

```
#variable declaration
#summation of all horizontal forces is zero & vertical forces is zero.
#Let the left support C be at a distance x metres from A.
P1=float(30) #vertical down load at A,KN
Pu=float(6) #uniform distributed load over whole span,KN/m,(20m of span)
P2=float(50) #vertical down load at B, KN
#Rc=Rd(given) reaction at C & D is equal.
Rc=(P1+P2+Pu*20)/2
Rd=Rc
#taking moment at A
x=(((Pu*20*10+P2*20)/100)-12)/2
print "X=", round(x,2),"m"
```