Chapter 5:Support Reactions

Example 5.1,Page No.101

In [1]:
import math

#Declaration Of Variables

#Lengths
L=6 #m
L_AC=2 #m
L_AD=4 #m
L_CD=L_DB=2 #m

#Forces
F_C=3 #KN
F_D=6 #KN

#Calculations

#LEt R_A and R_B be the reactions at A & B respectively
#R_A+R_B=F_C+F_D
#Taking Moment at pt A
R_B=(F_D*(L_AC+L_CD)+F_C*L_AC)*L**-1 #KN
R_A=(F_C+F_D)-R_B #KN

#Result
print"Reaction at A is",round(R_A,2),"KN"
print"Reaction at B is",round(R_B,2),"KN"

Reaction at A is 4.0 KN
Reaction at B is 5.0 KN

Example 5.2,Page No102

In [2]:
import math

#Declaration Of Variables

#Lengths
L_AC=6 #m
L_AB=9 #m

#Load
w=10 #KN/m #u.d.l

#Calculations

#LEt R_A and R_B be the reactions at A & B respectively
#R_A+R_B=w*L_AC
#Taking Moment at pt A
R_B=w*L_AC*L_AC*2**-1*L_AB**-1 #KN
R_A=w*L_AC-R_B

#Result
print"Reaction at A is",round(R_A,2),"KN"
print"Reaction at B is",round(R_B,2),"KN"

Reaction at A is 40.0 KN
Reaction at B is 20.0 KN

Example 5.3,Page No.103

In [3]:
import math

#Declaration Of Variables

#Lengths
L_AC=2 #m
L_CD=L_DB=4 #m
L=10 #m #span

#Forces & Loads
F_C=50 #KN
F_D=40 #KN
w=10 #KN/m #u.d.l

#Calculations

#LEt R_A and R_B be the reactions at A & B respectively
#R_A+R_B=w*L_CD-F_C-F_D
#Taking Moment at pt A
R_B=(F_C*L_AC+F_D*(L_AC+L_CD)+w*L_CD*(L_CD*2**-1+L_AC))*L**-1 #KN
R_A=w*L_CD+F_C+F_D-R_B #KN

#Result
print"Reaction at A is",round(R_A,2),"KN"
print"Reaction at B is",round(R_B,2),"KN"

Reaction at A is 80.0 KN
Reaction at B is 50.0 KN

Example 5.4,Page No.103

In [4]:
import math

#Declaration Of Variables

#Length
L_AB=9 #m

#Load
w=900 #N/m #u.v.l

#Calculations

#LEt R_A and R_B be the reactions at A & B respectively
#R_A+R_B=w*L_AB*2**-1
#Taking Moment at pt A
R_B=w*L_AB*2**-1*2*3**-1*L_AB*L_AB**-1 #KN
R_A=w*L_AB*2**-1-R_B

#Result
print"Reaction at A is",round(R_A,2),"KN"
print"Reaction at B is",round(R_B,2),"KN"

Reaction at A is 1350.0 KN
Reaction at B is 2700.0 KN

Example 5.5,Page No.104

In [5]:
import math

#Declaration Of Variables

#Length
L_AB=5 #m

#Loads
w1=800 #N/m #At A
w2=1600 #N/m #At B

#Calculations

#LEt R_A and R_B be the reactions at A & B respectively
#R_A+R_B=w2*2**-1*L_AB*2**-1+w1*L_AB
#Taking Moment at pt A
R_B=(w1*L_AB*L_AB*2**-1+w2*2**-1*L_AB*2**-1*2*3**-1*L_AB)*L_AB**-1 #KN
R_A=w2*2**-1*L_AB*2**-1+w1*L_AB-R_B

#Result
print"Reaction at A is",round(R_A,2),"KN"
print"Reaction at B is",round(R_B,2),"KN"

Reaction at A is 2666.67 KN
Reaction at B is 3333.33 KN

Example 5.6,Page No.105

In [6]:
import math

#Declaration Of Variables

#LEt the ends of beams be C and D respectively
#Lengths
L_CA=3 #m
L_AB=8 #m
L_BD=2 #m

#Let the Force 2000 acting be E
L_AE=5 #m
L_EB=3 #m

#Forces
F_C=800 #N
F_E=2000 #N
F_D=1000 #N

#Calculations

#LEt R_A and R_B be the reactions at A & B respectively
#R_A+R_B=(F_C+F_E+F_D)
#Taking Moment at pt A
R_B=(F_E*L_AE+F_D*(L_BD+L_AB)-F_C*L_CA)*L_AB**-1 #KN
R_A=(F_C+F_E+F_D)-R_B

#Result
print"Reaction at A is",round(R_A,2),"KN"
print"Reaction at B is",round(R_B,2),"KN"

Reaction at A is 1600.0 KN
Reaction at B is 2200.0 KN

Example 5.7,Page No.106

In [7]:
import math

#Declaration Of Variables

#Lengths
L_AB=4 #m
L_BC=2 #m
L_AC=6 #m

#Loads
F_C=2 #KN
w=2 #KN/m #u.d.l

#Calculations

#LEt R_A and R_B be the reactions at A & B respectively
#R_A+R_B=w*L_AC
#Taking Moment at pt A
R_B=(F_C*L_AC+w*L_AC*L_AC*2**-1)*L_AB**-1 #KN
R_A=w*L_AC-R_B+F_C #KN

#Result
print"Reaction at A is",round(R_A,2),"KN"
print"Reaction at B is",round(R_B,2),"KN"

Reaction at A is 2.0 KN
Reaction at B is 12.0 KN

Example 5.8,Page No.106

In [1]:
import math
from math import sin, cos, tan, radians, pi

#Declaration Of Variables

#lengths
L_AC=20 #cm
L_CD=L_EB=40 #cm
L_DE=70 #cm
L_AB=L_AC+L_CD+L_EB+L_DE #cm

#Forces
F_C=50 #N

#At pt D
F_D1=20*sin(pi*180**-1*60) #N
F_D2=20*cos(pi*180**-1*60) #N

#At pt E
F_E1=30*sin(pi*180**-1*45) #N
F_E2=30*cos(pi*180**-1*45) #N

#At pt B
F_B1=15*sin(pi*180**-1*80) #N
F_B2=15*cos(pi*180**-1*80) #N

#Calculations

#LEt R and R_B be the reactions at A & B respectively
#R_A+R_B=F_C+F_D1+F_E1+F_B1
#Taking Moment at pt A
R_B=(F_C*L_AC+F_D1*(L_AC+L_CD)+F_E1*(L_AC+L_CD+L_DE)+F_B1*(L_AC+L_CD+L_DE+L_EB))*L_AB**-1

#Vertical component of A
R_AY=F_C+F_D1+F_E1+F_B1-R_B #N

#Now horizontal component of A
R_AX=-(F_D2-F_E2+F_B2) #N
#the direction of R_AX will be towards left of A

#Reaction At A
R=(R_AY**2+R_AX**2)**0.5 #N

#Result
print"Reaction at A is:R",round(R,2),"N"
print"Reaction at B is",round(R_B,2),"N"

Reaction at A is:R 60.93 N
Reaction at B is 42.99 N

Example 5.9,Page No.108

In [2]:
import math
from math import sin, cos, tan, radians, pi

#Declaration Of Variables

#Lengths
L_AC=2 #m
L_CD=2 #m
L_DB=2 #m
L=6 #m

#Loads
w=1.5 #KN/m
F_C=5 #KN

#At pt D
F_D1=4*sin(pi*180**-1*(180-135))
F_D2=4*sin(pi*180**-1*(180-135))

#Calculations

#LEt R and R_B be the reactions at A & B respectively
#R_A+R_B=F_C+F_D1+F_E1+F_B1
#Taking Moment at pt A
R_B=((F_C*L_AC)+w*L_CD*(L_CD*2**-1+L_AC)+F_D1*(L_AC+L_CD))*L**-1

#Vertical component of A
R_AY=F_C+F_D1+w*L_AC-R_B #KN

#Now horizontal component of A
R_AX=(F_D2) #KN
#the direction of R_AX will be towards left of A

#Reaction At A
R=(R_AY**2+R_AX**2)**0.5 #KN


#Result
print"Reaction at A is:R",round(R,2),"KN"
print"Reaction at B is",round(R_B,2),"KN"

Reaction at A is:R 6.43 KN
Reaction at B is 5.05 KN

Example 5.10,Page No.110

In [3]:
import math
from math import sin, cos, tan, radians, pi

#Declaration Of Variables

#Lengths
L=10 #m
L_AC=2.5 #m
L_CD=2.5 #m
L_DE=3 #m
L_EB=2 #m

#Forces
F_C=4 #KN

#At pt D
F_D1=5*sin(pi*180**-1*45)
F_D2=5*cos(pi*180**-1*45)

F_E=5 #KN

#Calculations

#Let R and R_B be the reactions at A & B respectively

#Resolving R_B into R_B1 & R_B2
#R_B1*sin(30*pi*180**-1)
#R_B2*cos(30*pi*180**-1)

#R_A+R_B=F_C+F_D1+F_E
#Taking Moment at pt A
R_B1=(F_C*L_AC+F_D1*(L_AC+L_CD)+F_E*(L_AC+L_CD+L_DE))*(L*cos(pi*180**-1*30))**-1 #KN
R_B2=R_B1*sin(30*pi*180**-1) #KN

#Vertical component of A
R_AY=(F_C+F_D1+F_E-R_B1*cos(30*pi*180**-1)) #KN

#Now horizontal component of A
R_AX=(-F_D2+R_B2) #KN
#the direction of R_AX will be towards left of A

#Reaction At A
R=(R_AY**2+R_AX**2)**0.5 #KN


#Result
print"Reaction at A is:R",round(R,2),"KN"
print"Reaction at B is",round(R_B1,2),"KN"

Reaction at A is:R 5.78 KN
Reaction at B is 7.81 KN

Example 5.11,Page No.111

In [11]:
import math
from math import sin, cos, tan, radians, pi

#Declaration Of Variables

#Lengths
L_AC=L_CD=5 #m
L_AD=10 #m

#Forces
F_C=F_D=500 #N

#Calculations

#LEt R_A & R_B be the reactions at pt A & B respectively

#Now resolving Forces at pt C & D 
F_C1=F_D1=F_C*sin(30*pi*180**-1) #N
F_C2=F_D2=F_D*cos(30*pi*180**-1) #N

#Now taking Moment at pt A
#But In triangle BDA,
#cos(30*pi*180**-1)=L_AD*L_AB**-1
#After Further simplifying we get
L_AB=L_AD*(cos(30*pi*180**-1))**-1 #m

R_B=(F_C*L_AC+F_D*L_AD)*L_AB**-1 #N

#Now sum of components parallel to inclined surface AB
R_AH=F_C1+F_D1 #N

#Now sum of forces perpendicular to inclined surface AB
R_AV=F_C2+F_D2-R_B #N

#Reaction At A
R=(R_AV**2+R_AH**2)**0.5 #N

#Result
print"Reaction at A is",round(R,2),"KN"
print"Reaction at B is",round(R_B,2),"KN"

Reaction at A is 544.86 KN
Reaction at B is 649.52 KN

Example 5.12,Page No.113

In [12]:
import math
from math import sin, cos, tan, radians, pi

#Declaration Of Variables

#Lengths
L_AD=80*10**-2 #m
L_AE=L_EF=L_FB=60*10**-2 #m
L_AC=L_CD=40*10**-2 #cm

#Forces

#At pt D
F_D1=100*sin(pi*180**-1*30) #N
F_D2=100*cos(pi*180**-1*30) #N

#At pt C
F_C1=70*sin(pi*180**-1*45) #N
F_C2=70*cos(pi*180**-1*45) #N

w=250 #N/m #u.d.l

#Calculations

#Let R_A and R_B be the reactions at A & B respectively
#Resolving R_B into R_B1 & R_B2
#Taking Moment at pt A
R_B=-(-F_D2*L_AD+F_C2*L_AC-w*L_EF*(L_EF*2**-1+L_AE))*(cos(20*pi*180**-1)*(L_AE+L_EF+L_FB))**-1 #N

#Vertical component of A
R_AX=(-F_D2+F_C1+R_B*sin(20*pi*180**-1)) #N

#Now horizontal component of A
R_AY=(-F_D1-F_C2-R_B*cos(20*pi*180**-1)+w*L_EF) #KN

##Reaction At A
R=(R_AY**2+R_AX**2)**0.5 #KN


#Result
print"The Reaction at supports of an L-bent is",round(R,3),"KN"

The Reaction at supports of an L-bent is 51.988 KN

Example 5.13,Page No.115

In [13]:
import math

#Declaration Of Variables

#lengths
L_AC=2 #m
L_CD=3 #m
L_DB=2 #m
L=7 #m

#Loads
w=4 #KN/m
m1=4 #KN/m #moment at pt C
m2=8 #KN/m #moment at pt D

#Calculations

#Let R_A & R_B be the reactions at pt a nd B respectively
#R_A+R_B=w*L_CD*2**-1
#Taking moment at pt A
R_B=(w*L_CD*2**-1*(2*3**-1*L_CD+L_AC)+m1-m2)*L**-1
R_A=w*L_CD*2**-1-R_B

#Result
print"Reaction at A is",round(R_A,2),"KN"
print"Reaction at B is",round(R_B,2),"KN"

Reaction at A is 3.14 KN
Reaction at B is 2.86 KN

Example 5.14,Page No.116

In [14]:
import math
from math import sin, cos, tan, radians, pi

#Declaration Of Variables

#Lengths
L_AC=L_CD=L_DE=L_EB=2 #m
L=8 #M

#Forces
#At pt C
F_C1=40*sin(pi*180**-1*60) #KN
F_C2=40*cos(pi*180**-1*60) #KN

#At pt E
F_E1=50*sin(pi*180**-1*60) #KN
F_E2=50*cos(pi*180**-1*60) #KN

F_D=80 #KN
w=20 #KN/m

#Calculations

#LEt R_A and R_B be the reactions at A & B respectively
#Taking Moment at pt A
R_B=(F_C1*L_AC+w*L_CD*(L_CD*2**-1+L_AC)+F_D*(L_AC+L_CD)+F_E1*(L_AC+L_CD+L_DE))*(L*cos(30*pi*180**-1))**-1
R_B2=R_B*sin(30*pi*180**-1)

#Vertical component of A
R_AY=(F_C1+w*L_CD+F_D+F_E1-R_B*cos(30*pi*180**-1)) #KN

#Now horizontal component of A
R_AX=(-F_C2+F_E2+R_B2) #KN
#the direction of R_AX will be towards left of A

#Reaction At A
R=(R_AY**2+R_AX**2)**0.5 #KN


#Result
print"Reaction at A is:R",round(R,2),"KN"
print"Reaction at B is",round(R_B,2),"KN"

Reaction at A is:R 118.43 KN
Reaction at B is 111.01 KN