# Chapter8-Spring Design¶

## Ex1-pg160¶

In :
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-8.1 Page No.160\n');

Dm=0.625;            ##[in] Mean diameter of spring

K=1.25;           ##[] Wahl factor for Dm/Dw=6.25 (figure 8.8)
Q=190000.;         ##[lb/in^2] Expected ultimate strength

Dw=(K*8.*F*Dm/(LF*math.pi*Q))**(1/2.846); ##[in] Wire diameter

print'%s %.2f %s '%('\n The wire diameter of spring is ',Dw,' in.');

##Use U.S Steel 12-gage wire: Dw=0.105 in.

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-8.1 Page No.160

The wire diameter of spring is  0.10  in.


## Ex2-pg163¶

In :
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-8.2 Page No.163\n');

Dw=0.105;          ##[in] Wire diameter
Dm=0.620;          ##[in] Mean diameter of spring
G=11.85*10**6;      ##[lb/in^2] Shear modulus of elasticity
Delta=0.5;         ##[in] Deflection

Na=Delta*G*Dw**4./(8.*F*Dm**3); ##[] Number of active coils

Nat=Na+2.;          ##[] Total number of coils

Lf=2.;              ##[in] Free length of spring

P=(Lf-2.*Dw)/Nat;   ##[in] Pitch (Table 8.1)

print'%s %.2f %s '%('\n Pitch is ',P,' in.');

k=G*Dw**4./(8.*Dm**3*Na); ##[lb/in] Spring rate

print'%s %.2f %s '%('\n Spring rate is ',k,' lb/in.');

print'%s %.2f %s '%('\n The total number of coils necessary to meet design criteria are .',Nat,'');

##Note: The deviation of answer from the answer given in the book is due to round off error.(In the book values are rounded while in scilab actual values are taken)

##Note: The deviation of answer from the answer given in the book is due to round off error.(In the book values are rounded while in scilab actual values are taken)

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-8.2 Page No.163

Pitch is  0.14  in.

Spring rate is  70.00  lb/in.

The total number of coils necessary to meet design criteria are . 12.79


## Ex3-pg165¶

In :
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-8.3 Page No.165\n');
Lf=2.;            ##[in] Free length of spring
Dm=0.620;        ##[in] Mean diameter of spring

R=Lf/Dm;         ##[] Free lengtth to mean diameter ratio

print'%s %.2f %s '%('\n The ratio of the free length of spring to mean diameter of spring is .',R,'');
print(' From Figure 8.9 for squared and ground ends, this is a stable spring.');

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-8.3 Page No.165

The ratio of the free length of spring to mean diameter of spring is . 3.23
From Figure 8.9 for squared and ground ends, this is a stable spring.


## Ex4-pg165¶

In :
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-8.4 Page No.165\n');

k=73.3;            ##[lb/in] Spring rate

x=F/k;             ##[in] Deflection

print'%s %.2f %s '%('\n The deflection in the spring would be ',x,' in.');

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-8.4 Page No.165

The deflection in the spring would be  0.48  in.


## Ex5-pg166¶

In :
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-8.5 Page No.166\n');

b=12.;                  ##[in] Width of plate
h=1.;                   ##[in] Thickness of plate
L=72.;                  ##[in] Length of plate
I=b*h**3/12.;            ##[in^4] Moment of inertia

Delta=4.;               ##[in] Deflection
E=10*10**6;             ##[lb/in^2] Modulus of elasticity

F=3.*Delta*E*I/L**3;     ##[lb] Force

print'%s %.2f %s '%('\n The force at this point is ',F,' lb.');

k=F/Delta;             ##[lb/in] Stiffness

print'%s %.2f %s '%('\n stiffness is ',k,' lb/in.');

##Note: The deviation of answer from the answer given in the book is due to round off error.(In the book values are rounded while in scilab actual values are taken)

##Note: The deviation of answer from the answer given in the book is due to round off error.(In the book values are rounded while in scilab actual values are taken)

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-8.5 Page No.166

The force at this point is  321.50  lb.

stiffness is  80.38  lb/in.


## Ex6-pg167¶

In :
import math

print('MACHINE DESIGN \n Timothy H. Wentzell, P.E. \n EXAMPLE-8.6 Page No.167\n');

F=322.;             ##[lb] Force
Delta=4.;           ##[in] Deflection

U=F*Delta/2.;       ##[in*lb] Energy

print'%s %.2f %s '%('\n The energy from the 4-inch deflection was ',U,' lb*in.');

MACHINE DESIGN
Timothy H. Wentzell, P.E.
EXAMPLE-8.6 Page No.167

The energy from the 4-inch deflection was  644.00  lb*in.