Chapter 8 : Mechanical Testing¶

Example 8.1 pageno : 195¶

In [1]:
# Variables
b = 225.;			#in mm
h = 10. 			#in mm
l = 1100.;			#in mm
f1 = 250.;			#in N
f2 = 350;			#in N at which glass breaks

# Calculations
m = f1*l/4.;			#in N-mm
f = f1/2.;  			#in N
a = (6*m)/(b*h**2);			#in N/mm**2
t = (3*f)/(2*b*h);			#in N/sqmm
r = f2*l/4;			        #in N-mm
i = (b*h**3)/12;			#in mm**4
y = h/2;	        		#in mm
mr = r*y/i;		        	#in n/sqmm

# Results
print "Flexural Strength (in N/sqmm)  =  %.2f N/mm**2"%a
print "Shear Strength (in N/sqmm)  =  %3f N/mm**2"%t
print "Modulous of Rupture (in N/sqmm)  =  %.2f N/mm**2"%mr

Flexural Strength (in N/sqmm)  =  18.33 N/mm**2
Shear Strength (in N/sqmm)  =  0.083333 N/mm**2
Modulous of Rupture (in N/sqmm)  =  25.67 N/mm**2


Example 8.2 pageno : 201¶

In [2]:
import math

# Variables
d = 5.;     			#in mm

# Calculations
id = 32.5/10;			#indentation diameter in mm
p = 30*d**2;			#load for steel specimen in kgf
bhn = p/((3.14*d/2)*(d-math.sqrt(d**2-id**2)));			#in kgf/sqmm

# Results
print "Load P for steel specimen (in kgf)  =  %.f kgf"%p
print "BRINELL HARDNESS NUMBER of the steel specimen  =  %.1f"%bhn

Load P for steel specimen (in kgf)  =  750 kgf
BRINELL HARDNESS NUMBER of the steel specimen  =  79.6


Example 8.3 pageno : 209¶

In [8]:
import math

# Variables
l = 0.1;			#frictinal and windage losses in kgf-m
dr = 5.9;			#dial reading in kgf-m
w = 19.33;			#weight of hammer in kgf-m
t = 10.;			#in mm
ui = 30.;			#in kgf-m
a = 160.;			#angle in degrees
r = 0.8;			#swing radius in m

# Calculations
u = dr-l;	        		#in kgf-m
d = t/5;		        	#depth of V-notch in mm
te = t-d;		    	    #effective thickness in mm
ve = 75.*10*te; 			#effective volume in cu. mm
vem = ve*10.**-9;			#in cu. m
mr = u/vem;	        		#in kgf/sqm
ae = t*te;      			#effective area of cross section in sqmm
aem = ae*10**-6;			#in sqm
is_ = u/aem;		        	#in kg/m
uf = ui-u;			#in kgf-m
hf = uf/w;			#in m
B = math.degrees(math.acos(1-(uf/(w*r))))

# Results
print "Rupture Energy (in kgf-m)  =  %.1f kgf-m"%u
print "Modulous Of Rupture (in kgf/sqm)  =  %.1e kgf/m**2"%mr
print "Notch Imapct Strength (in kg/m)  =  %.2e kgm"%is_
print "Height risen by Hammer (in m)  =  %.2f m"%hf
print "Angle after Breaking the specimen (in degress)  =  %.1f degrees"%(B)

Rupture Energy (in kgf-m)  =  5.8 kgf-m
Modulous Of Rupture (in kgf/sqm)  =  9.7e+05 kgf/m**2
Notch Imapct Strength (in kg/m)  =  7.25e+04 kgm
Height risen by Hammer (in m)  =  1.25 m
Angle after Breaking the specimen (in degress)  =  124.4 degrees


Example 8.4 pageno : 211¶

In [10]:
# Variables
a_m = 70.;  	    		#mean stress in Mpa
a_r = 210.;	    	    	#stress amplitude in Mpa

# Calculations
a_max = ((2*a_m)+a_r)/2;			#maximum stress in MPa
a_min = 2*a_m-a_max;	    		#Minimum stress in MPa
s = a_min/a_max;			        #stress ratio
sr = a_max-a_min;       			#stress range in MPa

# Results
print "Maximum Stress Level (in MPa)  =  ",a_max
print "Minimum Stress Level (in MPa)  =  ",a_min
print "Stress Ratio  =  ",s
print "Stress Range (in MPa)  =  ",sr

Maximum Stress Level (in MPa)  =   175.0
Minimum Stress Level (in MPa)  =   -35.0
Stress Ratio  =   -0.2
Stress Range (in MPa)  =   210.0


Example 8.5 pageno : 212¶

In [11]:
# Variables
p_min = 20.;			#in kN
p_max = 50.;			#in kN
l = 500.;   			#in mm
d = 60.;	    		#in mm
a_u = 650.;		    	#in MPa
a_y = 520.;		    #in MPa
fos = 1.8;			    #factor of safety

# Calculations
m_max = p_max*l/4;			#maximum bending moment in kN mm
m_min = p_min*l/4;			#minimum bending moment in kN mm
m_m = (m_max+m_min)/2;			#mean bending moment in kN mm
m_a = (m_max-m_min)/2;			#alternating bending moment in kN mm
z = 3.14*d**3/32;
a_m = (m_m/z)*1000;			#mean bending stress in MPa
a_a = (m_a/z)*1000;			#alternating bending stress in MPa
a_e1 = a_a/((1/fos)-(a_m/a_u)**2*fos);			#in MPa
a_e2 = a_a/((1/fos)-(a_m/a_u));			#in MPa
a_e3 = a_a/((1/fos)-(a_m/a_y));			#in MPa

# Results
print "ENDURANCE STRESS FROM Gerbers Parabolic Function (in MPa)  =  %.2f MPa"%a_e1
print "ENDURANCE STRESS FROM Goodman Straight Line Relation (in MPa)  =  %.2f MPa"%a_e2
print "ENDURANCE STRESS FROM Soderberg Straight Line Relation (in MPa)  =  %.2f MPa"%a_e3

ENDURANCE STRESS FROM Gerbers Parabolic Function (in MPa)  =  236.52 MPa
ENDURANCE STRESS FROM Goodman Straight Line Relation (in MPa)  =  371.71 MPa
ENDURANCE STRESS FROM Soderberg Straight Line Relation (in MPa)  =  557.78 MPa