Transportation Curriculum Coordination Council

Appendix B

Inspector Math tip sheets

VOLUME OF A SHAFT
EQUATION	EXAMPLE
VOLUME OF A BELL
EQUATION	EXAMPLE
VOLUME OF A TOE OF BELL
EQUATION	EXAMPLE

CIRCUMFERENCES

SI Conversion Factors

APPROXIMATE CONVERSIONS FROM SI UNIT
Symbol	When You Know	Multiply By	To Find	Symbol
LENGTH
mm	millimeters	0.039	inches	in
m	meters	3.28	feet	ft
m	meters	1.09	yards	yd
km	kilometers	0.621	miles	mi
AREA
mm^2	square millimeters	0.0016	square inches	in^2
m^2	square meters	10.764	square feet	ft^2
ha	hectares	2.47	acres	ac
km^2	square kilometers	0.386	square miles	mi^2
VOLUME
ml	milliliters	0.034	fluid ounces	fl oz
l	liters	0.264	gallons	gal
m^3	cubic meters	35.71	cubic feet	ft^3
m^3	cubic meters	1.307	cubic yards	yd^3
MASS
g	grams	0.035	ounces	oz
kg	kilograms	2.205	pounds	lb
TEMPERATURE
°C	Celsius	1.8 C + 32	Fahrenheit	°F
WEIGHT DENSITY
g/cc	grams per cubic centimeter	62.4	poundforce/cubic foot	pcf
kN/m^3	kilonewton/cubic meter	6.36	poundforce/cubic foot	pcf
FORCE and LOAD
N	newtons	0.225	poundforce	lb
kN	kilonewtons	225	poundforce	lb
kg	kilogram (force)	2.205	poundforce	lb
MN	meganewtons	112.4	tons (force)	t
PRESSURE and STRESS*
kPa*	kilopascals	0.145	poundforce/square inch	psi
kPa	kilopascals	20.9	poundforce/square inch	psi
MPa	megapascals	10.44	tons per square foot	tsf
kg/cm^2	kilograms per square cm	1.024	tons per square foot	tsf

Notes: 1 kPa = kN/m² = one kilopascal = one kilonewton per square meter
For dimensionless graphics and equations, a reference stress of one atmosphere can be used, such that σ_a = ρ_atm = 1 bar = 100 kPa = 1tsf = 1 kpg/cm²

Shaft Areas and Volumes

Per Linear Foot
Shaft Diameter (in)	Volume (yd^3)	Side Shear Area (ft^2)	Bearing Area (ft^2)
12	0.03	3.14	0.79
14	0.04	3.67	1.07
16	0.05	4.19	1.40
18	0.07	4.71	1.77
20	0.08	5.24	2.18
22	0.10	5.76	2.64
24	0.12	6.28	3.14
26	0.14	6.81	3.69
28	0.16	7.33	4.28
30	0.18	7.85	4.91
32	0.21	8.38	5.59
34	0.23	8.90	6.31
36	0.26	9.42	7.07
38	0.29	9.95	7.88
40	0.32	10.47	8.773
42	0.36	11.00	9.62
44	0.39	11.52	10.65
46	0.43	12.04	11.54
48	0.47	12.57	12.57
50	0.51	13.09	13.64
52	0.55	13.61	14.75
54	0.59	14.14	15.90
56	0.63	14.66	17.10
58	0.68	15.18	18.35
60	0.73	15.71	19.63
62	0.78	16.23	20.97
64	0.83	16.76	22.34
66	0.88	17.28	23.76
68	0.93	17.80	25.22
70	0.99	18.33	26.73
72	1.05	18.85	28.27
74	1.11	19.37	29.87
76	1.17	19.90	31.50
78	1.23	20.42	33.18
84	1.43	21.99	38.48
90	1.64	23.56	44.18
96	1.86	25.13	50.27
102	2.10	26.70	56.75
108	2.36	28.27	63.62
114	2.63	29.85	70.88
120	2.91	31.42	78.54
126	3.21	32.99	86.59
132	3.52	34.56	95.03

Shaft Areas and Volumes

Per Linear Meter
Shaft Diameter (cm)	Volume (m^3)	Side Shear Area (m^2)	Bearing Area (m^2)
30	0.07	0.94	0.07
35	0.10	1.10	0.10
40	0.13	1.26	0.13
45	0.16	1.41	0.16
50	0.20	1.57	0.20
55	0.24	1.73	0.24
60	0.28	1.88	0.28
65	0.33	2.04	0.33
70	0.38	2.20	0.38
75	0.44	2.36	0.44
80	0.50	2.51	0.50
85	0.57	2.67	0.57
90	0.64	2.83	0.64
95	0.71	2.98	0.71
100	0.79	3.14	0.79
105	0.87	3.30	0.87
110	0.95	3.46	0.95
115	1.04	3.61	1.04
120	1.13	3.77	1.13
125	1.23	3.93	1.23
130	1.33	4.08	1.33
135	1.43	4.24	1.43
140	1.54	4.40	1.54
145	1.65	4.56	1.65
150	1.77	4.71	1.77
155	1.89	4.87	1.89
160	2.01	5.03	2.01
165	2.14	5.18	2.14
170	2.27	5.34	2.27
175	2.41	5.50	2.41
180	2.54	5.65	2.54
185	2.69	5.81	2.69
190	2.84	5.97	2.84
195	2.99	6.13	2.99
210	3.46	6.60	3.46
225	3.98	7.07	3.98
240	4.52	7.54	4.52
255	5.11	8.01	5.11
270	5.73	8.48	5.73
285	6.38	8.95	6.38
300	7.07	9.42	7.07
315	7.79	9.90	7.79
330	8.55	10.37	8.55

Previous

Table of Contents