MultiPhysicsVault/.raw/AFirstCourseInTheFiniteElementMethod/AFirstCourseInTheFiniteElementMethod_084.md

CONVERSION FACTORS U.S. Customary Units to SI Units

Quantity Converted from U.S. Customary	To	SI Equivalent
(Acceleration)
1 foot/second $^{2}$ (ft/s $^{2}$ )	meter/second $^{2}$ (m/s $^{2}$ )	0.3048 m/s $^{2}$
1 inch/second $^{2}$ (in./s $^{2}$ )	meter/second $^{2}$ (m/s $^{2}$ )	0.0254 m/s $^{2}$
(Area)
1 foot $^{2}$ (ft $^{2}$ )	meter $^{2}$ (m $^{2}$ )	0.0929 m $^{2}$
1 inch $^{2}$ (in. $^{2}$ )	meter $^{2}$ (m $^{2}$ )	645.2 mm $^{2}$
(Density, mass)
1 pound mass/inch $^{3}$ (lbm/in. $^{3}$ )	kilogram/meter $^{3}$ (kg/m $^{3}$ )	27.68 Mg/m $^{3}$
1 pound mass/foot $^{3}$ (lbm/ft $^{3}$ )	kilogram/meter $^{3}$ (kg/m $^{3}$ )	16.02 kg/m $^{3}$
(Energy, Work)
1 British thermal unit (BTU)	Joule (J)	1055 J
1 foot-pound force (ft-lb)	Joule (J)	1.356 J
1 kilowatt-hour	Joule (J)	3.60 × 10 $^{6}$ J
(Force)
1 kip (1000 lb)	Newton (N)	4.448 kN
1 pound force (lb)	Newton (N)	4.448 N
(Length)
1 foot (ft)	meter (m)	0.3048 m
1 inch (in.)	meter (m)	25.4 mm
1 mile (mi), (U.S. statute)	meter (m)	1.609 km
1 mile (mi), (international nautical)	meter (m)	1.852 km
(Mass)
1 pound mass (lbm)	kilogram (kg)	0.4536 kg
1 slug (lb-sec $^{2}$ /ft)	kilogram (kg)	14.59 kg
1 metric ton (2000 lbm)	kilogram (kg)	907.2 kg
(Moment of force)
1 pound-foot (lb·ft)	Newton-meter (N·m)	1.356 N·m
1 pound-inch (lb·in.)	Newton-meter (N·m)	0.1130 N·m
(Moment of inertia of an area)
1 inch $^{4}$	meter $^{4}$ (m $^{4}$ )	0.4162 × 10 $^{-6}$ m $^{4}$
(Moment of inertia of a mass)
1 pound-foot-second $^{2}$ (lb·ft·s $^{2}$ )	kilogram-meter $^{2}$ (kg·m $^{2}$ )	1.356 kg·m $^{2}$
(Momentum, linear)
1 pound-second (lb·s)	kilogram-meter/second (kg·m/s)	4.448 N·s
(Momentum, angular)
pound-foot-second (lb·ft·s)	Newton-meter-second (N·m·s)	1.356 N·m·s

CONVERSION FACTORS U.S. Customary Units to SI Units (Continued )

Quantity Converted from U.S. Customary	To	SI Equivalent
(Power)
1 foot-pound/second (ft·lb/s)	Watt (W)	1.356 W
1 horsepower (550 ft·lb/s)	Watt (W)	745.7 W
(Pressure, stress)
1 atmosphere (std)(14.7.lb/in.2)	Newton/meter2 (N/m2 or Pa)	101.3 kPa
1 pound/foot2 (lb/ft2)	Newton/meter2 (N/m2 or Pa)	47.88 Pa
1 pound/inch2 (lb/in.2 or psi)	Newton/meter2 (N/m2 or Pa)	6.895 kPa
1 kip/inch2 (ksi)	Newton/meter2 (N/m2 or Pa)	6.895 MPa
(Spring constant)
1 pound/inch (lb/in.)	Newton/meter (N/m)	175.1 N/m
(Temperature)
T(°F) = 1.8T(°C) + 32
(Velocity)
1 foot/second (ft/s)	meter/second (m/s)	0.3048 m/s
1 knot (nautical mi/h)	meter/second (m/s)	0.5144 m/s
1 mile/hour (mi/h)	meter/second (m/s)	0.4470 m/s
1 mile/hour (mi/h)	kilometer/hour (km/h)	1.609 km/h
(Volume)
1 foot3 (ft3)	meter3 (m3)	0.02832 m3
1 inch3 (in.3)	meter3 (m3)	16.39 × 10-6m3

Rectangle		Triangle
	A=bh	[A=1/2bh]	[A=1/2bh]
	Ix=bh3/12		Ix=bh3/36
	Ix=bh3/3		Ix=bh3/12
Circle		Semicircle
	A=πr2	[A=πr2/2]	[A=πr2/2]
	Ix=πr4/4		Ix=0.035πr4
	Jc=πr4/2		Jo=πr4/4
	Ix=5πr4/4		Iy=Ix=πr4/8
Thin Ring		Half of Thin Ring
	A=2πrave t	[A=πrt]	[A=πrt]
	Ix=πrave3t		Ix≈0.095πr3t
	Jc=2πrave3t		Iy=0.5πr3t
Quarter Ellipse
Ellipse
	A=πab	[A=πab/4]	[A=πab/4]
	Ix=πab3/4		Ix=0.0175πab3
	Jc=πab(a2+b2)/4		Ix=πab3/16
			Iy=πa3b/16
Quadrant of Parabola		Parabolic Spandrel
	A=2/3bh	[A=bh/3]	[A=bh/3]
	Ix=0.04bh3		Ix=0.0176bh3
	Ix=2bh3/15		Ix=bh3/21
	Iy=2hb3/7		Iy=hb3/5

1. Slender Rod

text_image

y z L d x

m = \frac {\pi d ^ {2} L \rho}{4}

I _ {y} = I _ {z} = \frac {m L ^ {2}}{1 2}

2. Thin Disk

text_image

t y d x z

m = \frac {\pi d ^ {2} t \rho}{4}

I _ {x} = \frac {m d ^ {2}}{8}

I _ {y} = I _ {z} = \frac {m d ^ {2}}{1 6}

3. Rectangular Prism

text_image

y b c a x z

m = a b c \rho

I _ {x} = \frac {m}{1 2} (a ^ {2} + b ^ {2})

I _ {y} = \frac {m}{1 2} \left(a ^ {2} + c ^ {2}\right)

I _ {z} = \frac {m}{1 2} (b ^ {2} + c ^ {2})

4. Circular Cylinder

text_image

y d L z x

m = \frac {\pi d ^ {2} L \rho}{4}

I _ {x} = \frac {m d ^ {2}}{8}

I _ {y} = I _ {z} = \frac {m}{4 8} (3 d ^ {2} + 4 L ^ {2})

5. Hollow Cylinder

text_image

y di do z L x

m = \frac {\pi L \rho}{4} (d _ {o} ^ {2} - d _ {i} ^ {2})

I _ {x} = \frac {m}{8} (d _ {o} ^ {2} + d _ {i} ^ {2})

I _ {y} = I _ {z} = \frac {m}{4 8} \left(3 d _ {o} ^ {2} + 3 d _ {i} ^ {2} + 4 L ^ {2}\right)

PHYSICAL PROPERTIES IN SI AND USCS UNITS

Property	Sl	USCS
Water (fresh)
specific weight	$9.81 \text{ kN/m}^{3}$	$62.4 \text{ lb/ft}^{3}$
mass density	$1000 \text{ kg/m}^{3}$	$1.94 \text{ slugs/ft}^{3}$
Aluminum
specific weight	$26.6 \text{ kN/m}^{3}$	$169/\text{lb/ft}^{3}$
mass density	$2710 \text{ kg/m}^{3}$	$5.26 \text{ slugs/ft}^{3}$
Steel
specific weight	$77.0 \text{ kN/m}^{3}$	$490 \text{ lb/ft}^{3}$
mass density	$7850 \text{ kg/m}^{3}$	$15.2 \text{ slugs/ft}^{3}$
Reinforced concrete
specific weight	$23.6 \text{ kN/m}^{3}$	$150 \text{ lb/ft}^{3}$
mass density	$2400 \text{ kg/m}^{3}$	$4.66 \text{ slugs/ft}^{3}$
Acceleration of gravity(on the earth’s surface)
Recommended value	$9.81 \text{ m/s}^{2}$	$32.2 \text{ ft/s}^{2}$
Atmospheric pressure(at sea level)
Recommended value	$101 \text{ kPa}$	$14.7 \text{ psi}$

TYPICAL PROPERTIES OF SELECTED ENGINEERING MATERIALS

Material	Ultimate Strength $\sigma_u$		0.2% Yield Strength $\sigma_y$		Modulus of Elasticity E(106 psi GPa)		Sheer Modulus G(106 psi)	Coefficient of Thermal Expansion, $\alpha$		Density, $\rho$
	ksi	MPa	ksi	MPa				10-6/°F	10-6/°C	lb/in. $^3$	kg/m $^3$
Aluminum
Alloy 1100-H14(99 % A1)	14	110(T)	14	95	10.1	70	3.7	13.1	23.6	0.098	2710
Alloy 2024-T3(sheet and plate)	70	480(T)	50	340	10.6	73	4.0	12.6	22.7	0.100	2763
Alloy 6061-T6(extruded)	42	260(T)	37	255	10.0	69	3.7	13.1	23.6	0.098	2710
Alloy 7075-T6(sheet and plate)	80	550(T)	70	480	10.4	72	3.9	12.9	23.2	0.101	2795
Yellow brass (65% Cu, 35% Zn)
Cold-rolled	78	540(T)	63	435	15	105	5.6	11.3	20.0	0.306	8470
Annealed	48	330(T)	15	105	15	105	5.6	11.3	20.0	0.306	8470
Phosphor bronze
Cold-rolled (510)	81	560(T)	75	520	15.9	110	5.9	9.9	17.8	0.320	8860
Spring-tempered(524)	122	840(T)	—	—	16	110	5.9	10.2	18.4	0.317	8780
Cast iron
Gray, 4.5%C, ASTM A-48	25	170(T)	—	—	10	70	4.1	6.7	12.1	0.260	7200
	95	650(C)
Malleable, ASTM A-47	50	340(T)	33	230	24	165	9.3	6.7	12.1	0.264	7300
	90	620(C)	—	—

TYPICAL PROPERTIES OF SELECTED ENGINEERING MATERIALS (Continued )

Material	Ultimate Strength $\sigma_u$		0.2% Yield Strength $\sigma_y$		Modulus of Elasticity E( $10^6$ psi GPa)		Sheer Modulus G( $10^6$ psi)	Coefficient of Thermal Expansion, $\alpha$		Density, $\rho$
	ksi	MPa	ksi	MPa				$10^{-6}/^{\circ}\text{F}$	$10^{-6}/^{\circ}\text{C}$	$\text{lb/in.}^3$	$\text{kg/m}^3$
Copper and its alloys
CDA 145 copper, hard	48	331(T)	44	303	16	110	6.1	9.9	17.8	0.323	8940
CDA 172 beryllium copper, hard	175	1210(T)	240	965	19	131	7.1	9.4	17.0	0.298	8250
CDA 220 bronze, hard	61	421(T)	54	372	17	117	6.4	10.2	18.4	0.318	8800
CDA 260 brass, hard	76	524(T)	63	434	16	110	6.1	11.1	20.0	0.308	8530
Magnesium alloy (8.5% A1)	55	380(T)	40	275	4.5	45	2.4	14.5	26.0	0.065	1800
Monel alloy 400 (Ni-Cu)
Cold-worked	98	675(T)	85	580	26	180	—	7.7	13.9	0.319	8830
Annealed	80	550(T)	32	220	26	180	—	7.7	13.9	0.319	8830
Steel
Structural (ASTM-A36)	58	400(T)	36	250	29	200	11.5	6.5	11.7	0.284	7860
High-strength low-alloy
ASTM-A242	70	480(T)	50	345	29	200	11.5	6.5	11.7	0.284	7860
Quenched and tempered alloy
ASTM-A514	120	825(T)	100	690	29	200	11.5	6.5	11.7	0.284	7860
Stainless, (302)
Cold-rolled	125	860(T)	75	520	28	190	10.6	9.6	17.3	0.286	7920
Annealed	90	620(T)	40	275	28	190	10.6	9.6	17.3	0.286	7920
Titanium alloy (6% A1, 4% V)	130	900(T)	120	825	16.5	114	6.2	5.3	9.5	0.161	4460
Concrete
Medium strength	4.0	28(C)	—	—	3.5	25	—	5.5	10.0	0.084	2320
High strength	6.0	40(C)	—	—	4.5	30	—	5.5	10.0	0.084	2320
Granite	35	240(C)	—	—	10	69	—	4.0	7.0	0.100	2770
Glass, 98% silica	7	50(C)	—	—	10	69	—	44.0	80.0	0.079	2190
Melamine	6	41(T)	—	—	2.0	13.4	—	17.0	30.0	0.042	1162
Nylon, molded	8	55(T)	—	—	0.3	2	—	45.0	81.0	0.040	1100
Polystyrene	7	48(T)	—	—	0.45	3	—	40.0	72.0	0.038	1050
Rubbers
Natural	2	14(T)	—	—	—	—	—	90.0	162.0	0.033	910
Neoprene	3.5	24(T)	—	—	—	—	—			0.045	1250
Timber, air dry, parallel to grain
Douglas fir, construction
grade	7.2	50(C)	—	—	1.5	10.5	—	varies	varies	0.019	525
Eastern spruce	5.4	37(C)	—	—	1.3	9	—	1.7-	3-	0.016	440
Southern pine,construction
grade	7.3	50(C)	—	—	1.2	8.3	—	3.0	5.4	0.022	610

The values given in the table are average mechanical properties. Further verification may be necessary for final design or analysis. For ductile materials, the compressive strength is normally assumed to equal the tensile strength. Abbreviations: C, compressive strength; T, tensile strength. For an explanation of the numbers associated with the aluminums, cast irons, and steels, see ASM Metals Reference Book, latest ed., American Society for Metals, Metals Park, Ohio 44073