materials - 37.1

37. ATOMIC MATERIAL DATA

Element	Atomic #	Atomic weight density g/cm3		Valances H
copper	29	63.57	8.96	w
				1/2
iron	26	55.85	7.86	2/3
aluminum	13	26.97	2.67	3
tungsten	74	183.85	19.3	6/8
zinc	30	65.37	7.13	2
silicon	14	28.09	2.33	4
carbon	6	12.01	2.1	2/4
titanium	22	47.9	4.51	3/4

F = 96,500 coulombs

37. MECHANICAL MATERIAL PROPERTIES

Table 1:

Material	Type	Density	E	G	poisson	ten - yield stress	ten - ult. stress	ten - yield strain	yield stress - comp.	ult. stress - comp.	ult. stress - shear	thermal expansion
		(Mg/m3)	(GPa)	(GPa)		(MPa)		(%)	(MPa)			10-6/deg C
aluminum	typical	2.6-2.8	70-79	26-30	0.33	35-500	100-550	1-45				23
	1100-h14
	2024-T6
	5456-h116
	2014-T6	2.8	73	36-41	0.33	410	480	13
	6061-T6	2.8	70	26	0.33	270	310	17
	7075-T6	2.7	72	26	0.33	480	550	11

materials - 37.2

Table 1:

Material	Type	Density	E	G	poisson	ten - yield stress	ten - ult. stress	ten - yield strain	yield stress - comp.	ult. stress - comp.	ult. stress - shear	thermal expansion
		(Mg/m3)	(GPa)	(GPa)		(MPa)		(%)	(MPa)			10-6/deg C
Brass	typical	8.4-8.6	96-110	36-41	0.34	70-550	200-620	4-60				19.1-
												21.2
Yellow Brass
	cold rolled
	annealed
Red Brass
	cold rolled
	annealed
Bronze	typical	8.2-8.8	96-120	36-44	0.34	82-690	200-830	5-60				18-21
Cast Iron	typical	7.0-7.4	83-170	32-69	0.2-0.3	120	69-480	0-1		340-		9.9-12
										1400
Concrete	typical	2.3	17-31	na	0.1-0.2					10-70		7-14
	reinforced	2.4	17-31	na	0.1-0.2
	lightweight	1.1-1.8	17-31	na	0.1-0.2
Copper	typical	8.9	110-120	40-47	0.33-	55-760	230-830	4-50				16.6-
					0.36							17.6
	annealed
	hard drawn
Glass	typical	2.4-2.8	48-83	19-35	0.17-		30-1000	0				5-11
					0.27
	Plate						70
	Fibers						7000-
							20000
Magnesium	typ. alloys	1.76-	41-45	15-17	0.35	80-280	140-340	2-20				26.1-
		1.83										28.8
Monel	67%Ni,30%	8.8	170	66	0.32	170-	450-	2-50				14
	Cu					1100	1200
Nickel		8.8	210	80	0.31	100-620	310-760	2-50				13

materials - 37.3

Table 1:

Material	Type	Density	E	G	poisson	ten - yield stress	ten - ult. stress	ten - yield strain	yield stress - comp.	ult. stress - comp.	ult. stress - shear	thermal expansion
		(Mg/m3)	(GPa)	(GPa)		(MPa)		(%)	(MPa)			10-6/deg C
Plastics
	Nylon	.88-1.1	2.1-3.4	na	0.4		40-80	20-100				70-140
	Polyethylene	.96-1.4	0.7-1.4	na	0.4		7-28	15-300				140-290
Rock												5-9
	Granite	2.6-2.9	40-100	na	0.2-0.3					50-
										280
	Marble	2.6-2.9	40-100	na	0.2-0.3					50-
										280
	Quartz	2.6-2.9	40-100	na	0.2-0.3					50-
										280
	Limestone	2.0-2.9	20-70	na	0.2-0.3					20-
										200
	Sandstone	2.0-2.9	20-70	na	0.2-0.3					20-
										200
Rubber	typical	.96-1.3	0.0007-	0.0002-	0.45-	1-7	7-20	100-800				130-200
			0.004	0.001	0.50
Sand,soil,gra		1.2-2.2
vel
Steel		7.85	190-210	75-80	0.27-							10-18
					0.30
	cold rolled
	annealed
	high strength					340-	550-	5-25				14
						1000	1200
	machine					340-700	550-860	5-25
	spring					400-	700-	3-15
						1600	1900
	stainless					280-700	400-	5-40
							1000
	tool					520	900	8
	structural					200-700	340-830	10-40				12
	astm-a48

materials - 37.4

Table 1:

Material	Type	Density	E	G	poisson	ten - yield stress	ten - ult. stress	ten - yield strain	yield stress - comp.	ult. stress - comp.	ult. stress - shear	thermal expansion
		(Mg/m3)	(GPa)	(GPa)		(MPa)		(%)	(MPa)			10-6/deg C
	astm-a47
	astm-a36					250	400	30				12
	astm-a5242
	astm-a441
	astm-a572					340	500	20				12
	astm-a514					700	830	15				12
	wire					280-	550-	5-40
						1000	1400
Stainless	aisi 302											17
Steel
Titanium	typ. alloys	4.5	100-120	39-44	0.33	760-	900-	10				8.1-11
						1000	1200
Tungsten		1.9	340-380	140-160	0.2		1400-	0-4				4.3
							4000
Water	fresh	1.0
	sea	1.02
Wood (dry)
	Douglas fir	.48-.56	11-13			30-50	50-80		30-50	40-70
	Oak	.64-.72	11-12			40-60	50-100		30-40	30-50
	Southern	.56-.64	11-14			40-60	50-100		30-50	40-70
	pine

37.1FORMULA SHEET

•A collection of the essential mechanics of materials formulas are given below

materials - 37.5

Axial/Normal Stress/Strain	σ	= ε E =	P	δ	= ε L =	PL
			--			------
			A			AE

Shear Stress/Strain	τ = γ G	γxy =	τ xy
			------
			G

Poisson’s ratio	ν			εlateral	E = 2G( 1 + ν )
			---------------------------
		= –ε
			longitudinal
	εx		σ x	σ y	σ z
		=	-----	-----	----
			E	– ν E – ν	E

Torsion				Tc			γ		=	τ max
	τ max		=	-----						----------
				J			max			G
			TL				J	=	π	r4	(cylinder)
	φ =		------						-------
			JG							2
	σ		=	–σ		= τ	J	=	π	4	4
		ten			comp				--	( ro	– ri ) (hollow tube)
									2
		ε =	γ				P =		2π fT
			--
			2

Beams

Buckling

materials - 37.6

σMy

=–-------

I

τVQ

=-------

Ib

L = ρθ

σMy

=–-------

I

<π 2EI P -----------

k2L2

	I	=	bh3	(for rectangle)
			--------
			12
	I	=	π r4	(for circle)
			-------
			2
ε	=	c
		--
max		ρ

ρEI

=-----

M

k=0.5 (both ends fixed)

k=0.7 (one end fixed, one pinned) k=1.0 (both ends pinned)

k=2.0 (one end pinned, one free)

K					d/2			r
3.0			P						P
2.5					d/2
2.0
1.5									r/d
0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0

				materials - 37.7
K						r
2.5
			P		D			d
									P
2.0
1.5				D/d = 2.0
				D/d = 1.5
					D/d = 1.25
					D/d = 1.1
1.0									r/d
0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0

			materials - 37.8
K
			T			r			T
					D			d
2.5
2.0
1.5									D/d = 2.0
									D/d = 1.33
									D/d = 1.2
1.0									D/d = 1.1
									r/d
0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09	0.1