Strength Materials
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Transcript of Strength Materials
Stress
Stress is the ratio of applied force F and cross section A, defined as "force per area".
Direct Stress or Normal Stress
Stress normal to the plane is usually denoted "normal stress" and can be expressed as
σ = Fn / A (1)
where
σ = normal stress ((Pa) N/m2, psi)
Fn = normal component force (N, lbf (alt. kips))
A = area (m2, in2)
a kip is a non-SI unit of force - it equals 1,000 pounds-force 1 kip = 4448.2216 Newtons (N) = 4.4482216 kilonewtons (kN)
Example - Tensile Force acting on a Rod
A force of 10 kN is acting on a circular rod with diameter 10 mm. The stress in the rod can be calculated as
σ = 10 103 (N) / (π (10 10-3 (m) / 2)2)
= 127388535 (N/m2)
= 127 (MPa)
Shear Stress
Stress parallel to the plane is usually denoted "shear stress" and can be expressed as
τ = Fp / A (2)
where
τ = shear stress ((Pa) N/m2, psi)
Fp = parallel component force (N, lbf)
A = area (m2, in2)
Strain
Strain is defined as "deformation of a solid due to stress" and can be expressed as
ε = dl / lo = σ / E (3)
where
dl = change of length (m, in)
lo = initial length (m, in)
ε = unitless measure of engineering strain
E = Young's modulus (Modulus of Elasticity) (Pa, psi)
Example - Stress and Change of Length
The rod in the example above is 2 m long and made of steel with Modulus of Elasticity 200 GPa. The change of length can be calculated by transforming (3) as
dl = σ lo / E
= 127 106 (Pa) 2 (m) / 200 109 (Pa)
= 0.00127 (m)
= 1.27 (mm)
Young's Modulus - Modulus of Elasticity (or Tensile Modulus) - Hooke's Law
Most metals have deformations that are proportional with the imposed loads over a range of loads. Stress is proportional to load and strain is proportional to deformation expressed by the Hooke's law like
E = stress / strain = (Fn / A) / (dl / lo) (4)
where
E = Young's modulus (N/m2) (lb/in2, psi)
Modulus of Elasticity or Young's Modulus are commonly used for metals and metal alloys and expressed in terms 106 lbf/in2, N/m2 or Pa. Tensile modulus are often used for plastics and expressed in terms 105 lbf/in2 or GPa.
Shear Modulus
S = stress / strain = (Fp / A) / (s / d) (5)
where
S = shear modulus (N/m2) (lb/in2, psi)
Fp = force parallel to the faces which they act
A = area (m2, in2)
s = displacement of the faces (m, in)
d = distance between the faces displaced (m, in)
Elastic Moduli
Material
Young's Modulus Shear Modulus Bulk Modulus
1010 N/m2 106 lb/in2 1010 N/m2 106 lb/in2 1010 N/m2 106 lb/in2
Aluminum 7.0 10 2.4 3.4 7.0 10
Brass 9.1 13 3.6 5.1 6.1 8.5
Copper 11 16 4.2 6.0 14 20
Glass 5.5 7.8 2.3 3.3 3.7 5.2
Iron 9.1 13 7.0 10 10 14
Lead 1.6 2.3 0.56 0.8 0.77 1.1
Steel 20 29 8.4 12 16 23
Young Modulus:
It is convenient to express the elasticity of a material with the ratio stress to strain, a parameter also termed the tensile elastic modulus or Young's modulus of the material. This is usually given the symbol - E.
Modulus of Elasticity for some common metals at various temperatures according ASME B31.1-1995 are indicated below:
1 psi (lb/in2) = 1 psi (lb/in2) = 144 psf (lbf/ft2) = 6,894.8 Pa (N/m2) = 6.895x10-3 N/mm2
T(oC) = 5/9[T(oF) - 32]
Young's Modulus of Elasticity - E - (106 psi)
Metal
Temperature (oC)
-200
-129
-73 21 93 149 204 260 316 371 427 482 538 593 649
Temperature (oF)
-325
-200
-100
70 200 300 400 500 600 700 800 900100
0110
0120
0
Cast iron
Gray cast iron
13.4
13.2
12.9
12.6
12.2
11.7
11.0
10.2
Steel
Carbon steel C
<= 0.3%
31.4
30.8
30.2
29.5
28.8
28.3
27.7
27.3
26.7
25.5
24.2
22.4
20.4 18.0
Carbon steel C
=> 0.3%
31.2
30.6
30.0
29.3
28.6
28.1
27.5
27.1
26.5
25.3
24.0
22.2
20.2 17.9 15.4
Carbon-moly steels
31.1
30.5
29.9
29.2
28.5
28.0
27.4
27.0
26.4
25.3
23.9
22.2
20.1 17.8 15.3
Nickel steels Ni 2% - 9%
29.6
29.1
28.5
27.8
27.1
26.7
26.1
25.7
25.2
24.6
23.0
Cr-Mo steels Cr 1/2% -
2%
31.6
31.0
30.4
29.7
29.0
28.5
27.9
27.5
26.9
26.3
25.5
24.8
23.9 23.0 21.8
Young's Modulus of Elasticity - E - (106 psi)
Metal
Temperature (oC)
-200
-129
-73 21 93 149 204 260 316 371 427 482 538 593 649
Temperature (oF)
-325
-200
-100
70 200 300 400 500 600 700 800 900100
0110
0120
0
Cr-Mo steels Cr 2 1/4% -
3%
32.6
32.0
31.4
30.6
29.8
29.4
28.8
28.3
27.7
27.1
26.3
25.6
24.6 23.7 22.5
Cr-Mo steels Cr 5% - 9%
32.9
32.3
31.7
30.9
30.1
29.7
29.0
28.6
28.0
27.3
26.1
24.7
22.7 20.4 18.2
Chromium steels Cr 12%,
17%, 27%
31.2
30.7
30.1
29.2
28.5
27.9
27.3
26.7
26.1
25.6
24.7
23.2
21.5 19.1 16.6
Austenitic steels
(TP304, 310, 316, 321, 347)
30.3
29.7
29.1
28.3
27.6
27.0
26.5
25.8
25.3
24.8
24.1
23.5
22.8 22.1 21.2
Copper and copper alloys
Comp. and
leaded-Sn
bronze (C83600,
14.8
14.6
14.4
14.0
13.7
13.4
13.2
12.9
12.5
12.0
Young's Modulus of Elasticity - E - (106 psi)
Metal
Temperature (oC)
-200
-129
-73 21 93 149 204 260 316 371 427 482 538 593 649
Temperature (oF)
-325
-200
-100
70 200 300 400 500 600 700 800 900100
0110
0120
0
C92200)
Naval brass Si
& Al bronze
(C46400, C65500, C95200, C95400)
15.9
15.6
15.4
15.0
14.6
14.4
14.1
13.8
13.4
12.8
Copper (C11000)
16.9
16.6
16.5
16.0
15.6
15.4
15.0
14.7
14.2
13.7
Copper red brass Al-bronze (C10200, C12000, C12200, C12500, C14200, C23000, C61400)
18.0
17.7
17.5
17.0
16.6
16.3
16.0
15.6
15.1
14.5
Nickel and Nickel Alloys
Young's Modulus of Elasticity - E - (106 psi)
Metal
Temperature (oC)
-200
-129
-73 21 93 149 204 260 316 371 427 482 538 593 649
Temperature (oF)
-325
-200
-100
70 200 300 400 500 600 700 800 900100
0110
0120
0
Monel 400
(N04400)
27.8
27.3
26.8
26.0
25.4
25.0
24.7
24.3
24.1
23.7
23.1
22.6
22.1 21.7 21.2
Titanium
Unalloyed titanium grades 1, 2, 3 and
7
15.5
15.0
14.6
14.0
13.3
12.6
11.9
11.2
Aluminum and aluminum alloys
Grades 443,
1060, 1100, 3003, 3004, 6063
11.1
10.8
10.5
10.0
9.6 9.2 8.7
1 psi (lb/in2) = 6,894.8 N/m2 (Pa) T(oC) = 5/9[T(oF) - 32]
Strength:
To describe elastic properties of linear objects like wires, rods, or columns which are stretched or compressed, a convenient parameter is the ratio of the stress to the strain, a parameter called the "Young's modulus" or "Modulus of Elasticity" of the material. Young's modulus can be used to predict the elongation or compression of an object as long as the stress is less than the yield strength of the material.
Material
Young's Modulus (Modulus of Elasticity)
- E -
Ultimate Tensile
Strength- Su -
(106 N/m2, MPa)
Yield Strength
- Sy -(106 N/m2,
MPa)(106 psi)(109 N/m2,
GPa)
ABS plastics 2.3 40
Acrylic 3.2 70
Aluminum 10.0 69 110 95
Aluminium Bronze 120
Antimony 11.3
Aramid 70 - 112
Beryllium (Be) 42 287
Material
Young's Modulus (Modulus of Elasticity)
- E -
Ultimate Tensile
Strength- Su -
(106 N/m2, MPa)
Yield Strength
- Sy -(106 N/m2,
MPa)(106 psi)(109 N/m2,
GPa)
Bismuth 4.6
Bone 9170
(compression)
Boron 3100
Brass 102 - 125 250
Brass, Naval 100
Bronze 96 - 120
Cadmium 4.6
Carbon Fiber Reinforced Plastic 150
Cast Iron 4.5% C, ASTM A-48 170
Chromium 36
Cobalt 30
Concrete, High Strength (compression)
3040
(compression)
Copper 17 117 220 70
Material
Young's Modulus (Modulus of Elasticity)
- E -
Ultimate Tensile
Strength- Su -
(106 N/m2, MPa)
Yield Strength
- Sy -(106 N/m2,
MPa)(106 psi)(109 N/m2,
GPa)
Diamond (C) 1220
Douglas fir Wood 1350
(compression)
Fiberboard, Medium Density 4
Flax fiber 58
Glass 50 - 9050
(compression)
Glass reinforced polyester matrix
17
Graphene 1000
Grey Cast Iron 130
Gold 10.8
Hemp fiber 35
Iridium 75
Iron 28.5
Material
Young's Modulus (Modulus of Elasticity)
- E -
Ultimate Tensile
Strength- Su -
(106 N/m2, MPa)
Yield Strength
- Sy -(106 N/m2,
MPa)(106 psi)(109 N/m2,
GPa)
Lead 2.0
Magnesium metal (Mg) 6.4 45
Manganese 23
Marble 15
Mercury
Molybdenum (Mo) 40 329
Nickel 31
Niobium (Columbium) 15
Nylon 2 - 4 75 45
Oak Wood (along grain) 11
Osmium (Os) 80 550
Phosphor Bronze 116
Pine Wood (along grain) 9 40
Platinum 21.3
Plutonium 14
Material
Young's Modulus (Modulus of Elasticity)
- E -
Ultimate Tensile
Strength- Su -
(106 N/m2, MPa)
Yield Strength
- Sy -(106 N/m2,
MPa)(106 psi)(109 N/m2,
GPa)
Polycarbonate 2.6 70
Polyethylene HDPE (high density)
0.8 15
Polytehylene, LDPE (low density)
0.238
Polyethylene Terephthalate, PET
2 - 2.7 55
Polyimide 2.5 85
Polypropylene 1.5 - 2 40
Polystyrene 3 - 3.5 40
Potassium
Rhodium 42
Rubber 0.01 - 0.1
Selenium 8.4
Silicon 16 130 - 185
Silicon Carbide 450 3440
Silver 10.5
Material
Young's Modulus (Modulus of Elasticity)
- E -
Ultimate Tensile
Strength- Su -
(106 N/m2, MPa)
Yield Strength
- Sy -(106 N/m2,
MPa)(106 psi)(109 N/m2,
GPa)
Sodium
Stainless Steel, AISI 302 180 860 502
Steel, Structural ASTM-A36 200 400 250
Steel, High Strength Alloy ASTM A-514
760 690
Tantalum 27
Teflon. PTFE 0.5
Thorium 8.5
Titanium 16
Titanium Alloy 105 - 120 900 730
Tungsten (W) 400 - 410
Tungsten Carbide (WC) 450 - 650
Uranium 24
Vanadium 19
Wrought Iron 190 - 210
Material
Young's Modulus (Modulus of Elasticity)
- E -
Ultimate Tensile
Strength- Su -
(106 N/m2, MPa)
Yield Strength
- Sy -(106 N/m2,
MPa)(106 psi)(109 N/m2,
GPa)
Zinc 12
1 N/m2 = 1x10-6 N/mm2 = 1 Pa = 1.4504x10-4 psi 1 psi (lb/in2) = 144 psf (lbf/ft2) = 6,894.8 Pa (N/m2) = 6.895x10-3 N/mm2
Note! Use the pressure unit converter on this page to switch the values to other units.
Strain
Strain can be expressed as
strain = dL / L (1)
where
strain = (m/m) (in/in)
dL = elongation or compression (offset) of the object (m) (in)
L = length of the object (m) (in)
Stress
Stress can be expressed as
stress = F / A (2)
where
stress = (N/m2) (lb/in2, psi)
F = force (N) (lb)
A = area of object (m2) (in2)
Young's Modulus (Tensile Modulus)
Young's modulus or Tensile modulus can be expressed as
E = stress / strain = (F / A) / (dL / L) (3)
where
E = Young's modulus (N/m2) (lb/in2, psi)
Elasticity
Elasticity is a property of an object or material which will restore it to its original shape after distortion.
A spring is an example of an elastic object - when stretched, it exerts a restoring force which tends to bring it back to its original length. This restoring force is in general proportional to the stretch described by Hooke's Law.
Hooke's Law
One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon stretching force is called Hooke's law which can be expressed as
Fs = -k dL (4)
where
Fs = force in the spring (N)
k = spring constant (N/m)
dL = elongation of the spring (m)
Yield strength
Yield strength, or the yield point, is defined in engineering as the amount of stress that a material can undergo before moving from elastic deformation into plastic deformation.
Ultimate Tensile Strength
The Ultimate Tensile Strength - UTS - of a material is the limit stress at which the material actually breaks, with sudden release of the stored elastic energy.