It is defined as the ability of a material to resist deformation under stress. The resistance of a material to elastic deformation or deflection is called stiffness or rigidity.

Stiffness relates to how a component bends under load while still returning to its original shape once the load is removed. Since the component dimensions are unchanged after load is removed, stiffness is associated with elastic deformation.

A material can have high strength and low stiffness. If a metal cracks easily, it has low strength, but if it has low stiffness, it can deflect a high load.  The article  explains that stiffness depends on the modulus of elasticity, also known as Young’s Modulus, which is constant for a given metal. Because Young’s Modulus for steel is three times that of aluminum, an aluminum part under load will deflect three times as much as a similarly loaded steel part. The thickness and shape of the formed part also contributes to its stiffness.

All steel has approximately the same stiffness, but comes in many different strengths depending on the alloying metals used.  Stainless steel comes in more than 100 grades which are created by adding alloys such as chromium, silicon, nickel, carbon, nitrogen, and manganese to impart properties such as heat resistance, strength, flexibility, and ductility. Martensitic or semi-austenitic steels are the strongest due to the addition of elements such as aluminum, copper and niobium.

Steel starts out as flat sheet metal or plates and must be manufactured to precise thickness specifications depending on the application for which it is used. It must also be easily machinable so that it can be formed into its permanent shape without cracking. While strength is an advantage in many applications, adding strengthening alloys may contribute poor machinability, meaning the material is difficult to cut and wears down the tooling. Accurate thickness measurement of process-line steel ensures the finished products have specific mechanical properties, including the appropriate strength and stiffness for their application. An excellent way to accomplish this is by processing the material through a cold rolling mill. Cold rolling is a metal forming process in which a sheet of metal is pressed through a pair of rolls to reduce thickness, increase strength and improve surface finish. 

It is frequently necessary to determine how much a part will deform under load to ensure that excessive deformation does not destroy the usefulness of the part. This can occur at stresses well below the yield strength of the material, especially in very long members or in high-precision devices. Stiffness of a material is a function of its modulus of elasticity, sometimes called Young’s modulus:

The modulus of elasticity, E, is a measure of the stiffness of a material determined by the slope of the straight-line portion of the stress–strain curve. It is the ratio of the change of stress to the corresponding change in strain.

This can be stated mathematically as :

Modulus of Elasticity, Young’s modulus, stiffness, formulation of young''s modulus, formulation of Modulus of Elasticity
Formulation of Young”s Modulus

Therefore, a material having a steeper slope on its stress–strain curve will be stiffer and will deform less under load than a material having a less steep slope. Figure illustrates this concept by showing the straight-line portions of the stress–strain curves for steel, titanium, aluminum, and magnesium. It can be seen that if two otherwise identical parts were made of steel and aluminum, respectively, the aluminum part would deform about three times as much when subjected to the same load.

Hooke’s law
Modulus of Elasticity for different metals

The design of typical load-carrying members in machines and structures is such that the stress is below the proportional limit, that is, in the straight-line portion of the stress–strain curve. Here we define Hooke’s law:

When the level of stress in a material under load is below the proportional limit and there is a straight-line relationship between stress and strain, it is said that Hooke’s law applies.

Many of the formulas used for stress analysis are based on the assumption that Hooke’s law applies. This concept is also useful for experimental stress analysis techniques in which strain is measured at a point. The corresponding stress at the point can be computed from a variation of Equation:

σ = EԐ

This equation is valid only where strain occurs in only one direction. This is called uniaxial strain, and it applies to members subjected to axial tension or compression and to beams in pure bending. When stresses occur in two directions (biaxial stress), an additional effect of the second stress must be considered.

Flexural Strength and Flexural Modulus

Other stiffness and strength measures often reported, particularly for plastics, are called the flexural strength and flexural modulus. As the name implies, a specimen of the material is loaded as a beam in flexure (bending) with data taken and plotted for load versus deflection. From these data and from knowledge of the geometry of the specimen, stress and strain can be computed. The ratio of stress to strain is a measure of the flexural modulus. American Society for Testing and Materials (ASTM) standard D790* defines the complete method. Note that the values are significantly different from the tensile modulus because the stress pattern in the specimen is a combination of tension and compression. The data are useful for comparing the strength and stiffness of different materials when a load-carrying part is subjected to bending in service. ISO standard 178 describes a similar method for determining flexural properties.

Comparison of Specific Strength and Specific Stiffness for Selected Materials

specific strength and specific stiffness
Comparison of specific strength and specific stiffness for selected materials

Differencies Table of  among Young’s Modulus – Ultimate Tensile Strength – Yield Strength

Material Tensile Modulus
(Young’s Modulus, Modulus of Elasticity)– E –
Ultimate Tensile Strength
– σu –
Yield Strength
– σy –
ABS plastics 1.4 – 3.1 40
A53 Seamless and Welded Standard Steel Pipe – Grade A 331 237
A53 Seamless and Welded Standard Steel Pipe – Grade A 331 207
A53 Seamless and Welded Standard Steel Pipe – Grade B 414 241
A106 Seamless Carbon Steel Pipe – Grade A 400 248
A106 Seamless Carbon Steel Pipe – Grade B 483 345
A106 Seamless Carbon Steel Pipe – Grade C 483 276
A252 Piling Steel Pipe – Grade 1 345 207
A252 Piling Steel Pipe – Grade 2 414 241
A252 Piling Steel Pipe – Grade 3 455 310
A501 Hot Formed Carbon Steel Structural Tubing – Grade A 400 248
A501 Hot Formed Carbon Steel Structural Tubing – Grade B 483 345
A523 Cable Circuit Steel Piping – Grade A 331 207
A523 Cable Circuit Steel Piping – Grade B 414 241
A618 Hot-Formed High-Strength Low-Alloy Structural Tubing – Grade Ia & Ib 483 345
A618 Hot-Formed High-Strength Low-Alloy Structural Tubing – Grade II 414 345
A618 Hot-Formed High-Strength Low-Alloy Structural Tubing – Grade III 448 345
API 5L Line Pipe 310 – 1145 175 – 1048
Acetals 2.8 65
Acrylic 3.2 70
Aluminum Bronze 120
Aluminum 69 110 95
Aluminum Alloys 70
Antimony 78
Aramid 70 – 112
Beryllium (Be) 287
Beryllium Copper 124
Bismuth 32
Bone, compact 18 170
Bone, spongy 76
Boron 3100
Brass 102 – 125 250
Brass, Naval 100
Bronze 96 – 120
CAB 0.8
Cadmium 32
Carbon Fiber Reinforced Plastic 150
Carbon nanotube, single-walled 1000
Cast Iron 4.5% C, ASTM A-48 170
Cellulose,  cotton, wood pulp and regenerated 80 – 240
Cellulose acetate, molded 12 – 58
Cellulose acetate, sheet 30 – 52
Cellulose nitrate, celluloid 50
Chlorinated polyether 1.1 39
Chlorinated PVC (CPVC) 2.9
Chromium 248
Cobalt 207
Concrete 17
Concrete, High Strength (compression) 30 40
Copper 117 220 70
Diamond (C) 1220
Douglas fir Wood 13 50
Epoxy resins 3-2 26 – 85
Fiberboard, Medium Density 4
Flax fiber 58
Glass 50 – 90 50
Glass reinforced polyester matrix 17
Gold 74
Granite 52
Graphene 1000
Grey Cast Iron 130
Hemp fiber 35
Inconel 214
Iridium 517
Iron 210
Lead 13.8
Magnesium metal (Mg) 45
Manganese 159
Marble 15
MDF – Medium-density fiberboard 4
Molybdenum (Mo) 329
Monel Metal 179
Nickel 170
Nickel Silver 128
Nickel Steel 200
Niobium (Columbium) 103
Nylon-6 2 – 4 45 – 90 45
Nylon-66 60 – 80
Oak Wood (along grain) 11
Osmium (Os) 550
Phenolic cast resins 33 – 59
Phenol-formaldehyde molding compounds 45 – 52
Phosphor Bronze 116
Pine Wood (along grain) 9 40
Platinum 147
Plutonium 97
Polyacrylonitrile, fibers 200
Polybenzoxazole 3.5
Polycarbonates 2.6 52 – 62
Polyethylene HDPE (high density) 0.8 15
Polyethylene Terephthalate, PET 2 – 2.7 55
Polyamide 2.5 85
Polyisoprene, hard rubber 39
Polymethylmethacrylate (PMMA) 2.4 – 3.4
Polyimide aromatics 3.1 68
Polypropylene, PP 1.5 – 2 28 – 36
Polystyrene, PS 3 – 3.5 30 – 100
Polyethylene, LDPE (low density) 0.11 – 0.45
Polytetrafluoroethylene (PTFE) 0.4
Polyurethane cast liquid 10 – 20
Polyurethane elastomer 29  – 55
Polyvinylchloride (PVC) 2.4 – 4.1
Rhodium 290
Rubber, small strain 0.01 – 0.1
Sapphire 435
Selenium 58
Silicon 130 – 185
Silicon Carbide 450 3440
Silver 72
Steel, High Strength Alloy ASTM A-514 760 690
Steel, stainless AISI 302 180 860 502
Steel, Structural ASTM-A36 200 400 250
Tantalum 186
Thorium 59
Tin 47
Titanium Alloy 105 – 120 900 730
Tooth enamel 83
Tungsten (W) 400 – 410
Tungsten Carbide (WC) 450 – 650
Uranium 170
Vanadium 131
Wrought Iron 190 – 210
Zinc 83
  • 1 Pa (N/m2) = 1×10-6 N/mm2 = 1.4504×10-4 psi
  •  1 MPa = 106 Pa (N/m2) = 0.145×103 psi (lbf/in2) = 0.145 ksi
  • 1 GPa = 109 N/m2 = 106 N/cm2  = 103 N/mm2 = 0.145×106 psi (lbf/in2)
  • 1 Mpsi = 106 psi = 103 ksi
  • 1 psi (lb/in2) = 0.001 ksi = 144 psf (lbf/ft2) = 6,894.8 Pa (N/m2) = 6.895×10-3 N/mm2

Tension Unit Converter

psi, MPa, ksi, Mpsi
Tension Unit Converter

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