The practical units used are megapascals (MPa or N/mm 2) or gigapascals (GPa or kN/mm 2). In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is defined as the ratio of shear stress to the shear strain: The following chart gives typical values for the shear modulud of rigidity. Surface subjected to time varying shear traction An isotropic, linear elastic half space with shear modulus and Poisson’s ratio and mass density occupies the region. In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is defined as the ratio of shear stress to the shear strain: The following chart gives typical values for the shear modulud of rigidity. Pressure is the ratio of force to the area over which that force is distributed. In English units, shear modulus is given in terms of pounds per square inch (PSI) or kilo (thousands) pounds per square. The elastic modulus (E), often referred to as Young’s modulus is the ratio of stress (σ) to strain (ε) when deformation is totally elastic. the shear modulus of any orthotropic material in which one axis of elastic symmetry is aligned with the longitudinal axis of the cylinder, provided, of course, that a circular cylindrical specimen of the material can be prepared. Concrete Floor Slabs On Grade Sujected to Heavy Loads - index. The shear modulus is defined as the ratio of shear stress to shear strain. The first answer, given by Niel Leon, deals with the bending moment 9 years ago. Compare this value of G to the shear modulus determined from the tensile test results (i. The minimum tensile strength of a 12. Youngs Modulus is a Measure of Stiffness YOUNG'S MODULUS also called Modulus of Elasticity quantifies the stiffness of an elastic material. The factor of 0. The formula for the modulus of rigidity Calculating shear modulus Finding the shear stress Skills Practiced. magnitude of a number or other mathematical expression disregarding its sign; thus, the absolute value is positive, whether the original expression is. Like the modulus of elasticity, the shear modulus is governed by. ) Mp plastic moment, = p y ≤ 1. b) Container for the shear box. The shear modulus is the elastic modulus in this case. Shear strength: The apparatus used was a one dimentional shear apparatus (direct shear apparatus). It is derived here for a rectangular beam but is valid for any shape. • Reciprocal of bulk modulus is commonly referred to as the “compressibility”. Calculate the displacement, stress and strain fields. The shear modulus is the elastic modulus in this case. And we found that Hooke's Law in Shear was valid in the linear elastic region and it was tau equals, tau being the shear stress, is equal to the modulus of rigidity or the shear's modulus times the shear strain. When the ultimate bearing capacity of the soil is reached, it may fail in one of the following three failure mode. K = bulk modulus; as you should know: σx = Eεx; when there are a tensile stress along x axis it also produces. These equations are useful for a wide variety of polymers, densities, and polymer thermal properties [63]. where bw = the beam width or the minimum width of the stem. Since the section modulus is 170 in 3, it will resist a bending moment of 170,000 lb-in or 14,200 lb-ft. See full list on toppr. Flexure Formula Stresses caused by the bending moment are known as flexural or bending stresses. The normalized shear strength, æ 𝜎′ , is dependent on 𝐿. 2 MPa 8000 psi ASTM D732. 8; k2 = 4 – their values depend on the variation of shape factor; S – the shape factor. Punch And Die Clearance. The shear force that can be resisted is the shear stress x cross section area: V c = u c x b w d. It is defined as = shear stress/shear strain. Modulus of rigidity is given by. When measuring the shear modulus of wood by static bending tests, the basic theory is dependent on Timoshenko's bending theory. 2 Elastomer shear modulus Shear modulus, G, is the most important material property for design, and it is, therefore, the preferred means of specifying the elastomer. The best possible way to elucidate this behaviour would be to make use of some (as yet unknown) formula for shear modulus, containing the desired effects in it explicitly. discussion on shear stress. Elastic modulus is an intrinsic material property and fundamentally related to atomic bonding. The ratio of shear stress and shear strain is called shear modulus. – E = Young’s modulus (elastic modulus, modulus of elasticity) can be used The Hooke’s law – The most primitive stress vs. Shear modulus is commonly denoted by \(S\):. 9 bolt has a minimum yield strength of 1100 MPa. Some of these are Bulk modulus and Shear modulus etc. Refraction - Snell's Law: That is the ratio of sine of the angle to the respective wave velocities are proportional. Like the modulus of elasticity, the shear modulus is governed by. Shear-wave source is at the zero-offset position in both profiles. Modulus of Elasticity: 113. Evans Journal of Applied Physics, 36, (1), pp. young modulus of api 5l x65 - fakefur. Ultimate strength determined in a flexure or torsion test. Using the same formula we use to find stress in a block subjected to a compressive force 3. The typical column size was an HSS 12"x12", with an unbraced length of 10'-0" for each level. Evans Journal of Applied Physics, 36, (1), pp. Shrinkage coefficient = 0. And the shear modulus is the stress divided by the strain: $$ G = \frac{\sigma}{\gamma} = \frac{Fl}{Ax} $$ So a high shear modulus means the material is very hard to deform sideways and conversely a low shear stress means the material is very easy to deform sideways. Elastic constants includes Young's modulus, shear modulus, Poisson's raito, bulk modulus, and Lame's constnat. Since stress relaxation measurements cannot be carried out using deformations small enough. the correct value of the shear modulus. 5 m and the lower face is fixed. Where, A0 is the enclosed area by the median line. It is represented by C or G or N. The secant modulus can be expressed as a percentage of the Young's Modulus (e. 25 = = Design masonry φ =φ ′ shear strength. The test results showed that rolling shear modulus of WCL from the two-plate shear test was 72. The shear modulus is the proportionality constant in Equation \ref{12. Ninety-three oocytes collected from 38 in-vitro fertilization patients. When a shear force is applied on a body which results in its lateral deformation, the elastic coefficient is called the shear modulus of elasticity. Find out information about Modulus of complex number. where: Stress = force / cross sectional area. The modulus of rigidity is anywhere from one third to one half the magnitude of the modulus of elasticity for most materials. 1 Shear and Bulk Moduli. Refraction - Snell's Law: That is the ratio of sine of the angle to the respective wave velocities are proportional. 2) A cylindrical bar of width 10 mm is stretched from its original length to 10 mm using a force of 100 N. Hence, C 3232. However, it is not commonly used elsewhere and no published. The basic difference between stress and strain is that stress is the deforming force per unit area. E: Young's modulus, v: Poisson's ratio, K: bulk modulus, G: shear modulus, M: stiffness modulus (under oedometric conditions = vertical compression without lateral displacement). S: If you want to calculate hydraulic press tonnage, you can use our hydraulic press tonnage calculator. 2 MPa 8000 psi ASTM D732. Image/URL (optional) Mass density. [Read the Full article about the Modulus. 92 × 10 7) / (6 × 10-4) = 6. The Modulus (G) for extension springs and compression springs deals with "shear or torsion" where the Modulus (E) for torsion springs addresses "bending". 1) τ= T*C/J. If the beam is 30 ft high, and a force acts at the end of it, the force will be 473 lb, and this will be the shear in the beam. #7546 - #7504 - #8102 - #9008 Small Block Chevy Manifold (W/O Divider Plate) Small Block Chevy Manifold (W/ Divider Plate) Performance Street/Strip Cam/Lift Kit with Divider Plate. 345 for aluminum. Details The modulus of resilience E r is the area contained under the elastic portion of the stress-strain curve. Choose from a wide variety of compression test machines that measure characteristics such as ultimate compression strength, yield strength, deflection and modulus. Bending a steel section that has a larger section modulus than another will be stronger and harder to bend. The nominal shear strength (Vn) is composed of the sum of the nominal shear strength provided by "concrete" (Vc) and the nominal shear strength provided by shear reinforcement (Vs). If we let k represent the bulk modulus of a material, m the shear-modulus, and r the density, then the P-wave velocity, which we represent by a, is defined by: A modulus is a measure of how easy or difficulty it is to deforms a material. The shear modulus G is also known as the rigidity modulus, and is equivalent to the 2nd Lamé constant m mentioned in books on continuum theory. Coefficient of Mutual Influence: relates shear strain due to shear stress in that plane to extensional strain or, relates extensional strain due to extensional stress to shear strain. Horizontal Shear Stress 4. Two physical origins are identiﬁed for the non-vanishing bending stiffness of the atomically thin graphene sheet, one due to the. Strain in a Beam; Strain in a Beam (Non-symmetric Cross Section) Stress in a Beam. In the theory of reinforced concrete, it is assumed that concrete is elastic, isotropic […]. Shear Modulus: relates shear strain in the plane of shear loading to that shear stress. In accordance with IBC 1607. Refraction - Snell's Law: That is the ratio of sine of the angle to the respective wave velocities are proportional. How to convert load vs displacement curve to stress-strain curve?. The complex shear modulus (G*) can be considered the sample’s total resistance to deformation when repeatedly sheared, while the phase angle (δ), is the lag between the applied shear stress and the resulting shear strain (Figure 5). extension → Young modulus E shear → shear modulus G compression → bulk modulus B bending* → bending modulus E b *three-point bending, 4 point bending E=2G(1+µ)=3B(1!2µ)!! " # $ $ % & =' long lat ((µ The lateral strain ε lat is the strain normal to the uniaxial deformation. Q What is damping?. It's an one of a most important functions in strength of materials, frequently used to analyse the rigidity of a solid material. The minimum yield strength of a bolt is the pressures needed to stretch the metal of the bolt. • Reciprocal of bulk modulus is commonly referred to as the “compressibility”. Measured using the SI unit pascal or Pa. At a first glance we observe that the static value of the Young's modulus is lower than the dynamic one, however, it is higher than the one in the intermediate range. complex dynamic shear modulus, G*(co), which is a function of frequency co. It is the energy absorbed per volume unit up to the elastic limit. + 1325°F/8 hr, F. At time t = 0, apply instantaneous shear strain γ 0 The shear relaxation modulus G(t,γ 0) ≡ σ(t)/γ 0 (2-1) For small strains, the modulus does not depend on strain. The warping normal stress (σw) due to bending moment in-plane of flanges (bi-moment) is given by σw = - E. It is used extensively in quantitative seismic interpretation, rock physics, and rock mechanics. 4: Two-plates model used to define the shear strain using the parameters deflection path s of the upper, movable plate, and distance h between the plates (left). Just understand the fol. Shear modulus. Ramirez 1. – Equation 11 – Rule of mixtures for poisson’s ratio v12 Equation 12. It is also known as the modulus of rigidity and may be denoted by G or less commonly by S or μ. d /2 from face of support. it is the same whatever the size of the test-piece. Tensile modulus is defined as the stress change divided by change in strain within the linear viscoelastic region of the stress/strain curves. For masonry, they advise using a shear modulus of 0. ) using n=0. G = 32 (1500 N ⋅ m) (20 cm) π (0. The shear area of the member is a. G= shear modulus or modulus of rigidity. Bending a steel section that has a larger section modulus than another will be stronger and harder to bend. No need to memorize: f. Many applications require stiff materials, e. It is defined as the ratio between pressure increase and the resulting decrease in a material's volume. The modulus of resilience is the maximum elastic energy absorbed by a material when a load is applied. In this article, we will discuss its concept and Young’s Modulus Formula with examples. modulus Y (or E in some books). 8 GPa: 16500 ksi : Compressive Yield Strength: 970 MPa: 141000 psi : Notched Tensile Strength: 1450 MPa: 210000 psi K t (stress concentration factor) = 6. Rubbery materials have high values of bulk modulus (1. Similarly, a shear stress causes a proportional shear strain and a pressure p results in a proportional fractional volume change (or “dilatation”) : where G is the shear modulus and K the bulk modulus. Viscosity experiments are carried out in the zero-shear-rate Newtonian plateau (low shear rate). the correct value of the shear modulus. When oscillatory shear measurements are performed in the linear viscoelastic regime, the storage modulus G' (elastic response) and loss modulus G'' (viscous behavior) are independent of the strain amplitude. It is convenient to use a. 45 GPa 500 ksi ASTM D695 Shear Strength 55. 85E), and it is used to describe the stiffness of a material in the inelastic region of the stress-strain diagram. Inclusion of shear deformation in analysis requires the values of shear modulus (modulus of rigidity, G) and the shear area of the member. I need to calculate shear modulus in axial and radial direction. Refraction - Snell's Law: That is the ratio of sine of the angle to the respective wave velocities are proportional. Distance of shear plane from nearest support Ef = stress—strain modulus of pile material (kN/m2) If = moment of inertia of pile (m4) = Poisson's ratio of soil. In the latter case, the relation between Young’s modulus E and shear modulus G was taken as G= E/3, assuming a Poisson ratio of 0. The ultimate nominal shear strength provided by. The correction factor, 𝜇, equals the shear strength from fall cone test to the shear strength from direct simple shear test, è 𝑆=𝜇∗ è. Large V (shear force), Small M (bending moment) Little flexural cracking prior to formation of diagonal cracks. Rolling shear strength of WWW measured using the three-point bending method was 2. The formula is E = σ / ε Pa. For homogeneous isotropic materials simple relations exist between elastic constants (Young's modulus E, shear modulus G, bulk modulus K, and Poisson's ratio ν) that allow calculating them all as long as two are known: Approximate values. Pressure, Stress, Young’s Modulus Converter. Only small distortions are introduced, ensuring linearity of response. Poisson’s ratio describes the transverse strain; therefore, it is obviously related to shear. The shear modulus can be calculated in terms of and. It defines the relationship between stress (force per unit area) and strain (proportional deformation) in a material in the linear elasticity regime of a uniaxial deformation. This leads to the shear modulus being \(3/8\), or 37. Dry bulk (Kd) and shear (µ) modulus ratio for consolidated rock (3a) and deep-water sands (3b) from Gulf of Mexico as function of differential pressure. Relation with Strength 6. Similar to the modulus of elasticity (E) for a body under tension, a shaft in torsion has a property known as the shear modulus (also referred to as the modulus of elasticity in shear, or the modulus of rigidity). Story Data Tab. G= shear modulus or modulus of rigidity. The ratio of a force applied to a material to the increment of change (e. The shear modulus can be calculated in terms of and. And GigaPascals (GPa) are often used. The ordinate on this graph is Young's Modulus divided by density (gm/cc), so multiply the Y axis value by density to obtain Y. ISO178 Flexural modulus(MPa) 117. An illustration of Eq. Polar moment of inertia is a quantity used to predict an object's ability to resist torsion, in objects (or segments of objects) with an invariant circular cross-section. Modulus of Resilience: The area under the curve which is marked by the yellow area. 6 used to change from tensile to shear force could vary from 0. The derived SI unit of shear. 85E), and it is used to describe the stiffness of a material in the inelastic region of the stress-strain diagram. The fact that all steels have the same E and G means that for members whose design is controlled by a stiffness limit states (i. The compressive. 19) and used in both analysis and design. It makes use of the fact that shear stresses always occur in a flexure test. Normal and shear stresses come in a wide variety of applications, each stress application with its own calculation formula. 5 × 10-2) = 10 5 N/m². Measured using the SI unit pascal or Pa. Maximum Shear Stresses, τ max, at Angle, θ τ-max Like the normal stress, the shear stress will also have a maximum at a given angle, θ τ-max. when graphed, the resulting plot will look something similar to this: The Young's modulus is the slope of the initial section of the curve (i. Roller Mill Shear Stress Formula - westfass. τ max =Grθ τ=Gγ max r r. ! •The tensile test and the engineering stress-strain curves. Aim: To determine the viscoelastic properties of the porcine lens Methods: Linear viscoelastic shear properties of the stroma of four porcine lenses were measured within 5 hours post-mortem, using sinusoidal oscillatory shear deformation. Youngs Modulus is a Measure of Stiffness YOUNG'S MODULUS also called Modulus of Elasticity quantifies the stiffness of an elastic material. using high modulus fiber such as carbon fiber or b. Thus the relaxation modulus is actually the response of the system to an instantaneous unit shear. In determining beam responses, it is very convenient, if not essential, to first determine the shear and bending moment diagrams. Design shear force ( ) ( )(in)(in) psi k V nm A nv f m 0. rate of shear data. Section modulus is a geometric property for a given cross-section used in the design of beams or flexural members. Evans Journal of Applied Physics, 36, (1), pp. The shear area of the member is a. modulus of rigidity – Is a material stiffness property (it is a material-specific property). young's modulus of api 5l x65 high qualite. It is used to determine the rigidity of the object. w P V(x) M(x. New York ISBN: 978-1461485162. The dimensional formula of Shear modulus is M 1 L -1 T -2. This is for the case of a cubic material. Large V (shear force), Large M (bending moment) Formation of flexure cracks precedes formation of shear cracks. Mathematically, shear modulus is calculated by dividing a sample's shear stress by its shear strain. m-2; F is the force acting on the body; l is the initial length ∆x is the change in length; A is the area; A shear modulus is applicable for the small deformation of the material by applying less shearing force which is capable to return to its original state. Where μ = 1/m(Poisson’s ratio) The relation between Young’s Modulus and Shear Modulus. It is defined as the ratio of uniaxial stress to uniaxial strain when linear elasticity applies. Reading comprehension - ensure that you draw the most important information from the. Calculate the normalized shear modulus Gi g i i μ μ G =, (2) SEG/San Antonio 2007 Annual Meeting 1716. C = modulus of rigidity of the material. Analysis of slabs The objective is to find the following internal forces by analysis: (l) Moments M M and. The inventive imaging method consists in generating a mechanical wave having shearing and compressional components in a viscoelastic medium and in determining the movement parameter of said viscoelastic medium at different points during the propagation of said mechanical wave. 25 *10 6 N/m 2. Calculate the elastic section modulus (Sx), plastic section modulus (Zx), and shape factor (f) for a built up T-shape 3. 0005 after 1 year 3. + 1325°F/8 hr, F. The warping shear stress (τw) at a point is given by (2) t ESwms w φ τ ′′′ = − where E = Modulus of elasticity Swms = Warping statical moment at a particular point S chosen. The height of the block is 1 cm. Modulus of Rigidity or Shear Modulus: It is defined as the ratio of shear stress to the corresponding shear strain within elastic limit. Direct shear test is conducted in the following steps: 1. ) Mp plastic moment, = p y ≤ 1. All three of these moduli have the same dimensions as stress, that of force per unit area (N/m 2 or Pa). 4 X modulus of elasticity. Limit: Shear Parallel to Grain, Max Shear Strength (0-1. This section covers shear force and bending moment in beams, shear and moment diagrams, stresses in beams, and a table of common beam deflection formulas. The shear modulus can be calculated in terms of and. I need to calculate shear modulus in axial and radial direction. 2 Deﬁnitions of Terms Speciﬁc to This Standard: 3. Where: V L = Shear Modulus: more information: Shear Wave Velocity Calculations. When dealing with mechanics of materials, choosing the correct formula to calculate the stress at a given point can be difficult. The ratio of shear stress and shear strain is called shear modulus. where G is the shear modulus (a material property) and γ is the shear strain. "Youngs' Modulus, Shear Modulus and Poisson's Ratio in Silicon and Germanium", 1965 J. 53 × 10 10 N/m² Ans: Shear stress = 3. T1 - Direct Method for Measuring Shear Modulus in Gels. 769, and the 95% confidence interval of modulus of elasticity is within the range of ±8000 MPa, as shown in Figure. Shear Stress Distribution Diagram 6. 42Ec for concrete. Elastic Section Modulus. http://www. Derivation Of Formula 5. Using the same formula we use to find stress in a block subjected to a compressive force 3. It is called as “modulus of elasticity in bending,” but other names are also used, such as modulus of elasticity, elastic modulus, or simply modulus. I Beam Section Modulus Formula Posted on September 2, 2020 by Sandra Cross section properties mechanicalc equation of strain on beams kyowa calculator for ers area moment calculating the section modulus triangle geometric properties. discussion on shear stress. In determining beam responses, it is very convenient, if not essential, to first determine the shear and bending moment diagrams. 19) and used in both analysis and design. 01 in4/ft Typical Thickness 0. Modulus elasticity is the ratio of stress to strain of a material in deflection (say in a beam) and is sometimes called ‘Young’s modulus’. 9 ISO180 Notched Izod impact strength (J/m) 21-75 32-641 59-747 32-214 ASTM Hardness, Rockwell R 80-102 75-117 65-96 81-105. Using the structural engineering calculator located at the top of the page (simply click on the the "show/hide calculator" button) the following properties can be calculated: Calculate the Area of a Rectangle. Reading comprehension - ensure that you draw the most important information from the. In a torsion test, modulus of rupture in torsion is the maximum shear stress in the extreme fiber of a circular member at failure. To do so, add a minus sign in front of noYieldSurf, then provide noYieldSurf pairs of shear strain (γ) and modulus ratio (G s) values. Story Data Tab. Linear response means that stress is proportional to the strain, and thus the modulus is independent of strain. 2 ft/sec 2) shear modulus; tabulated shear modulus; specific gravity transverse shear modulus of a stress-laminated system gross vehicle weight. We examined the applicability of Timoshenko's theory and propose an empirical equation that can derive the shear modulus properly. So, the next best option is surely to have in hand a formula that, although it is known to be. Calculation: Substitute 20 cm for L, 1500 N ⋅ m for T, 0. Where: V L = Shear Modulus: more information: Shear Wave Velocity Calculations. Consider an isotropic, flat circular plate of radius R, thickness h, mass density ρ, Poisson's ratio ν, Young's modulus E and shear modulus G(=E/[2(1+ν)]). Θ = [180*T*L/(π*J*G)] (eq. The container is supported over rollers to facilitate lateral movement of lower-half of the shear box when shear force is applied to the lower shear box through a geared jack. The shear modulus is the proportionality constant in Equation \ref{12. Shear force is an unbalanced force, parallel to the cross-section, mostly vertical, but not always, either the right or left of the section. where bw = the beam width or the minimum width of the stem. The formula gave accurate results. v = V Q I b (Statical moment about the [Shear Stress = (Shear force) X nuetral axis of the area above the plane)] (Moment of Inertia) X (width of beam). • Lap Fillet Weld; Formula for calculating the stresses in lap fillet welds subject to shear. Two physical origins are identiﬁed for the non-vanishing bending stiffness of the atomically thin graphene sheet, one due to the. , when a force is applied parallel to one surface of the sample and an opposing force is applied to the opposite face, as shown in Figure 3). Shear modulus equation Questions: 1) Calculate the shear modulus of a body that experienced a stress of 5*10 4 N/m 2 and a strain 4*10 (-2). Reading comprehension - ensure that you draw the most important information from the. 10 GPa, and nu = 0. The SI unit of shear modulus is the Pascal (Pa), but values are usually expressed in gigapascals (GPa). Shear Strain It is labeled with an xy subscript because we are looking at the shear strain in the xy plane I have labeled it with a y subscript because it is the angle made with the y-axis. 2) A cylindrical bar of width 10 mm is stretched from its original length to 10 mm using a force of 100 N. 42 g/cc “Dupont Kapton Polyimide Film General Specifications, Bulletin GS-96-7”. Modulus of rigidity is given by. ; ASTM D695 Compressive Modulus 3. The unit of shear stress in Newton per meter squared or normally known as Pascal. Dry bulk and shear modulus p 1. These seismic wave velocities are related to each other through Poisson. How to convert load vs displacement curve to stress-strain curve?. To verify the FE simulations, diagonal compression tests were conducted on 30 CLT samples. T1 - Direct Method for Measuring Shear Modulus in Gels. Please share the formula ,if you have. In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is defined as the ratio of shear stress to the shear strain: = = / / = where = / = shear stress is the force which acts is the area on which the force acts = shear strain. Let us assume E = 206. The formula for intermediate columns uses the tangential modulus of elasticity (E t). Find Your Query Syllabus. The formula for the modulus of resilience is 1/2 x σ x ε = 0. Notations Used In Shear Modulus Formula. Figure 12 Illustrating computations of an effective shear modulus obtained by inverting Hill's equation for drained ()and for undrained patchy saturation conditions. Strain in a Beam; Strain in a Beam (Non-symmetric Cross Section) Stress in a Beam. The shear modulus S is defined as the ratio of the stress to the strain. Modulus of rigidity or shear modulus is the rate of change of unit shear stress with respect to unit shear strain for the condition of pure shear within the proportional limit. Where μ = 1/m(Poisson’s ratio) The relation between Young’s Modulus and Shear Modulus. The SI unit of shear modulus is the Pascal (Pa), but values are usually expressed in gigapascals (GPa). New York ISBN: 978-1461485162. Parallel to Grain, Max Crushing Strength: Compress. 2) Maximum bending stress Wb = section modulus (in bending) Shear stress SA’ = first moment of area A’ (see Section 12. 4) Cw warping constant (in. In addition, because circular CFSTs provide. Shear box test - advantages Easy and quick test for sands and gravels Larggyge deformations can be achieved by reversing shear direction. 6 shear modulus (G) [FL–2], n—the elastic modulus in shear or torsion. 5 M F Z M y My moment corresponding to the onset of yielding at the extreme fiber from an elastic stress distribution = M F S y y x. 265 in Depth of Sheet 8. Abbreviated by G. B) Shear-wave profile recorded at site TRE on Quaternary alluvium in Reseda, California. It will help in deciding whether the failure will be on the compression face or on the tension face of the beam. The SHEAR FORCE on a given SHEAR PLANE = P/(number of shear planes) The bolt cross sectional area is critical to the prior calculation. Elastic Modulus. 6 Thermal strain 3. The shear strain ( )is determined by measuring the strain at a 45° angle, as shown in Figure E. Instead of automatic surfaces generation (Note 2), you can define yield surfaces directly based on desired shear modulus reduction curve. Here follows a short example of how to work out the shear force of a piece of steel. Shrinkage coefficient = 0. All of these are elastic constant which are used to design any machinery part or structure. 2 A rectangular block of aluminium of size 60 mm × 50 mm × 40 mm is subjected to a shear force of 45 kN on the top surface as shown in. It is defined as the fractional change in volume per unit change in pressure. This test standard requires a very unique articulating bend fixture with pressure pads to help provide the most accurate and consistent core shear results possible, even with the sometimes difficult to control process of manufacturing sandwich constructions. strain relationship – The Hooke’s law is valid only in the elastic region For shearing, – use G = modulus of rigidity or shear modulus E G. 4) What is the bulk modulus of a material, if a cube of 100 mm changes its volume to 4000 mm 3 when subjected to compressive force of 2. ! •True stress and true strain. / Elastic Section Modulus. 1 shows an example of how the longitudinal piezoelectric modulus can be represented in 3D. Fused silica is a noncrystalline (glass) form of silicon dioxide (quartz, sand). 05 m for D and 0. Investigating the relation between the measured displacement data and the stress wave vector, the proposed algorithm uses an iterative reconstruction formula based. Limit: Shear Parallel to Grain, Max Shear Strength (0-1. Determination of Modulus of Elasticity 3. Also known as shear modulus, shear modulus of elasticity, or torsional modulus. Ec is the bending modulus of elasticity, and Ev is the shear modulus of elasticity. 4: Two-plates model used to define the shear strain using the parameters deflection path s of the upper, movable plate, and distance h between the plates (left). • The transverse loads cause internal shear forces and bending moments in the beams as shown in Figure 1 below. Stress strain calculator solving for Young's modulus given stress and strain. The shear modulus is the earth's material response to the shear deformation. The height of the block is 1 cm. Elastic Section Modulus. 42 g/cc “Dupont Kapton Polyimide Film General Specifications, Bulletin GS-96-7”. \[ {G \over E} = {3 \over 8} \qquad \qquad \text{metals} \] Bulk Modulus Return to the. It is convenient to use a. 345 for aluminum. All the characteristics of the sample are monitored (level of consolidation, saturation ecc. Shear Wave Velocity. τ = shear stress induced at the outer surface of the shaft or maximum shear stress. The normalized shear strength follows SGI empirical correlation, æ 𝜎′ =0. Member Lengths can be a single span simply supported or a 2, 3 or 4 span continuous over middle supports. In determining beam responses, it is very convenient, if not essential, to first determine the shear and bending moment diagrams. When compared to other methods of obtaining the small-strain shear modulus, bender elements technique provided good agreement or slightly overestimated values in tests performed by Youn et al. R = radius of the shaft. Poisson's ratio describes the transverse strain; therefore, it is obviously related to shear. , for a force, F, normal to the surface of a beam having a cross sectional area of A, the shear stress is = F/A. The minimum tensile strength of a 12. Definition: It is defined as the ratio of shear stress to corresponding shear strain within elastic limit. Today we will learn about relation between Young Modulus, Bulk Modulus and Modulus of Rigidity. Since the cell was discovered by humans, it has been an important research subject for researchers. From the 2005 MSJC Code, Section 3. 9 ISO180 Notched Izod impact strength (J/m) 21-75 32-641 59-747 32-214 ASTM Hardness, Rockwell R 80-102 75-117 65-96 81-105. Consider an isotropic, flat circular plate of radius R, thickness h, mass density ρ, Poisson's ratio ν, Young's modulus E and shear modulus G(=E/[2(1+ν)]). Hence, C 3232. K = bulk modulus; as you should know: σx = Eεx; when there are a tensile stress along x axis it also produces. The end area of the elemental cylinder is. The modulus of rigidity is anywhere from one third to one half the magnitude of the modulus of elasticity for most materials. If the shear strength (of the core) is inadequate, you can do one of three things; 1. Evans Journal of Applied Physics, 36, (1), pp. It is used to determine the rigidity of the object. For this lin- early elastic region, the shear stress and shear strain are proportional, and therefore we have the following equation for Hookes law in shear: t Gg (1-14) in which G is the shear modulus of elasticity (also called the modulus of rigidity). In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is defined as the ratio of shear stress to the shear strain: The following chart gives typical values for the shear modulud of rigidity. This is useful for determining the residual strength of a soil Large samples may be tested in large shear boxes. The shear strain, g, is defined in engineering notation, and therefore equals the total change in angle: g=q. shear modulus and soil physical and mechanical properties. All of them arise in the generalized Hooke's law:. The bulk modulus, K, may be determined from Young's modulus, E, and the shear modulus, G, by the equation K = G·E / (9·G - 3·E). Also known as shear modulus, shear modulus of elasticity, or torsional modulus. Like the modulus of elasticity, the shear modulus is governed by. The dimensional formula of Shear modulus is M 1 L -1 T -2. Although modulus is most commonly reported during tensile testing, modulus of elasticity can also be reported as compressive modulus of elasticity for compression tests, flexural modulus of elasticity for flexural tests, shear modulus of elasticity for shear tests, or torsional modulus of elasticity for torsion tests. For simple liquids such as water or toluene, Equation (2) reasonably describes their viscosity, especially at low shear rates. In accordance with IBC 1607. Section modulus is a geometric property for a given cross-section used in the design of flexural members. ACI The modulus of subgrade reaction is an often misunderstood and misused concept for the thickness design of slabs-on-ground. RESULTS AND DISCUSSION:. For instance, in the above diagram, the shear strain is given by:. It is the ratio of shear stress to shear strain in a body. The ratio of shear stress and shear strain is called shear modulus. The area of shear surface was about 20 cm'. The complex shear modulus (G*) can be considered the sample’s total resistance to deformation when repeatedly sheared, while the phase angle (δ), is the lag between the applied shear stress and the resulting shear strain (Figure 5). Story Data Tab. complex dynamic shear modulus, G*(co), which is a function of frequency co. The analysis results are produced in a tabular form and are also plotted in 3 graphs for rapid comprehension. And the shear modulus is the stress divided by the strain: $$ G = \frac{\sigma}{\gamma} = \frac{Fl}{Ax} $$ So a high shear modulus means the material is very hard to deform sideways and conversely a low shear stress means the material is very easy to deform sideways. The present study investigated the association between oocyte zona pellucida shear modulus (ZPSM) and implantation rate (IR). It is derived from. Direct shear test is conducted in the following steps: 1. When dealing with mechanics of materials, choosing the correct formula to calculate the stress at a given point can be difficult. Ultimate strength determined in a flexure or torsion test. 5 for the interlayer. According to the deformation theory of cantilever beam, it can be seen that: Formula indicates the horizontal distance between the engagement point and the base circle; indicates the distance between the engagement point and the symmetrical line of the teeth; and respectively represent the elastic modulus and shear modulus of the gear. m in y = mx + b). Example -2: What pressure should be applied to a lead block to reduce its volume by 10% Bulk modulus for lead = 6 × 10 9 N/m²?. An analytic formula is derived for the elastic bending modulus of monolayer graphene based on an empirical potential for solid-state carbon atoms. 9 bolt is 732 MPa. Khan Academy is a 501(c)(3) nonprofit organization. Site Investigation: Enviromental Conditions. Shear and Bending Moment Diagrams: The loading on most beams is such that the stress resultant on planes perpendicular to the axis of the beam consists of a shear force, V, and a bending moment, M. Elastic constants for some of the materials are given in the table:. 62 and will depend on application. Modulus of elasticity E s, lb/in2 (MPa) 2. Modulus of rigidity is given by. The shear stress τ varies inversely with t. Modulus of Rigidity or Shear Modulus: It is defined as the ratio of shear stress to the corresponding shear strain within elastic limit. The elastic modulus (E), often referred to as Young’s modulus is the ratio of stress (σ) to strain (ε) when deformation is totally elastic. The SI unit of shear modulus is the Pascal (Pa), but values are usually expressed in gigapascals (GPa). If the beam is 30 ft high, and a force acts at the end of it, the force will be 473 lb, and this will be the shear in the beam. The shear stress has a maximum value at the minimum thickness. STAAD would calculate the shear stress using the shear areas calculated on the basis of the following for the AISC code: 1. Shear box equipment consisting of: a) Shear box, 60 mm square & 50 mm deep so that sample of size 60 x 60 x 20 mm may be tested. In California, the resistance value (R-value) is typically used as a measure of the subgrade strength (structural quality) of pavement materials. It's an one of a most important functions in strength of materials, frequently used to analyse the rigidity of a solid material. It is denoted by C or G or N The formula of modulus of rigidity is given by. ; ASTM D695 Compressive Modulus 3. No need to memorize: f. Stress is defined as a force applied over a unit area, with typical units of pounds per square inch (psi) or Newtons per square meter — also known as pascals (Pa). E modulus of elasticity for steel (29,000 ksi) G shear modulus for steel (11,200 ksi) J torsional constant (in. AU - Orkisz, Michal J. along the length of the member. Looking again at figure one, it can be seen that both bending and shear stresses will develop. Calculate the. Terzaghi in 1955 (Ref. If the shear strength (of the core) is inadequate, you can do one of three things; 1. 5 Poisson's ratio Poisson's ratio for concrete is 0. Shear Wave Velocity Wavelength Where: V L = Longitudinal Wave Velocity E = Modulus of Elasticity ρ = Density μ = Poisson’s Ratio Where: V s = Shear Wave Velocity E = Modulus of Elasticity ρ = Density μ = Poisson’s Ratio G = Shear Modulus Where: λ = Wavelength V = Velocity F = Frequency Refraction (Snellʼs Law) Acoustic Impedance. The minimum yield strength of a bolt is the pressures needed to stretch the metal of the bolt. The shear modulus S is defined as the ratio of the stress to the strain. The shear modulus can be determined by the ratio of the shear stress to the shear strain of the object. But one of the formula's factors is the airplane's ability to withstand a specified vertical gust (30 feet per second for planes certificated before August 1969 and 50 feet per second after this date) and not exceed its maximum load limit. modulus of rigidity – Is a material stiffness property (it is a material-specific property). มอดุลัสของยัง (Young's modulus) หรือ โมดูลัสยืดหยุ่น (modulus of elasticity หรือ elastic modulus) เป็นค่าบอกระดับความแข็งเกร็ง (en:stiffness) ของวัสดุ ค่ามอดุลัสของยังหาจาก ค่าลิมิตของ. The normalized shear strength, æ 𝜎′ , is dependent on 𝐿. Linear response means that stress is proportional to the strain, and thus the modulus is independent of strain. Types of Young Elastic Modulus 5. Modulus elasticity is the ratio of stress to strain of a material in deflection (say in a beam) and is sometimes called ‘Young’s modulus’. 2 ft/sec 2) shear modulus; tabulated shear modulus; specific gravity transverse shear modulus of a stress-laminated system gross vehicle weight. 769, and the 95% confidence interval of modulus of elasticity is within the range of ±8000 MPa, as shown in Figure. Calculate the elastic section modulus, Sx, and plastic section modulus, Zx, for a plate girder bent about its strong axis 2. The method is based on torsional oscillations of a gel sample. Large V (shear force), Small M (bending moment) Little flexural cracking prior to formation of diagonal cracks. 1 — Sketches showing the dimensions of a shear-tension test coupon. 2) A cylindrical bar of width 10 mm is stretched from its original length to 10 mm using a force of 100 N. Calculation: Substitute 20 cm for L, 1500 N ⋅ m for T, 0. Since stress was the independent variable in this study, modulus values were calculated by taking the inverse of the slope of strain versus stress curves. Hardness has strong usefulness in characterization of different types of microstructures in metals and is frequently used in the context of comparing. In this article, we will discuss its concept and Young’s Modulus Formula with examples. Surface subjected to time varying shear traction An isotropic, linear elastic half space with shear modulus and Poisson’s ratio and mass density occupies the region. 0 x 10-6/°F 2. According to the deformation theory of cantilever beam, it can be seen that: Formula indicates the horizontal distance between the engagement point and the base circle; indicates the distance between the engagement point and the symmetrical line of the teeth; and respectively represent the elastic modulus and shear modulus of the gear. Let us assume E = 206. Calculation: Substitute 20 cm for L, 1500 N ⋅ m for T, 0. The real part of the modulus, G'(~), determines the magnitude of the in-phase response of the medium to an applied oscillatory shear, and thus reflects the elasticity or energy stored by the material. The shear modulus (G) is the ratio of shear stress to shear strain. The magnitude of the shear stress becomes important when designing beams in bending that are thick or short – beams can and will fail in shear while bending. This test standard requires a very unique articulating bend fixture with pressure pads to help provide the most accurate and consistent core shear results possible, even with the sometimes difficult to control process of manufacturing sandwich constructions. 2 Deﬁnitions of Terms Speciﬁc to This Standard: 3. The shear stress for beams (one way): so. Pressure may be measured in any unit of force divided by any unit of area. G, is defined as: t= Gg Again, note, that this relationship only holds if a pure shear is applied to a specimen. The value of the tensile modulus of a material defines how well it resists elastic deformation, which occurs when a force is applied to a material that causes its shape to change. Hence, C 3232. Analyze a beam supporting a concrete slab and subjected to dead and live loads per LRFD and ASD 4. For instance, in the above diagram, the shear strain is given by:. And, from the Eq. 65 cm by a tangential force of 0. It is used to determine the rigidity of the object. In soft tissues, local stiffness is described by the Young modulus E and can be approximated by E ≈ 3μ ( 13 ). The shear modulus G is also known as the rigidity modulus, and is equivalent to the 2nd Lamé constant m mentioned in books on continuum theory. θ= angle of twist in radians on a length l. 2 Elastomer shear modulus Shear modulus, G, is the most important material property for design, and it is, therefore, the preferred means of specifying the elastomer. The quantity “τ t” is the shear flow “q” because it resembles liquid flow in channels. Consider a beam to be loaded as shown. Bulk Modulus, Poisson Ratio, Shear Modulus, Strain, Stress, Young's Modulus. See full list on toppr. 6 shear modulus (G) [FL–2], n—the elastic modulus in shear or torsion. The ordinate on this graph is Young's Modulus divided by density (gm/cc), so multiply the Y axis value by density to obtain Y. Materials with low modulus of elasticity are less resistant to stress, while materials with high modulus of elasticity resist stress and hold their shape better. The SHEAR FORCE on a given SHEAR PLANE = P/(number of shear planes) The bolt cross sectional area is critical to the prior calculation. RESULTS Complex Modulus and Characteristic Times The storage modulus, G9, and the loss modulus, G0, for solution f288-01 are plotted against the angular frequency, v, in Figure 1. The shear modulus G, MPa, is the deformability characteristic determined by the ratio of the tangential stress r applied to the ground to the shear angle y (Figure 8. The shear modulus itself may be expressed mathematically as. , for a force, F, normal to the surface of a beam having a cross sectional area of A, the shear stress is = F/A. In this topic, we will discuss the Shear Modulus Formula with examples. The shear box is placed in a large container and is tightly held in position at the bottom in the container. discussion on shear stress. In order to do this, you need the modulus of elasticity and shear modulus to determine deflection. The shear area of the member is a. The shear wave speed v is linked with shear modulus μ by the equation μ = ρv 2, where ρ is the local density (constant and equal to 1000 kg·m −3 in soft tissues). The shear modulus of steel (G) is approximately 80 GPa (11,500,000 psi), the shear modulus of concrete is around 21 GPa (3,000,000 psi), and the shear modulus of aluminum is about 28 GPa. Consider an isotropic, flat circular plate of radius R, thickness h, mass density ρ, Poisson's ratio ν, Young's modulus E and shear modulus G(=E/[2(1+ν)]). N2 - A direct method is presented for measuring the shear modulus of gels. 0) 10^6 psi: inches: psi: psi: psi. a shearing force applied to the top face produces a displacement of 0. increase the modulus by using a process that will increase the glass content of the skin, thereby increasing the modulus. shear modulus. Steel Beam Sizing Formula. Investigating the relation between the measured displacement data and the stress wave vector, the proposed algorithm uses an iterative reconstruction formula based. Derivation Of Formula 5. In this article, we will discuss its concept and Young’s Modulus Formula with examples. Assumed properties shall not exceed half of gross section properties, unless a cracked-section analysis is performed. Its unit is the same as pressure which is N/m²,While strain is the apparent change in the shape, volume or length of object caused due to stress is called strain. A 07 Solutions 46060 5/26/10 2:04 PM Page 475. The quantity “τ t” is the shear flow “q” because it resembles liquid flow in channels. 2) A cylindrical bar of width 10 mm is stretched from its original length to 10 mm using a force of 100 N. CEE 218X (section 1) Shaping the Future of the Bay Area (CEE 118X, ESS 118X, ESS 218X, GEOLSCI 118X, GEOLSCI 218X, GEOPHYS 118X, GEOPHYS 218X, POLISCI 218X, PUBLPOL 118X, PUBLPOL 218X). Engineering Materials | Strength of Materials. Shear modulus tells how effectively a body will resist the forces applied to change its shape. The shear modulus is related to Young modulus and Poisson's ratio,. Shear modulus is commonly denoted by \(S\):. Roller Mill Shear Stress Formula - westfass. The container is supported over rollers to facilitate lateral movement of lower-half of the shear box when shear force is applied to the lower shear box through a geared jack. Hence, the modulus of subgrade reaction, which is the function of soil settlement and the external pressure,is used for flexible foundation design. The ratio of a force applied to a material to the increment of change (e. extension → Young modulus E shear → shear modulus G compression → bulk modulus B bending* → bending modulus E b *three-point bending, 4 point bending E=2G(1+µ)=3B(1!2µ)!! " # $ $ % & =' long lat ((µ The lateral strain ε lat is the strain normal to the uniaxial deformation. We have discussed about these three constant in our last post and know all of them are ratio of stress to strain in different conditions. This equation is a specific form of Hooke's law of elasticity. Learn in details about Brookfield different verity of Rheometers. 85E), and it is used to describe the stiffness of a material in the inelastic region of the stress-strain diagram. This is useful for determining the residual strength of a soil Large samples may be tested in large shear boxes. See the reference section for details on the methodology and the equations used. The "BeamAnal" calculates Shear Force, Bending Moment and Deflection at 31 positions along the member length. Normal and shear stresses come in a wide variety of applications, each stress application with its own calculation formula. The shear modulus obtained by static bending is a much smaller value than that derived by other methods. The shear flow q = τ t is constant. If the shear strength (of the core) is inadequate, you can do one of three things; 1. Integrated into each beam case is a calculator that can be used to determine the maximum displacements, slopes, moments. In addition, the writers concluded that the ACI expression for elastic modulus overestimates the stiffness for very early-age concretes. Parallel to Grain, Max Crushing Strength: Compress. The shape of the cross-sectional area does not matter since all displacement is assumed to be longitudinal in this model. This will also explain why our bones are strong and yet can be fractured easily. The shear modulus or the modulus of rigidity, G = = τ φ Shear stress Shear strain Example 1. Direct shear test is conducted in the following steps: 1. It measures the rigidity of a b ody. Tension formula with angle. If you stopped the test, when the load was removed the specimen would spring back to its original length. Shear strain defined as the ratio of the change in deformation to its original length perpendicular to the axes of the member due to shear stress. This tab is where you specify the distinct wall levels. Bending a steel section that has a larger section modulus than another will be stronger and harder to bend. 1 shows an example of how the longitudinal piezoelectric modulus can be represented in 3D. The particular material models described above—the Mooney-Rivlin and neo-Hookean forms—can also be obtained from the general Ogden strain energy potential for special choices of μ i and α i. All data can be recalculated and the is a unit convertsion calculator for unique materials. For masonry, they advise using a shear modulus of 0. 0 x 10-6/°F 2. Two of the most important parameters in any dynamic analysis involving soils are the shear modulus and damping ratio. modulus? A While Young’s modulus, which is calculated from the slope of the initial part of a stress-strain curve, is similar conceptually to the storage modulus, they are not the same. document titled Buckling of a ﬂush-mounted plate in simple shear ﬂow is about Mechanics. using high modulus fiber such as carbon fiber or b. The shear modulus itself may be expressed mathematically as. Shear force of steel and bolts. Now let’s see the typical shear and bending stress distribution across the cross section for a rectangular section beam. deflection or vibration), the type of steel used is. The dry bulk modulus K d and shear modulus are kept constant during the fluid substitution, and the new values of undrained bulk modulus for varying saturations representing monitor cases are computed using the Gassmann's equation (4. Also called modulus of rigidity or torsional modulus. The Stiffness of Carbon Fiber can be compared using its Young's Modulus. The shear modulus value is always a positive number and is expressed as an amount of force per unit area. These materials combine the strength, hardness and wear resistance of carbon with the corrosion resistance and self lubricating properties of graphite. ¾Extend time or frequency range with TTS. The strength reduction factor for shear = 0. Its unit is the same as pressure which is N/m²,While strain is the apparent change in the shape, volume or length of object caused due to stress is called strain. Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),. 05 m for D and 0. Thermal coefficient of expansion = 6. Coefficient of Mutual Influence: relates shear strain due to shear stress in that plane to extensional strain or, relates extensional strain due to extensional stress to shear strain. Shear stress is a stress state where the stress is parallel or tangential to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. 2 Elastomer shear modulus Shear modulus, G, is the most important material property for design, and it is, therefore, the preferred means of specifying the elastomer. It is defined as the ratio between pressure increase and the resulting decrease in a material's volume. The shape factor for an elastomer layer was first defined by Keys in. The shear strain is defined as ∆x/L. This indicator is used in calculating the stability of structures and soil massifs, soil pressure on fences and underground structures, in calculating the sediment under. bComputed from (E-2G)/2G, where E is Young’s Modulus and G is torsional. we have a mathematical relation between the Bulk modulus(K) and the Youngs modulus(E) is given by. It is denoted by C or G or N The formula of modulus of rigidity is given by. Shear Strain It is labeled with an xy subscript because we are looking at the shear strain in the xy plane I have labeled it with a y subscript because it is the angle made with the y-axis. When a shear force is applied on a body which results in its lateral deformation, the elastic coefficient is called the shear modulus of elasticity. The real part of the modulus, G'(~), determines the magnitude of the in-phase response of the medium to an applied oscillatory shear, and thus reflects the elasticity or energy stored by the material. Where: V L = Shear Modulus: more information: Shear Wave Velocity Calculations. Using the same formula we use to find the shear stress in a bolt Select one: A. c) Grid plates two pairs, one pair plain and another pair perforated. Equation 10. STAAD would calculate the shear stress using the shear areas calculated on the basis of the following for the AISC code: 1. The elastic modulus was observed to grow very rapidly at early ages. The shear modulus can be determined by the ratio of the shear stress to the shear strain of the object. Shear Wave Velocity Where: Vs = Shear Wave Velocity E = Modulus of Elasticity r = Density m = Poisson's Ratio G = Shear Modulus 7. Influences of selected glass component additions on the bulk modulus of a specific base glass, calculated from the Young's modulus and the shear modulus. The typical column size was an HSS 12"x12", with an unbraced length of 10'-0" for each level. General, Local and Punching shear failures depending upon the compressibility of soil and depth of footing with respect to its breadth (i. E: Young's modulus, v: Poisson's ratio, K: bulk modulus, G: shear modulus, M: stiffness modulus (under oedometric conditions = vertical compression without lateral displacement). 3b Figure 3. These biomechanical behaviors have wide applications in the fields of disease research and micromanipulation. ACI The modulus of subgrade reaction is an often misunderstood and misused concept for the thickness design of slabs-on-ground. m in y = mx + b). Ec is the bending modulus of elasticity, and Ev is the shear modulus of elasticity. the formula, (GPa) (cP) (s) g i i μ η τ =, (1) where τi is the relaxation time, ηi is the viscosity and μg is the reference shear modulus. Let's explore a new modulus of elasticity called shear modulus (rigidity modulus). Wavelength. The shear modulus of material gives us the ratio of shear stress to shear strain in a body. The shear modulus, G, is a measure of the shear stiffness of the material. Homework Equations E=3(1−2ν)K 3. K = bulk modulus; as you should know: σx = Eεx; when there are a tensile stress along x axis it also produces. where E is Young's modulus, is the Poisson ratio, G is the shear modulus, K is the bulk modulus, is the density, is P-wave speed, and is the S-wave speed.