Thick walled Pressure Vessel

Different Types of Induced Stress

Machine components transmit forces and motion from one point to another. The transmission of force can be envisioned as a flow or force distribution that can be further visualized by isolating internal surfaces within the component. Force distributed over a surface leads to the concept of stress, stress components, and stress transformations (Mohrs circle) for all possible surfaces at a point.Stresses and strains: When any solid body is subjected to external forces, resisting forces are set up within the body. These internal forces per unit area are called unit stresses. The stress is tensile where the force tends to elongate fibers in the member collinear with the stress, compressive where the force tends to shorten fibers in the member collinear with the stress, and shear where the forces in the member tend to make adjacent planes in the member slide relative to each other. It is evident that elements of area in the member may be subjected to a force which has components both parallel and perpendicular to the area such that the stresses at the area may be both shear and tension or compression.

The forces acting on a body cause changes in the geometry of the body; these changes increase as the forces increase. These changes in the geometry or shape of the body are called deformations or strains; if measured on a body of unit dimension or per unit length of the body, they are called unit strains.

In engineering practice, the machine parts are subjected to various forces which may be due to either one or more of the following:

1. Energy transmitted,2. Weight of machine,3. Frictional resistances,4. Inertia of reciprocating parts,5. Change of temperature, and6. Lack of balance of moving parts.

LOADIt is defined as any external force acting upon a machine part. The following four types of the load are important from the subject point of view:1. Dead or steady load. A load is said to be a dead or steady load, when it does not change in magnitude or direction.2. Live or variable load. A load is said to be a live or variable load, when it changes continually.3. Suddenly applied or shock loads. A load is said to be a suddenly applied or shock load, when it is suddenly applied or removed.4. Impact load. A load is said to be an impact load, when it is applied with some

Engineering StressWhen some external system of forces or loads acts on a body, the internal forces (equal and opposite) are set up at various sections of the body, which resist the external forces. This internal force per unit area at any section of the body is known as unit stress or simply a stress. It is denoted by a Greek letter sigma (). Mathematically,

Where:F: load applied perpendicular to specimen cross-section; A: cross-sectional area (perpendicular to the force) before application of the load.

In S.I. units, the stress is usually expressed in Pascal (Pa) such that 1 Pa = 1 N/m2. In actual practice, we use bigger units of stress i.e. megapascal (MPa) and gigapascal (GPa), such that

Engineering StrainWhen a system of forces or loads acts on a body, it undergoes some deformation. This deformation per unit length is known as unit strain or simply a strain. It is denoted by a Greek letter epsilon (). Mathematically,

Where: = Change in length of the bodyL = Original length of the body.

Essence of Designing1. Know your MaterialTypes of Material Ductile High Resistance against Deformation Basically Soft High Resistance to Impact Load Define Yield Point Fails by Sliding, Necking or Yielding

Brittle Low Resistance against Deformation Basically Hard Low Resistance to Impact Load No define Yield Point Fails by Fracture

Carbon Content Wrought Iron = 0 - 0.08% Low Carbon Steel = 0.04 - 0.30% Medium Carbon Steel = 0.30 - 0.60% High Carbon Steel = 0.60 - 1.70% Cast Iron = 1.70 - 4.50%

2. Know Your Strength of Material

Fig 2.1 Stress-Strain Diagram for Ductile Specimen

Fig 2.2 Stress-Strain Diagram for Brittle Specimen

Fig 2.3 Properties on Stress-Strain Curve

Fig 2.4 The Elastic Line Stress is directly proportional to Strain ()

Stress-Strain DiagramIn designing various parts of a machine, it is necessary to know how the material will function in service. For this, certain characteristics or properties of the material should be known. The mechanical properties mostly used in mechanical engineering practice are commonly determined from a standard tensile test. This test consists of gradually loading a standard specimen of a material and noting the corresponding values of load and elongation until the specimen fractures. The load is applied and measured by a testing machine. The stress is determined by dividing the load values by the original cross-sectional area of the specimen. The elongation is measured by determining the amounts that two reference points on the specimen are moved apart by the action of the machine. The original distance between the two reference points is known as gauge length. The strain is determined by dividing the elongation values by the gauge length.

The values of the stress and corresponding strain are used to draw the stress-strain diagram of the material tested. A stress-strain diagram for mild steel under tensile test is shown in Fig 2.4.a the various properties of the material are discussed below:

Fig 2.4.a: Stress-strain diagram for mild steel under tensile test

1. Proportional limit, we see from the diagram that from origin to A is a straight line, which represents that the stress is proportional to strain. Beyond point A, the curve slightly deviates from the straight line. It is thus obvious, that Hooke's law holds good up to point A and it is known as proportional limit. It is defined as that stress at which the stress-strain curve begins to deviate from the straight line.

2. Elastic limit. It may be noted that even if the load is increased beyond point A up to the point B, the material will regain its shape and size when the load is removed. This means that the material has elastic properties up to the point B. This point is known as elastic limit. It is defined as the stress developed in the material without any permanent set.Note: Since the above two limits are very close to each other, therefore, for all practical purposes these are taken to be equal.

3. Yield point. If the material is stressed beyond point B, the plastic stage will reach i.e. on the removal of the load; the material will not be able to recover its original size and shape. A little consideration will show that beyond point B, the strain increases at a faster rate with any increase in the stress until the point C is reached. At this point, the material yields before the load and there is an appreciable strain without any increase in stress. In case of mild steel, it will be seen that a small load drops to D, immediately after yielding commences. Hence there are two yield points C and D. The points C and D are called the upper and lower yield points respectively. The stress corresponding to yield point is known as yield point stress.

4. Ultimate stress. At D, the specimen regains some strength and higher values of stresses are required for higher strains, than those between A and D. The stress (or load) goes on increasing till the point E is reached. The gradual increase in the strain (or length) of the specimen is followed with the uniform reduction of its cross-sectional area. The work done, during stretching the specimen, is transformed largely into heat and the specimen becomes hot. At E, the stress, which attains its maximum value, is known as ultimate stress. It is defined as the largest stress obtained by dividing the largest value of the load reached in a test to the original cross-sectional area of the test piece.

5. Breaking stress. After the specimen has reached the ultimate stress, a neck is formed, which decreases the cross-sectional area of the specimen. A little consideration will show that the stress (or load) necessary to break away the specimen, is less than the maximum stress. The stress is, therefore, reduced until the specimen breaks away at point F. The stress corresponding to point F is known as breaking stress.

Note: The breaking stress (i.e. stress at F which is less than at E) appears to be somewhat misleading. As the formation of a neck takes place at E which reduces the cross-sectional area, it causes the specimen suddenly to fail at F. If for each value of the strain between E

and F, the tensile load is divided by the reduced cross-sectional area at the narrowest part of the neck, then the true stress-strain curve will follow the dotted line EG. However, it is an established practice, to calculate strains on the basis of original cross-sectional area of the specimen.

6. Percentage reduction in area. It is the difference between the original cross-sectional area and cross-sectional area at the neck (i.e. where the fracture takes place). This difference is expressed as percentage of the original cross-sectional area.

Modulus of Elasticity, EThe ratio of the compressive or tensile force applied to a substance per unit surface area to the change in volume of the substance per unit volume. Also known as bulk modulus; compression modulus; hydrostatic modulus; modulus of compression; modulus of volume elasticity.

Slope of the stress-strain curve in the elastic region.

Derivation:1.01.1 1.2 1.3 If is given: 1.4 Hookes Law it is name after Robert Hooke, who first established it by experiments in 1678.

Where: E is a constant of proportionality known as Young's modulus or modulus of elasticity.

In S.I. units, it is usually expressed in GPa i.e. GN/m2 or kN/mm2. It may be noted that Hooke's law holds good for tension as well as compression.

The following table shows the values of modulus of elasticity or Young's modulus (E) for the materials commonly used in engineering practice.

Table 2.1 Values of E for the commonly used engineering MaterialsMaterialModulus of elasticity (E) in GPai.e GN/m2 or kN/mm2

Steel and Nickel200 to 220

Wrought iron190 to 200

Cast iron100 to 160

Copper90 to 110

Brass80 to 90

Aluminum60 to 80

Timber10

Theories of Elastic FailureThere are number of machine components, which are subjected to several types of loads simultaneously. For example, a power screw is subjected to torsional moment as well as axial force. Similarly an overhang crank is subjected to bending and torsional moments. The bolts of the bracket are subjected to forces that cause tensile stress and shear stress. Crankshaft, propeller shaft and connecting rods are examples of components subjected to several types of loads, combined stresses are induced. For example, torsional moment induces torsional shear stress, while bending moment causes bending stresses in transmission shaft.

The failures of such components are broadly classified into two groups-elastic failure and yielding and fracture. Elastic failure results in excessive elastic deformation, which makes the machine component, unfit to perform its function satisfactorily. Yielding results in excessive plastic deformation after the yield point is reached, while fracture results in breaking the component into two or more pieces.

The design of machine parts subjected to combine loads should be related to experimentally determined properties of material under similar conditions. However, it is not possible to conduct such tests for different possible combinations of loads and obtain mechanical properties. In practice, the mechanical properties are obtained from a simple tension test. They include yield strength, ultimate tensile strength and percentage elongation. In the tension test, the specimen is axially loaded on tension. It is not subjected to either bending moment or torsional moment or a combination of loads.

Theories of elastic failure provide a relationship between the strength of machine component subjected to complex state of stresses with the mechanical properties obtained in tension test. With the help of these theories, the data obtained in the tension test can be used to determine the dimensions of the component, irrespective of the nature stresses induced in the component due to complex loads

Basic Designing EquationSafe or Allowable or working design stress=Failure Causing Stress Applied to the member due to the load

Basis is Strength of Material as TestedBasis is Nominal Stress Formula based on Loading

Design Strength=Induced Strength

For Good Design:

Applied Factor of Safety

Fig 2.5 Graphical illustration of stress-strain on ductile specimen

.

Fig 2.6 Graphical illustration of stress-strain on brittle specimen

For Axially- loaded member: For Ductile materialFor brittle materialFactor of SafetyFactor of safety, also known as safety factor, is a term describing the structural capacity of a system beyond the expected loads or actual loads. Essentially, how much stronger the system is than it usually needs to be for an intended load. Safety factors are often calculated using detailed analysis because comprehensive testing is impractical on many projects, such as bridges and buildings, but the structure's ability to carry load must be determined to a reasonable accuracy.Many systems are purposefully built much stronger than needed for normal usage to allow for emergency situations, unexpected loads, misuse, or degradation.It is defined, in general, as the ratio of the maximum stress to the working stress. Mathematically,

In case of ductile materials e.g. mild steel, where the yield point is clearly defined, the factor of safety is based upon the yield point stress. In such cases,

In case of brittle materials e.g. cast iron, the yield point is not well defined as for ductile materials. Therefore, the factor of safety for brittle materials is based on ultimate stress,

This relation may also be used for ductile materials.Note: The above relations for factor of safety are for static loading.

Selection of Factor of SafetyThe selection of a proper factor of safety to be used in designing any machine component depends upon a number of considerations, such as the material, mode of manufacture, type of stress, general service conditions and shape of the parts. Before selecting a proper factor of safety, a design engineer should consider the following points:

1. The reliability of the properties of the material and change of these properties during service.2. The reliability of test results and accuracy of application of these results to actual machine parts.3. The reliability of applied load.4. The certainty as to exact mode of failure.5. The extent of simplifying assumptions.6. The extent of localized stresses.7. The extent of initial stresses set up during manufacture.8. The extent of loss of life if failure occurs.9. The extent of loss of property if failure occurs.

Each of the above factors must be carefully considered and evaluated. The high factor of safety results in unnecessary risk of failure. The values of factor of safety based on ultimate strength for different materials and type of load are given in the following table.Table 2.2 Basic Factor of SafetyBASIC YIELDBASIC ULTIMATE

1.0Steady Loads1.5 - 2.03.0 - 4.0

2.0Moderate Shock3.0 - 4.06.0 - 8.0

3.0Heavy Shock6.0 - 8.012.0 - 16.0

Table 2.3 Values of Factor of SafetyMaterialSteady loadLive LoadShock Load

Cast iron5 to 68 to 1216 to 20

Wrought iron4716 to 15

Soft material and alloys6915

Leather91215

Timber710 to 1520

Summary of Design Stress

Members Subjected to Direct Tensile LoadsFailure Profile:1. Fibers are elongated beyond its strength (strength failure)2. Fibers are elongated beyond its deformation limit (deformation failure)

Design Steps:

1. Check Strength Failure for Good Design2. Check deformation failure if limit in specified used Hookes Law:

While: Where:A - cross-sectional area - the elongation

F tensile ForceE modulus of elasticity

d =

1. if is not specified:Base your design on pure strength only.Table 2.4 Units and Conversions

SIFPSCGSMKS

1 MPa145.0377 psi10,000,000 Ba0.001

F1 N0.22481 100000 dyne1

A1 10.763910000 1

1 m3.2808 ft100 cm1 m

L1 m3.2808 ft100 cm1 m

Induced Stresses or Stresses Caused by Loading1. Direct Axial Loads (F A)The strength against an axially loaded member of a structure is assessed on the magnitude of stress, the intensity of the axial force, i.e., the force per unit area and is denoted by the Greek letter (sigma).

Tensile Stress (Tensile Stressis the stress state leading to expansion, that is, the length of a material tends to increase in the direction of the force / stress while the volume of the material stays constant. Generally, tensile stressoccurs when a material is subjected to pulling or stretching force.

When a body is subjected to two equal and opposite axial pulls P (also called tensile load) as shown in Fig. 2.9 (a), then the stress induced at any section of the body is known as tensile stress as shown in Fig. 2.9 (b). A little consideration will show that due to the tensile load, there will be a decrease in cross-sectional area and an increase in length of the body. The ratio of the increase in length to the original length is known as tensile strain.

Fig. 2.9 Tensile stress and strain.

Compressive Stress (Compressive stress is the reverse oftensile stress.Adjacent parts of the material tend to press against each other through a typical stress plane. Compressive stress is the stress on materials that leads to a smaller volume.

When a body is subjected to two equal and opposite axial pushes P (also called compressive load) as shown in Fig. 2.10(a), then the stress induced at any section of the body is known as compressive stress as shown in Fig. 2.10 (b). A little consideration will show that due to the compressive load, there will be an increase in cross-sectional area and a decrease in length of the body. The ratio of the decrease in length to the original length is known as compressive strain.

Fig. 2.10 Compressive stress and strain.2. Transverse Load (F Neutral Axis)Transverse loadingis type of applied force perpendicular to the longitudinal axis line. This loading cause objects to bend and gets deflected from the original point of contact. It hascompressive strains and internal tensileresulting in curvature change.

Fig. 2.11 Cantilever

Shearing Stress: When a body is subjected to two equal and opposite forces acting tangentially across the resisting section, as a result of which the body tends to shear off the section, then the stress induced is called shear stress. The corresponding strain is known as shear strain and it is measured by the angular deformation accompanying the shear stress.

Fig. 2.12 Single shearing of a riveted joint.Considering a body consisting of two plates connected by a rivet as shown in Fig. 2.12 (a). In this case, the tangential force P tends to shear off the rivet at one cross-section as shown in Fig. 2.12 (b). It may be noted that when the tangential force is resisted by one cross-section of the rivet (or when shearing takes place at one cross-section of the rivet), then the rivets are said to be in single shear.

Considering two plates connected by the two cover plates as shown in Fig. 2.13 (a). In this case, the tangential force P tends to shear off the rivet at two cross-sections as shown in Fig. 2.13 (b). It may be noted that when the tangential force is resisted by two cross-sections of the rivet (or when the shearing takes place at two cross-sections of the rivet), then the rivets are said to be in double shear.

Fig. 2.13. Double shearing of a riveted joint.Notes: 1. All lap joints and single cover butt joints are in single shear, while the butt joints with double cover plates are in double shear.2. In case of shear, the area involved is parallel to the external force applied.3. When the holes are to be punched or drilled in the metal plates, then the tools used to perform the operations must overcome the ultimate shearing resistance of the material to be cut. If a hole of diameter d is to be punched in a metal plate of thickness t, then the area to be sheared,A = d tand the maximum shear resistance of the tool or the force required to punch a hole,P = A u = d t uwhere u = Ultimate shear strength of the material of the plate.

Load converted as the moment (Flexural or Bending stress)Flexural strength is defined as a material's ability to resist deformation under load. The transverse bending test is most frequently employed, in which a rod specimen having either a circular or rectangular cross-section is bent until fracture using athree point flexural testtechnique. The flexural strength represents the highest stress experienced within the material at its moment of rupture.

Figure 2.14 Bending Moment

Bending stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend. When a load is applied perpendicular to the length of a beam (with two supports on each end), bending moments are induced in the beam.

Flexural theory states that most materials will exhibit linear-plastic behavior, i.e. they will respond to an applied load by deflecting in accordance to Hooke's Law, and will return to their original shape and form when the load is removed. This stress-strain relation exists only up to a certain load, after which the material will undergo some irretrievable deformation. Hooke's Law states that deformation of an object under loading is proportional to the magnitude of the load.

Materials which are said to be "elastic" become distorted when they are compressed, stretched, or bent. This behavior is due to the forces that different parts of a member exert on each other when a structure is subjected to loads. A simply supported beam of length L, subjected to a concentrated transverse load P at midspan would exhibit vertical deflection (and start to curve) due to bending caused by the two reaction loads at the supports. At midspan, the top of the beam would be the location at which the maximum compression occurs in the beam due to contraction in the top fibers. The bottom of the beam would experience maximum tension due to the elongation in the bottom fibers.

Torque or Twisting MomentTorsionis the twisting of an object due to an appliedtorque. In sections perpendicular to the torque axis, the resultantshear stressin this section is perpendicular to the radius.

Fig 2.15Twisting Moment

Bearing stress

Fig 2.16 Bearing Stress In a Riveted JointA localized compressive stress at the surface of contact between two members of a machine part that are relatively at rest is known as bearing stress or crushing stress. The bearing stress is taken into account in the design of riveted joints, cotter joints, knuckle joints, etc.Bearing stress is the stress cause by a force which is perpendicular to the resisting area (Ab). It is the contact pressure between two separate bo0dies.

Where:= Bearing Stress= Perpendicular force to the resisting area= resisting area (projected area) perpendicular to the force

Shear Modulus or Modulus of RigidityIt has been found experimentally that within the elastic limit, the shear stress is directly proportional to shear strain. Mathematically

Where: = Shear stress, = Shear strain, and = Constant of proportionality, known as shear modulus or modulus of rigidity. It is also denoted by N or G.The following table shows the values of modulus of rigidity (C) for the materials in everyday use.Table 2.5 Values of C for the commonly used materialsMaterialModulus of Rigidity (C) in GPa i.e. GN/m2 or kN/mm2

Steel80 to 100

Wrought iron80 to 90

Cast iron40 to 50

Copper30 to 50

Brass30 to 50

Timber10

Working StressWhen designing machine parts, it is desirable to keep the stress lower than the maximum or ultimate stress at which failure of the material takes place. This stress is known as the working stress or design stress. It is also known as safe or allowable stress.Note: By failure it is not meant actual breaking of the material. Some machine parts are said to fail when they have plastic deformation set in them, and they no more perform their function satisfactory.

For Tensile Stress:

Where: - tensile stressA cross-sectional areaF External force or load

For Compressive Stress:

Where: - compressive stressA cross-sectional areaF axial compressive force acting on a body

For Transverse Load:

;

; (for double shear)Where: shearing stressA resisting areaF tangential force

For Flexural Stress:

Where: - bending stressM moment about the neutral axisC perpendicular distance to the neutral axisI second moment of area about the neutral axis

For Twisting Moment:

;

Where: shearing stressT torqueR - radial distance of point from center of sectionJ polar moment of inertia

Compressive Stress1. A column supports a compressive load of 200kN. Determine the outside diameter of column if inside diameter is 170 mm and compressive stress of 40MPa.Given:

Solution:Solving for the Area of the column:

Solving for the Outside Diameter of the column:From: 5

2. A short hollow steel cylinder with a wall thickness of 35mm is to carry a compression load applied uniformly on the end of 6800kN. If the allowable working stress in steel in compression is 135MPa, then the minimum outside diameter of the cylinder required to safely support the load is:Given:

Solution:Solving for the area of the hollow steel cylinder:

Solving for the outside Diameter of the hollow steel cylinder:Since:Thus,From:

Tensile Stress1. Determine the minimum mean diameter of a taper pin for use to fix a lever to a shaft, if it is to transmit a maximum torque of 760 in-lbs. the shaft diameter is 4 inches and the material allowable stress is 30000 psi. Use factor of safety 4.Given:

Solution:

:

2. A hallow steel tube is used to carry a tensile load of 400kN at a stress of 130MPa. If outside diameter is 10 times the tube thickness, find the thickness of the tube.Given:

Solution:Solving for Area of the steel:

Solving for Inside Diameter, :

Since Area of steel & Inside Diameter is now given,Solve for the thickness of the tube:From:

Bearing Stress1. A journal bearing with a diameter of 80mm is subjected to a load of 5500N while rotating at 200 rpm. If its coefficient of friction is 0.02 and L/D = 2.5, find its projected area in mm2.Given:

Solution:From:

Solving for the Projected Area:

3. A lap joint consists of steel plate 250mm by 18mm in thickness is connected by 4-20mm diameter rivets. Compute the bearing capacity of the rivet connection if the allowable bearing stress is 210MPa.Given:

Solution:From: Where:Then:

Flexural or Bending Stress1. A simply supported timber beam is 60mm by 300mm in cross-section and 5m long. If the fiber stress is not to exceed 8.3MPa and the beam weight is neglected, find the maximum mid-span concentrated load that the beam can support if the 200 mm dimension is vertically oriented.Given:

Solution:For rectangular beam:Where:Thus,

For simply supported beam:

7470

2. The gear reducer of a shaft has a flexural stress of 250 psi and a force acting unit which is 2000 lb. if the diameter of the gear is 4 in. Calculate the actual length of the shaft.

Given :f = 250 psiF = 2000 lbD = 4 inL = ?

Solution :f =

Where :

M =

f =

=

250 psi = L = 2.513 in

Shear Stress1. If the ultimate shearing strength of a steel plate is 3000 Mpa. What force is necessary to punch a 25 mm diameter hole in 8 mm thick plate?Given: Ss = 3000 Mpa t = 8 mmD = 25 mmSolution:

F = Ss x A F = 3000 N/mm2 ()(25mm)(8mm)F = 1884.9556 kN

2. What force is necessary to punch a 1 inch hole in a 1/8 inch steel plate if the ultimate shearing stress is 60000psi and the ultimate compressive stress is 80000psi?Given:

Solution:Solving for the shearing area during punching:From:

Thus,

Torsional stress1. A 3 inches shaft is subjected to 3kN-m torque. Find the stress developed.Given:

Solution:Using the shaft stress formula:

Terminologies

MECHANICAL ENGINEERING DEPARTMENT

Republic of the PhilippinesBATAAN PENINSULA STATE UNIVERSITYMain Campus, Province of Bataan, City of Balanga C-2100COLLEGE OF ENGINEERING AND ARCHITECTURE

Page 147

Chapter 2: Different Types of Induced Stress

Page 147

AAdhesion. Intimate sticking of metal surfaces under compressive stresses by formulation of metallic bonds.

Adhesive bond. The forces such as dipole bonds which attract adhesives and base materials to each other.

Adhesive strength. The strength of an adhesive bond, usually measured as a force required to separate two objects of standard bonded area by either shear or tensile stress.

Airy stress function. A biharmonic function of two variables whose second partial derivatives give the stress components of a body subjected to plain strain.

Allowable stress. The maximum force per unit area that may be safely applied to a solid.

Alternating stress. A stress produced in a material by forces which are such that each force alternately acts in opposite directions.

Anelasticity. Deviation from a proportional relationship between stress and strain.

Axial modulus. The ratio of a simple tension stress applied to a material to the resulting strain parallel to the tension when the sides of the sample are restricted so that there is no lateral deformation.

BBearing pressure. Also known as bearing stress, it is the load on a bearing surface divided by its area.

Bending Strength. The quality of a material which resists forces from causing a member to bend or deflect in the direction in which the load is applied.

Bending stress. An internal tensile or compressive longitudinal stress developed in a beam in response to curvature induced by an external force.

Biaxial stress. The condition in which there are three mutually perpendicular principal stresses.

Bows notation. A graphical method of representing coplanar forces and stress using alphabetical letters, in the solution of stresses or in determining the resultant of a system of concurrent force.

Boussinesqs problem. The problem of determining the stresses and strain in an infinite body.

Breaking load. The stress which, when steadily applied to a structural member is just sufficient to break or rupture it.

Breaking strength. The ability of a material to resist breaking or rupture from a tension force.

Breaking stress. The stress required to fracture a material whether by compression, tension, or shear.

Buckling stress. Fore exerted by the crippling load

CCasting strain. Any strain that result from cooling of a casting stress.

Casting stress. Any stress that develops in a casting due to geometry and casting shrinkage.

Cohesive strength. Hypothetically the stress causing tensile fracture without plastic deformation.

Cold stress. Forces tending to deform steel, cement, and other materials resulting from low temperature.

Cold stretch. A pulling operation on extruded plastic filaments in which little or no heat is used: improve tensile properties.

Combined stresses. Bending or twisting stresses in a structural member combined with direct tension or compression.

Compliance constant. Any one of the components of the relationship in the generalized Hookes law used to express strain components as linear function of the stress components.

Compressibility. The property of a substance or material capable of being reduced in volume by application of pressure.

Compression. Reduction in volume of a substance due to pressure.

Compression failure. Buckling or collapse caused by compressive force.

Compression modulus. Bulk modulus of elasticity.

Compression member. A beam or other structural member which is subjected to compressive stress.

Compressive strength. The maximum compressive stress a material can withstand without failure.

Compressive stress. A stress which causes an elastic body to shorten in the direction of the applied load.

Cooling stress. Stress resulting from uneven contraction during cooling of metals and ceramics due to uneven temperature distribution.

Creep. A time dependent strain of solid caused by stress.

Creep rupture strength. The stress which, at a given temperature, will cause a material to rupture in a given time.

Creep strength. The stress which, at a given temperature will result in creep rate of 1% deformation within 100,000 hour.

Creep limit. The maximum stress a given material can withstand in a given time without exceeding a specified quantity of creep.

Crushing strength. The compressive stress required to a cause a solid to fail by fracture.

DDamaging stress. Minimum unit stress for a given material and use that will cause damage to the member and make it unfit for its expected length of service.

Deformation. Any alteration of shape or dimension of a body caused by stresses, thermal expansion or contraction, chemical or metallurgical transformations, or shrinkage and expansions due to moisture change.

Deformation curve. A curve showing the relationship between stress and load on a structure.

Design factor. A safety factor based on the ratio of ultimate load to maximum permissible load that can be safely placed on a structure.

Design stress. A permissible maximum stress to which a machine part or structural member may be subjected, which is large enough to prevent failure in case the loads exceed expected values, or other uncertainties turn out unfavorably.

Deviatonic stress. The portion of the total stress that differs from an isostatic hydrostatic pressure, it is equal to the difference between the total stress and spherical stress.EElastic body. A solid body for which the additional deformation produced by an increment of stress completely disappears when the increment is removed.

Elastic buckling. An abrupt increase in lateral deflection of a column at a critical load while the stresses acting on the column are wholly elastic.

Elastic center. The point of a beam in the plane of the kinetic energies of translation of the participating systems is the same after the collision as before.

Elastic curve. The curved shape of the longitudinal centroidal surface of a beam when the transverse loads acting on it produced wholly elastic stresses.

Elastic deformation. Reversible alteration of the form or dimension of a solid body under stress or strain.

Elastic equilibrium. The condition of an elastic body in which each volume element of the body is in equilibrium under the combined effect of elastic stresses and externally applied body force.

Elastic failure. Failure of a body to recover its original size and shape after a stress is removed.

Elasticity. The property whereby a solid material changes its shape and size under action or opposing forces, but recovers its original structure when the forces are removed.Elastic limit. The maximum stress a solid can sustain without undergoing permanent deformation.

Elastic recovery. The fraction of a given deformation of a solid which behaves elastically.

Elastoplasticity. The state of a substance subjected to a stress greater than its elastic limit but not so great as to cause it to rapture, in which it exhibits both elastic and plastic properties.

Elongation. The fractional increase in a materials length due to stress in tension or to thermal expansion.

Endurance Limit. Also known as fatigue limit the maximum stress that will not cause failure when the force is reverse indefinitely.

Equivalent bending moment. A bending moment which acting alone would produce in a circular shaft a normal stress of the same magnitude as the maximum normal stress produced by a given bending moment and a given twisting moment acting simultaneously.

Equivalent twisting moment. A twisting moment which acting alone would produce in a circular shaft a shear stress of the same magnitude as the shear stress produced by a given twisting moment and a given bending moment acting simultaneously

Erection stress. The internal force exerted on a structural member during construction.FFactor of safety. The ratio between the breaking load on a member, appliance or hoisting rope and the safe permissible load on it.

Failure. Condition caused by collapse, break or bending so that a structure or structural element can no longer fulfill its purpose.

Failure fatigue. The number of applied repeated stress cycles a material can endure before failure.

Fatigue limit. The maximum stress a material can endure for an infinite number of stress cycle without breaking.

Fatigue ratio. The ratio of a fatigue limits or fatigue strength to the static tensile strength.

Fatigue strength. The maximum stress a material can endure for a given number of stress cycles without breaking.

Fiber stress. The tensile or compressive stress on the fibers of a fiber metal or other fibrous material, especially when fiber orientation is parallel with neutral axis.

Flow curve. The stress-strain curve of a plastic material.

Flow stress. The stress along one axis at a given value of strain that is required to produce plastic deformation.

Fluid stress. Stress associated with plastic deformation in a solid material.

Fracture stress. The minimum tensile stress that will cause fractureGGrinding stress. Residual tensile or compressive stress or combination of both on the surface of a material due to grinding.

HHookean deformation. Deformation of a substance which is proportional to force applied to it.

Hookean solid. An ideal solid which obeys Hookes law exactly for all values of stress.

Hookes law. The law that the stress of a solid is directly proportional to strain applied to it.

Hydrostatic strength. The ability of a body to withstand hydrostatic stress.

Hydrostatic stress. The condition in which there are equal compressive stresses or equal tensile stresses in all direction, and no shear stresses on any plane.

IImpact stress. Force per unit area imposed on a material by a sudden applied force.

Inelastic buckling. Sudden increase of deflection or twisting in a column when compressive stress reaches the elastic limit but before elastic buckling develops.

Inelastic stress. Force acting on a solid which produced the deformation such that the origin size or shape of the solid are not restored after removal of force

Instantaneous recovery. The immediate reduction in the strain of a solid when a stress is removed or reduced, in contrast to creep recovery.

Internal stress. A stress system within a solid that is not dependent on external stress.

Isostatic. In photoelasticity studies of stress analyses to which represent the progressive change in principal-plane directions.

LLoad stress. Stress that result from a pressure or gravitational load.

Local structural discontinuity. The effect of intensified stress on a small portion of a structure.

MMean normal stress. In a system stressed multiaxially, the algebra mean of the three principal stresses.

Mean stress. The algebraic mean of the maximum and minimum values of a periodically varying stresses.

Membrane stress. Stresses which is equivalent to the average stress across section involved and normal to the reference plane.

Modulus of rupture in torsion. The maximum stresses per unit area that a specimen can withstand without breaking when its ends are twisted, as calculated from the breaking load under the consumption that the specimen is elastic until rupture takes place.

Modulus of deformation. The modulus of elasticity of a material that deforms other than according to Hookes law.

Modulus of elasticity. The ratio of the increment of some specified form of stress to the increment of some specified form of strains such as young modulus or the shear modulus.

NNormal stress. The stress component at a point in a structure which is perpendicular to the reference plane.

OOperating stress. The stress to which a structural unit is subjected in service.

PPlane stress. A state of stress in which two of the principal stresses are always parallel to a given plane and are constant in the normal direction.

Plastic deformation. Permanent change in shape or size of a solid body without fracture resulting from application of sustained stress beyond the elastic limit.

Plasticity. The property of a solid body whereby it undergoes a permanent change in shape or size when subjected to stress.

Poissons ratio. Is the ratio of a lateral unit deformation to axial unit deformation.

Proportional limit. Is the stress at which stress-strain curve deviates from a straight line.

Primary stress. A normal or shear stress component in a solid material which is under a condition of equilibrium and is not self-limiting.

Principal stress. A stress occurring at right angles to a principal plane of stress

RRadial stress. Tangential stress at the periphery of an opening.

Recovery. The return of a body to its original dimension after it has been subjected to stress possibly over a considerably period of time.

Relaxation. Relief of stress in a strained material due to creep.

Residual stress. Internal inherent, trapped locked-up body stress that exists within a material as a result of things other than external loading such as cold working, heating or cooling, etching, repeated stressing and electroplating.

SShear strength. Is the ability of metal to withstand forces thus following a number of twist.

Shearing stress. A stress in which the material on one side of a surface pushes on the material on the other side of the surface with a force which is parallel to the surface.

Stiffness. The ratio of the steady force acting on a deformable elastic medium to the resulting displacement.

Strength. Is the ability of metal to withstand loads without breaking down.

Stress. The force acting across a unit area in a solid material resisting the separation, compacting, or sliding that tends to be induced by external forces

TTensile strength. Stress developed by a material bearing a tensile load.

Tension stress. The exerted force by a support on a stretching object.

Torque. For a single force, the cross product of a vector from some reference point to the point of acceleration of the force with the force itself. Also known as moment of force; rotation movement.

Thermal stress. Mechanical stress induced in a body when some or all of its parts are not free to expand or contract in response to change of temperature.

UUniaxial stress. A state of stress in which two of the three principal stresses is zero.

Unit stress. The load per unit of area.

YYield point. The stress at which low or medium steel undergoes a marked elongation without an increase in load.

Yield strength. The stress at which the material exhibits a specified deviation from proportionality of stress and strain. Also called total extension.

Yield stress. The lowest stress at which the extension of the tensile test piece increases without increase in load.

Youngs modulus. The ratio of a simple tension stress applied to a material to the resulting strain parallel