Strength of Materials I Practice Flashcards

Vocabulary terms and definitions covering the fundamental concepts of Strength of Materials, including material properties, stress/strain analysis, beam behavior, torsion, columns, and pressure vessels.

Rigid material

A material which does not undergo any change in its geometry, size, or shape when subjected to external influence.

Deformable material

A material in which a change in size, shape, or both occurs when it is subjected to force or moment.

Nominal stress

Also known as Engineering stress, it is calculated as $\frac{\text{Load}}{\text{Original Area}}$.

True stress

Stress calculated using the actual instantaneous area, defined as $\frac{\text{Load}}{\text{Actual Instantaneous Area}}$.

Complimentary shear stresses

Shear stresses on adjacent and perpendicular faces of an element that are equal in magnitude and have directions pointing either both towards or both away from the line of intersection of the faces.

Factor of Safety (F.O.S) for Ductile material

Ratio typically applied on the yield stress, defined as $\frac{\text{Yield stress}}{\text{Allowable stress}}$.

Factor of Safety (F.O.S) for Brittle material

Ratio typically applied on the ultimate stress, defined as $\frac{\text{Ultimate stress}}{\text{Allowable stress}}$.

Extensometer

An instrument used to measure normal strain or deformation per unit length.

Hooke's law

A law relating stress and strain that is valid only up to the proportional limit ($A$) of a material.

Necking

A phenomenon in ductile materials between the ultimate stress point ($F$) and fracture point ($G$) where the diameter of a portion decreases due to instability.

Bauschinger's effect

An effect observed in steel where, after undergoing plastic deformation from a tensile load, a decrease in strength is seen when the direction of the load is reversed.

Creep

The property by virtue of which a material undergoes additional deformation over time under sustained loading.

Relaxation

The decrease in stress in steel over time as a result of creep under prolonged strain.

Fatigue

Deterioration of a material under repeated cycles of stress or strain resulting in progressive cracking and eventual fracture.

Endurance Limit

The stress level below which a material can withstand a large number of stress cycles without fatigue failure; for structural steel, it is approximately $1/2 \times \text{ultimate strength}$.

Modulus of Resilience

The elastic strain energy stored per unit volume, calculated as $\frac{\sigma_y^2}{2E}$.

Toughness

The ability of a material to absorb mechanical energy up to the point of failure.

Hardness

The ability of a material to resist indentation, surface abrasion, or scratching.

Poisson's Ratio ($\mu$)

The ratio of lateral strain to axial strain; it is $0$ for cork, $0.1$ to $0.2$ for concrete, and $0.5$ for perfectly elastic rubber/incompressible fluids.

Bulk Modulus ($K$)

An elastic constant relating hydrostatic pressure to volumetric strain, defined by the formula $K = \frac{E}{3(1 - 2\mu)}$.

Modulus of Rigidity ($G$)

Also known as Shear Modulus, it relates shear stress and shear strain, defined as $G = \frac{E}{2(1 + \mu)}$.

Number of Independent Elastic Constants

Unique constants required to define material behavior: $2$ for Homogenous and Isotropic, $9$ for Orthotropic (wood), and $21$ for Anisotropic materials.

Saint-Venant Principle

The principle stating that stress distribution is independent of the actual mode of application of loads, except in the immediate vicinity of the application point.

Shear Force (S.F.)

The resultant of all transverse forces to the right or left of a section.

Bending Moment (B.M.)

The resultant moment at a section due to all transverse forces to the left or right of that section.

Point of Contraflexure

A point where the Bending Moment is zero and changes its sign.

Principal Stress

The maximum or minimum normal stress developed on a loaded body; the plane of principal stress carries zero shear stress.

Mohr\u2019s Circle

A locus of points representing the magnitude of normal and shear stress at various planes in a given stress element.

Angle of Obliquity ($\alpha$)

The angle that the line of action of the resultant stress on a plane makes with the normal to that plane.

Flexural Rigidity

The product of the Modulus of Elasticity and the Moment of Inertia ($EI$).

Maxwell's Reciprocal Theorem

The theorem stating that the deflection at point $B$ due to a load $P$ at point $A$ is equal to the deflection at point $A$ due to a load $P$ at point $B$.

Conjugate Beam Method

A method where slope and deflection in a real beam correspond to shear and bending moment in a fictional conjugate beam loaded with the $M/EI$ diagram.

Rankine's Theory

Also known as maximum principal stress theory, it states failure occurs when the maximum principal stress exceeds the yield strength; it is applicable to brittle materials.

Tresca Theory

Also known as the maximum shear stress theory, it is the most conservative theory for ductile materials.

Kern

The area of a cross-section where a compressive load can be applied without causing tension anywhere on that section.

Pure Bending

The bending of a beam under a constant Bending Moment with zero shear force.

Section Modulus ($Z$)

A geometric property for a given cross-section computed as $Z = \frac{I}{y_{\text{max}}}$ used in design for bending stresses.

Shear Centre

The point through which a transverse bending load must pass for the beam to experience bending without twisting/torsion.

Pure Torsion

A state where a member is subjected only to torsional moments without axial forces, bending moments, or transverse shear.

Polar Moment of Inertia ($J$)

A geometric property for a given cross-section used to calculate resistance to torsion; for a solid circular shaft, it is $\frac{\pi D^4}{32}$.

Slenderness Ratio ($\lambda$)

The ratio of the effective length of a column to its least radius of gyration ($L_{\text{eff}}/r_{\text{min}}$).

Euler's Buckling Load ($P_e$)

The critical load at which a long column will buckle, calculated as $P_e = \frac{\pi^2 EI_{\text{min}}}{L_{\text{eff}}^2}$.

Hoop Stress (Thin Cylinder)

The circumferential stress in a thin-walled pressure vessel, given by $\sigma_h = \frac{pd}{2t}$.

Longitudinal Stress (Thin Cylinder)

The stress parallel to the axis of a thin-walled pressure vessel, given by $\sigma_L = \frac{pd}{4t}$.

Lame's Theorem

A method used for the analysis of stresses in thick-walled pressure vessels where stress is not uniform through the thickness.